%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.72",
%%%     date            = "18 October 2014",
%%%     time            = "14:59:26 MDT",
%%%     filename        = "benfords-law.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "45228 26797 113282 1137798",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; Benford's Law;
%%%                        Bradford's Law; First Digit Phenomenon;
%%%                        Gibrat's Law; Gibrat's Rule of Proportionate
%%%                        Growth; Heaps' Law; Herdan's Law; Law of
%%%                        Anomalous Numbers; Lotka's Law; Pareto
%%%                        Distribution; Pareto Law; Pareto Principle;
%%%                        power law; Significant Digit Law; Simon--Yule
%%%                        model of text generation; Stigler's Law; Yule
%%%                        process; Zipf's Law",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography about a numerical
%%%                        curiousity variously known as Benford's Law
%%%                        (see particularly entries Newcomb:1881:NFU,
%%%                        Benford:1938:LAN, Pinkham:1961:DFS,
%%%                        Logan:1978:FDP, Hill:1998:FDP, and
%%%                        Block:2010:GEB, Nigrini:2012:BLA), the Law of
%%%                        Anomalous Numbers, and the Significant Digit
%%%                        Law: in a table of physical constants (and in
%%%                        many other collections of measured numbers),
%%%                        the leading digits do not have equal
%%%                        probability of occurrence: the digit 1 is
%%%                        more common than 2, which is more common than
%%%                        3, and so on.
%%%
%%%                        Publications recorded here appear in about
%%%                        385 different journals from accounting,
%%%                        aerobiology, animal behavior, auditing,
%%%                        astronomy, bible studies, biology,
%%%                        biometrics, botany, business, chaos theory,
%%%                        chemistry, colloid science, complexity,
%%%                        computer science, conflict resolution,
%%%                        cognitive science, criminology, critical
%%%                        phenomena, demographics, drug design,
%%%                        dynamics, earthquake detection, economics,
%%%                        electoral studies, engineering, entropy,
%%%                        expert systems, extinction, finance,
%%%                        forensics, gambling, geography, geophysics,
%%%                        human resources, hydrology, imaging science,
%%%                        informetrics, language science, library
%%%                        science, linguistics, marine systems,
%%%                        marketing, mathematics, medicine, networking,
%%%                        neuroscience, nuclear engineering, nuclear
%%%                        science, operations research, physics,
%%%                        political analysis, probability, psychology,
%%%                        signal processing, simulation, sociology,
%%%                        statistical mechanics, statistics,
%%%                        stock-market trading, tax accounting, urban
%%%                        development, and urban growth, reflecting the
%%%                        broad interest in the unexpected phenomenon
%%%                        discovered and reported first by the
%%%                        Canadian/American astronomer and
%%%                        mathematician, Simon Newcomb, in a two-page
%%%                        note in 1881, and then independently, and
%%%                        with numerical evidence from much more
%%%                        measured data, by American physicist Frank
%%%                        Benford in 1938.
%%%
%%%                        In Benford's Law, the frequency of leading
%%%                        decimal digit p is roughly log10(1 + (1 /
%%%                        p)): that is, approximately 0.301, 0.176,
%%%                        0.125, 0.097, 0.079, 0.067, 0.058, 0.051, and
%%%                        0.046 for digits 1 through 9, instead of the
%%%                        expected 1/9 ~= 0.111 for values taken from a
%%%                        uniform distribution of random numbers.
%%%
%%%                        Another common statement of Benford's Law is
%%%                        that the probability that a decimal number
%%%                        representing a measured value begins with a
%%%                        nonzero digit not greater than p is log10(1 +
%%%                        p), that is, approximately 0.301, 0.477,
%%%                        0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and
%%%                        1.000 for digits 1 through 9.
%%%
%%%                        For the second digits, the probabilities are
%%%                        determined by the formula (see
%%%                        Todter:2009:BLI)
%%%
%%%                            sum(q = 1:9) log10(1 + 1 / (10*q + p)),
%%%
%%%                        that is, approximately 0.120, 0.114, 0.109,
%%%                        0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and
%%%                        0.085, for second decimal digits p = 0
%%%                        through 9.
%%%
%%%                        Probabilities for later digits are even
%%%                        closer: see entries Newcomb:1881:NFU,
%%%                        Feldstein:1976:CED, and Todter:2009:BLI.
%%%
%%%                        Benford's Law is not restricted to decimal
%%%                        numbers: for base b (as long as b is not
%%%                        huge, according to entry Schatte:1998:BLV),
%%%                        just change the 10 values to b in the
%%%                        previous formulas.  Here are some results for
%%%                        selected bases commonly used in computers,
%%%                        showing the probability of the first (D1) or
%%%                        second (D2) digit (first index) for base b
%%%                        (second index):
%%%
%%%                        P[D1,  2]:        1.000
%%%                        P[D2,  2]: 0.585, 0.415
%%%
%%%                        P[D1,  4]:        0.500, 0.292, 0.208
%%%                        P[D2,  4]: 0.304, 0.261, 0.230, 0.206
%%%
%%%                        P[D1,  8]:        0.333, 0.195, 0.138, 0.107,
%%%                                   0.088, 0.074, 0.064
%%%                        P[D2,  8]: 0.151, 0.141, 0.133, 0.126, 0.120,
%%%                                   0.115, 0.110, 0.105
%%%
%%%                        P[D1, 10]:        0.301, 0.176, 0.125, 0.097,
%%%                                   0.079, 0.067, 0.058, 0.051, 0.046
%%%                        P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100,
%%%                                   0.097, 0.093, 0.090, 0.088, 0.085
%%%
%%%                        P[D1, 16]:        0.250, 0.146, 0.104, 0.080,
%%%                                   0.066, 0.056, 0.048, 0.042, 0.038,
%%%                                   0.034, 0.031, 0.029, 0.027, 0.025,
%%%                                   0.023
%%%                        P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066,
%%%                                   0.065, 0.064, 0.062, 0.061, 0.060,
%%%                                   0.059, 0.058, 0.057, 0.056, 0.055,
%%%                                   0.054
%%%
%%%                        A small filter applied to the 1990 US Census
%%%                        data in the Project Gutenberg file
%%%                        uscen902.txt reports these frequencies of
%%%                        first and second digits for the 5148 integer
%%%                        values with at least 3 digits:
%%%
%%%                        F[D1]:        0.298, 0.215, 0.113, 0.082,
%%%                               0.098, 0.056, 0.055, 0.034, 0.049
%%%                        F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100,
%%%                               0.122, 0.076, 0.073, 0.066, 0.130
%%%
%%%                        For the 110 numbers in the atomic weights
%%%                        section of the GNU units utility data file,
%%%                        units.dat, we have
%%%
%%%                        F[D1]:        0.391, 0.309, 0.045, 0.036,
%%%                               0.055, 0.036, 0.036, 0.036, 0.055
%%%                        F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145,
%%%                               0.145, 0.055, 0.055, 0.091, 0.082
%%%
%%%                        From a snapshot of the country-area section
%%%                        of the US CIA World Factbook
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html
%%%
%%%                        taken at 18 November 2011, we find 1505
%%%                        numbers with these frequencies:
%%%
%%%                        F[D1]:        0.312, 0.275, 0.100, 0.067,
%%%                               0.058, 0.062, 0.046, 0.029, 0.050
%%%                        F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062,
%%%                               0.067, 0.075, 0.067, 0.083, 0.075
%%%
%%%                        From the country-population section
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html
%%%
%%%                        of that book, including only the 163 values
%%%                        of 1,000,000 or larger, we find
%%%
%%%                        F[D1]:        0.301, 0.202, 0.092, 0.135,
%%%                               0.055, 0.067, 0.055, 0.037, 0.055
%%%                        F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098,
%%%                               0.123, 0.086, 0.043, 0.049, 0.092
%%%
%%%                        From the section with the infant mortality
%%%                        rates per 1000 births,
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html
%%%
%%%                        there are 208 values with at least 4 digits,
%%%                        with these frequencies:
%%%
%%%                        F[D1]:        0.361, 0.293, 0.043, 0.072,
%%%                               0.062, 0.087, 0.038, 0.014, 0.029
%%%                        F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077,
%%%                               0.077, 0.106, 0.067, 0.043, 0.053
%%%
%%%                        In the 2010 annual financial report for IBM
%%%                        Corporation (its hundredth year of business)
%%%
%%%                            ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf
%%%
%%%                        there are 6126 numbers of two or more digits
%%%                        that do not look like year dates (19xx and
%%%                        20xx), and they have these digit frequencies:
%%%
%%%                        F[D1]:        0.333, 0.160, 0.163, 0.086,
%%%                               0.068, 0.053, 0.047, 0.045, 0.046
%%%                        F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085,
%%%                               0.095, 0.079, 0.074, 0.079, 0.068
%%%
%%%                        For the first 100,000 primes, we have
%%%
%%%                        F[D1]:        0.311, 0.091, 0.090, 0.087,
%%%                               0.086, 0.085, 0.084, 0.083, 0.082
%%%                        F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078,
%%%                               0.078, 0.078, 0.079, 0.078, 0.078
%%%
%%%                        For the Fibonacci numbers, f(n), which
%%%                        satisfy the recurrence f(n) = f(n-1) + f(n-2)
%%%                        with f(1) = f(2) = 1, using the first 10000
%%%                        such numbers (the last of which has 2091
%%%                        digits), we find for the 9994 f(n) values
%%%                        with at least two digits these frequencies:
%%%
%%%                        F[D1]:        0.301, 0.176, 0.125, 0.097,
%%%                               0.079, 0.067, 0.058, 0.051, 0.046
%%%                        F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100,
%%%                               0.097, 0.094, 0.090, 0.088, 0.085
%%%
%%%                        If we take the same set of Fibonacci numbers,
%%%                        we find these frequencies for values output
%%%                        in base 4:
%%%
%%%                        F[D1]:        0.500, 0.292, 0.208
%%%                        F[D2]: 0.303, 0.262, 0.230, 0.205
%%%
%%%                        The Fibonacci numbers, and the members of
%%%                        many other such sequences, can be proved
%%%                        mathematically to obey Benford's Law exactly
%%%                        (see entries Raimi:1976:FDP, Berger:2011:BLS,
%%%                        and Berger:2011:BTB).
%%%
%%%                        Simon Newcomb made another significant
%%%                        appearance in the history of science when he
%%%                        proposed that the then-not-understood
%%%                        perihelion advance of the planet Mercury
%%%                        could be explained by modifying Newton's law
%%%                        of gravitation from a $r^{-2}$ dependence to
%%%                        $r^{-2.000\,000\,157\,4}$.  His proposal was
%%%                        later shown to contradict more accurate
%%%                        measurements of the orbit of Earth's Moon.
%%%                        That story is told on pages 93--95 of
%%%                        Clifford M. Will's 1993 book, ``Was Einstein
%%%                        Right?'' (ISBN 0-465-09086-9).
%%%
%%%                        Although many papers purport to explain
%%%                        Benford's Law, a recent paper (entry
%%%                        Berger:2011:BLS) argues that several of the
%%%                        prior published explanations are flawed.  An
%%%                        earlier paper (entry Raimi:1976:FDP) examines
%%%                        the literature on Benford's Law up to 1976,
%%%                        and points out flaws in several previous
%%%                        explanations of the law.  That paper also
%%%                        gives a bibliography of previous important
%%%                        works on the problem.  A recent survey (entry
%%%                        Berger:2011:BTB) may provide stronger
%%%                        mathematical grounds for Benford's Law.
%%%
%%%                        Benford's Law has been applied to the problem
%%%                        of detection of fraud in data, elections, and
%%%                        finance (see, among other entries,
%%%                        Hill:1998:FDP, Nigrini:1992:DIE,
%%%                        Swanson:2003:DPF, Durtschi:2004:EUB,
%%%                        Geyer:2004:DFD, Bhattacharya:2005:CPA,
%%%                        Cleary:2005:ADA, Lu:2005:DFH, Lu:2006:AFD,
%%%                        Schneider:2006:RAS, Cho:2007:BBL,
%%%                        Diekmann:2007:FDU, Hand:2007:DDD,
%%%                        Todter:2009:BLI, Corazza:2010:CFM, and
%%%                        Roukema:2014:FDA, and the cautionary view in
%%%                        Diekmann:2010:BLF).
%%%
%%%                        Benford's Law also applies to floating-point
%%%                        numbers in computer arithmetic (see entries
%%%                        Konheim:1965:MDT, Hamming:1970:DN,
%%%                        Tsao:1974:DSD, Feldstein:1976:CED,
%%%                        Feldstein:1986:OUS, Schatte:1988:ASC), where
%%%                        it has implications for the frequency of
%%%                        significance loss in subtraction of
%%%                        like-signed numbers.
%%%
%%%                        This bibliography also includes publications
%%%                        about two related empirical laws: Heaps' Law
%%%                        and Zipf's Law, because they often occur in
%%%                        discussions of Benford's Law.
%%%
%%%                        Heaps' Law (see entry Heaps:1978:IRC) is an
%%%                        empirical observation from linguistics that
%%%                        the proportion of words from a vocabulary
%%%                        grows exponentially (but with a small
%%%                        exponent, often between 0.4 and 0.6) with the
%%%                        number of words in the text of documents.
%%%
%%%                        Zipf's Law says that if S is some stochastic
%%%                        (random) variable, the probability that S
%%%                        exceeds s is proportional to 1 / s.  The
%%%                        variable S might be, for example, the
%%%                        population of a city (small cities are more
%%%                        numerous than large ones).  Zipf's Law is
%%%                        a special case of the Pareto distribution
%%%                        (see remark in entry Pareto:1896:CEP).
%%%
%%%                        Zipf's law finds application in the design of
%%%                        information retrieval systems (e.g., hash
%%%                        tables, databases, filesystems, and Web
%%%                        searches), as well as in astronomy, biology,
%%%                        computer science, demography, earth science,
%%%                        economics, and physics.  See entry
%%%                        Newman:2005:PLP for an outstanding survey
%%%                        that deserves to be widely read by
%%%                        scientists, and entry Baldi:2003:MIW for a
%%%                        book-length treatment.
%%%
%%%                        There is an actively-maintained bibliography
%%%                        of Benford's Law at
%%%
%%%                            http://www.benfordonline.net/
%%%
%%%                        (see entry Berger:2009:BOB).  It includes
%%%                        material from entries Hurlimann:2006:BLB and
%%%                        Nigrini:1992:DIE.  Although BibTeX output is
%%%                        mentioned, it may not yet be implemented.
%%%
%%%                        There is an online bibliography of Zipf's Law
%%%                        at
%%%
%%%                            http://www.nslij-genetics.org/wli/zipf/
%%%
%%%                        (see entry Li:2011:ZLB).
%%%
%%%                        There is a collection of several papers on
%%%                        election-fraud detection, some of them using
%%%                        Benford's Law analyses, at
%%%
%%%                            http://www-personal.umich.edu/~wmebane/
%%%
%%%                        At version 1.72, the year coverage looked like
%%%                        this:
%%%
%%%                             1881 (   1)    1926 (   1)    1971 (   2)
%%%                             1882 (   0)    1927 (   1)    1972 (   6)
%%%                             1883 (   0)    1928 (   2)    1973 (   8)
%%%                             1884 (   0)    1929 (   1)    1974 (  11)
%%%                             1885 (   0)    1930 (   0)    1975 (  11)
%%%                             1886 (   0)    1931 (   1)    1976 (  10)
%%%                             1887 (   0)    1932 (   2)    1977 (   6)
%%%                             1888 (   0)    1933 (   0)    1978 (   8)
%%%                             1889 (   0)    1934 (   1)    1979 (   4)
%%%                             1890 (   0)    1935 (   1)    1980 (   8)
%%%                             1891 (   0)    1936 (   1)    1981 (  10)
%%%                             1892 (   0)    1937 (   0)    1982 (   8)
%%%                             1893 (   0)    1938 (   2)    1983 (   6)
%%%                             1894 (   0)    1939 (   0)    1984 (  15)
%%%                             1895 (   0)    1940 (   0)    1985 (   9)
%%%                             1896 (   1)    1941 (   0)    1986 (  10)
%%%                             1897 (   0)    1942 (   0)    1987 (  14)
%%%                             1898 (   0)    1943 (   1)    1988 (  12)
%%%                             1899 (   0)    1944 (   1)    1989 (  12)
%%%                             1900 (   0)    1945 (   2)    1990 (   6)
%%%                             1901 (   0)    1946 (   1)    1991 (   9)
%%%                             1902 (   0)    1947 (   0)    1992 (  10)
%%%                             1903 (   0)    1948 (   2)    1993 (   9)
%%%                             1904 (   0)    1949 (   2)    1994 (   9)
%%%                             1905 (   0)    1950 (   3)    1995 (  15)
%%%                             1906 (   0)    1951 (   0)    1996 (  19)
%%%                             1907 (   0)    1952 (   1)    1997 (  14)
%%%                             1908 (   0)    1953 (   1)    1998 (  17)
%%%                             1909 (   0)    1954 (   1)    1999 (  25)
%%%                             1910 (   0)    1955 (   1)    2000 (  15)
%%%                             1911 (   0)    1956 (   0)    2001 (  25)
%%%                             1912 (   1)    1957 (   5)    2002 (  26)
%%%                             1913 (   1)    1958 (   1)    2003 (  37)
%%%                             1914 (   0)    1959 (   1)    2004 (  41)
%%%                             1915 (   1)    1960 (   1)    2005 (  60)
%%%                             1916 (   1)    1961 (   2)    2006 (  57)
%%%                             1917 (   1)    1962 (   2)    2007 (  42)
%%%                             1918 (   0)    1963 (   1)    2008 (  40)
%%%                             1919 (   0)    1964 (   1)    2009 (  58)
%%%                             1920 (   1)    1965 (   4)    2010 (  76)
%%%                             1921 (   0)    1966 (   3)    2011 (  79)
%%%                             1922 (   1)    1967 (   2)    2012 (  39)
%%%                             1923 (   0)    1968 (   4)    2013 (  13)
%%%                             1924 (   0)    1969 (  11)    2014 (   1)
%%%                             1925 (   1)    1970 (   8)
%%%
%%%                             Article:        774
%%%                             Book:            72
%%%                             InCollection:    27
%%%                             InProceedings:   39
%%%                             Manual:           1
%%%                             MastersThesis:    4
%%%                             Misc:            16
%%%                             PhdThesis:        8
%%%                             Proceedings:      7
%%%                             TechReport:      46
%%%                             Unpublished:      3
%%%
%%%                             Total entries:  997
%%%
%%%                        Data for this bibliography have been
%%%                        collected from
%%%
%%%                            * the University of Utah Mathematics
%%%                              Department bibliography archives
%%%
%%%                            * the TeX User Group bibliography
%%%                              archives
%%%
%%%                            * the Karlsruhe Computer Science
%%%                              bibliography archives
%%%
%%%                            * the Karlsruhe virtual catalog at
%%%                              http://www.ubka.uni-karlsruhe.de/kvk_en.html
%%%
%%%                            * the US Library of Congress catalog at
%%%                              http://catalog.loc.gov/
%%%
%%%                            * the author's cattobib utility, which
%%%                              provides Z39.50 interfaces to many
%%%                              large libraries around the world, at
%%%                              http://www.math.utah.edu/pub/cattobib/
%%%
%%%                            * the American Institute of Physics
%%%                              Scitation database at
%%%                              http://scitation.aip.org/search_scitation
%%%
%%%                            * the American Physical Society PROLA
%%%                              database at
%%%                              http://publish.aps.org/search
%%%
%%%                            * the American Mathematical Society
%%%                              MathSciNet database at
%%%                              http://ams.rice.edu/mathscinet/search.html
%%%
%%%                            * the Bulletin of the Atomic Scientists
%%%                              (archives available, albeit inconveniently,
%%%                              via http://books.google.com/ and
%%%                              http://bos.sagepub.com/search)
%%%
%%%                            * the Canadian Journal of Physics
%%%                              database at
%%%                              http://www.nrcresearchpress.com/search/advanced
%%%
%%%                            * the European Mathematical Society
%%%                              Zentralblatt fuer Mathematik database
%%%                              at http://zb.msri.org/ZMATH/zmath/en/
%%%
%%%                            * the Europhysics journal archive at
%%%                              http://www.europhysicsnews.org/
%%%
%%%                            * the JSTOR database at
%%%                              http://www.jstor.org/
%%%
%%%                            * the Nature journal archive at
%%%                              http://www.nature.com/search/
%%%
%%%                            * the journal archives of the National
%%%                              Academy of Science at
%%%                              http://www.pnas.org/
%%%
%%%                            * the Project Euclid archives at
%%%                              http://projecteuclid.org/
%%%
%%%                            * the SAO/NASA Astrophysics Data System at
%%%                              http://adsabs.harvard.edu/
%%%
%%%                            * the Science journal archive at
%%%                              http://www.sciencemag.org/search
%%%
%%%                            * the SPIRES high-energy physics
%%%                              literature database at the Stanford
%%%                              Linear Accelerator at Stanford
%%%                              University at
%%%                              http://www.slac.stanford.edu/spires/hep/search/
%%%
%%%                            * the Springer journal database at
%%%                              http://www.springer.com/?SGWID=0-102-13-0-0
%%%
%%%                            * the Wiley journal database at
%%%                              http://onlinelibrary.wiley.com/
%%%
%%%                            * many online library catalogs, including
%%%                              those of the British Library, the
%%%                              Karlsruhe Virtual Library catalog, the
%%%                              Oxford University Library, the University of
%%%                              California library system, and the US
%%%                              Library of Congress.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

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%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-mjn =   "Mark J. Nigrini"}

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-ACCOUNT-HIST-J        = "Accounting Historians Journal"}

@String{j-ACCOUNT-RES           = "Accountability in Research"}

@String{j-ACCOUNT-REV           = "The Accounting Review"}

@String{j-ACCOUNTANCY           = "Accountancy: The journal of the {Institute of
                                  Chartered Accountants in England and Wales}"}

@String{j-ACTA-ARITHMETICA      = "Acta Arithmetica"}

@String{j-ACTA-ASTRONAUT        = "Acta Astronautica"}

@String{j-ADV-APPL-STAT         = "Advances and Applications in Statistics"}

@String{j-ADV-COMPLEX-SYST      = "Advances in Complex Systems"}

@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}

@String{j-AEROBIOLOGIA          = "Aerobiologia"}

@String{j-AM-J-ECON-SOCIOL      = "The American Journal of Economics and
                                  Sociology"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AM-J-MATH-MANAGE-SCI  = "American Journal of Mathematical and
                                  Management Sciences"}

@String{j-AM-SCI                = "American Scientist"}

@String{j-AMER-J-PHYSICS        = "American Journal of Physics"}

@String{j-AMER-J-PSYCHOLOGY     = "The American Journal of Psychology"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-ANALYST               = "The Analyst"}

@String{j-ANIM-BEHAV            = "Animal Behaviour"}

@String{j-ANN-APPL-PROBAB       = "Annals of Applied Probability"}

@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of Statistical
                                  Mathematics (Tokyo)"}

@String{j-ANN-MATH-STAT         = "Annals of Mathematical Statistics"}

@String{j-ANN-PROBAB            = "Annals of Probability"}

@String{j-ANN-STAT              = "Annals of Statistics"}

@String{j-APPL-ECON-LETT        = "Applied Economics Letters"}

@String{j-APPL-FINANC-ECON      = "Applied Financial Economics"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-STAT             = "Applied Statistics"}

@String{j-AQUAT-BOT             = "Aquatic Botany"}

@String{j-ASIA-PAC-MATH-NEWSL   = "Asia Pacific Mathematics Newsletter"}

@String{j-ASLIB-PROC            = "ASLIB Proceedings"}

@String{j-ASTROPART-PHYS        = "Astroparticle Physics"}

@String{j-AUDITING              = "Auditing: A Journal of Practice \& Theory"}

@String{j-AUSTRALIAN-COMP-J     = "Australian Computer Journal"}

@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}

@String{j-BELL-SYST-TECH-J      = "The Bell System Technical Journal"}

@String{j-BIOINFORMATICS        = "Bioinformatics"}

@String{j-BIOMETRIKA            = "Biometrika"}

@String{j-BIOSYSTEMS            = "Biosystems (A6E)"}

@String{j-BRAIN-COGN            = "Brain and Cognition"}

@String{j-BULL-INST-MATH-STAT   = "Bulletin --- Institute of Mathematical
                                  Statistics"}

@String{j-C-R-ACAD-SCI-I        = "Comptes rendus de l'Acad{\'e}mie des
                                  sciences. S{\'e}rie I, Math{\'e}matique"}

@String{j-C-R-ACAD-SCI-PARIS-SER-AB = "Comptes Rendus Hebdomadaires des
                                  S{\'e}ances de l'Acad{\'e}mie des Sciences.
                                  S{\'e}ries A et B"}

@String{j-C-R-BIOL              = "Comptes Rendus Biologies"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CAN-J-MATH            = "Canadian Journal of Mathematics = Journal
                                  canadien de math{\'e}matiques"}

@String{j-CHANCE                = "Chance: a magazine for people interested in
                                  the analysis of data"}

@String{j-CHAOS                 = "Chaos (Woodbury, NY)"}

@String{j-CHAOS-SOLITONS-FRACTALS = "Chaos, Solitons \& Fractals"}

@String{j-CHIN-PHYS-LETT        = "Chinese Physics Letters"}

@String{j-COGN-SCI              = "Cognitive Science"}

@String{j-COGNITION             = "Cognition"}

@String{j-COLLEGE-MATH-J        = "College Mathematics Journal"}

@String{j-COLLOQ-MATH           = "Colloquium Mathematicum"}

@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}

@String{j-COMM-STAT             = "Communications in Statistics"}

@String{j-COMM-THEOR-PHYS       = "Communications in Theoretical Physics"}

@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMP-MATH-APPL        = "Computers and Mathematics with Applications"}

@String{j-COMP-MUSIC-J          = "Computer Music Journal"}

@String{j-COMP-NET              = "Computer Networks"}

@String{j-COMP-NET-AMSTERDAM    = "Computer Networks (Amsterdam, Netherlands:
                                  1999)"}

@String{j-COMP-SURV             = "ACM Computing Surveys"}

@String{j-COMPLEXITY            = "Complexity"}

@String{j-COMPOS-MATH           = "Compositio Mathematica"}

@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}

@String{j-COMPUTING             = "Computing: Archiv f{\"u}r Informatik und
                                  Numerik"}

@String{j-CONTEMP-PHYS          = "Contemporary Physics"}

@String{j-DEC-SUPP-SYS          = "Decision Support Systems"}

@String{j-DEMOGRAPHY            = "Demography"}

@String{j-DEUTSCH-MATH-V        = "Jber. Deutsch. Math.--Verein"}

@String{j-DISCRETE-CONTIN-DYN-SYST = "Discrete and Continuous Dynamical Systems.
                                  Series A"}

@String{j-DISCRETE-DYN-NAT-SOC  = "Discrete Dynamics in Nature and Society"}

@String{j-DISCRETE-MATH         = "Discrete Mathematics"}

@String{j-DOKL-AKAD-NAUK        = "Doklady Akademii Nauk SSSR"}

@String{j-DOKL-MATH             = "Doklady Mathematics"}

@String{j-DRUG-DISCOVERY-TODAY  = "Drug Discovery Today"}

@String{j-ECONOM-LETT           = "Economics Letters"}

@String{j-ECONOMIST             = "The Economist"}

@String{j-EDPACS                = "EDPACS"}

@String{j-ELECT-J-COMB          = "Electronic Journal of Combinatorics"}

@String{j-ELECT-STUDIES         = "Electoral Studies"}

@String{j-ELECTRON-COMMUN-PROBAB = "Electronic Communications in Probability"}

@String{j-ELECTRON-J-PROBAB     = "Electronic Journal of Probability"}

@String{j-ELEK-INFO-KYBER       = "Elektronische Informationsverarbeitung und
                                  Kybernetik (EIK)"}

@String{j-ELEM-MATH             = "Elemente der Mathematik"}

@String{j-EMPIRICA              = "Empirica"}

@String{j-ENTROPY               = "Entropy"}

@String{j-EUR-J-OPER-RES        = "European Journal of Operational Research"}

@String{j-EUR-J-PHYS            = "European Journal of Physics"}

@String{j-EUR-PHYS-J-A          = "European Physical Journal A: Hadrons and
                                  Nuclei"}

@String{j-EUR-PHYS-J-B          = "European Physical Journal B: Condensed Matter
                                  and Complex Systems"}

@String{j-EUROPHYS-LETT         = "Europhysics Letters"}

@String{j-EXP-MATH              = "Experimental Mathematics"}

@String{j-EXPERT-SYST-APPL      = "Expert Systems with Applications"}

@String{j-EXPO-MATH             = "Expositiones Mathematicae"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FORUM-MATH            = "Forum Mathematicum"}

@String{j-FRACTALS              = "Fractals"}

@String{j-FUNDAM-MATH           = "Fundamenta mathematicae"}

@String{j-GER-ECON-REV          = "German Economic Review"}

@String{j-GLOB-FINANCE-J        = "Global Finance Journal"}

@String{j-IEEE-ANN-HIST-COMPUT  = "IEEE Annals of the History of Computing"}

@String{j-IEEE-POT              = "IEEE Potentials"}

@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}

@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}

@String{j-IEEE-TRANS-ELECTROMAGN-COMPAT = "IEEE Transactions on Electromagnetic
                                  Compatibility"}

@String{j-IEEE-TRANS-FUZZY-SYSTEMS = "IEEE Transactions on Fuzzy Systems"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-NETWORKING = "IEEE\slash ACM Transactions on Networking"}

@String{j-IEEE-TRANS-NUCL-SCI   = "IEEE Transactions on Nuclear Science"}

@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                  Distributed Systems"}

@String{j-IEEE-TRANS-RELIAB     = "IEEE Transactions on Reliability"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-INF-CONTROL           = "Information and Control"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INFO-PROC-MAN         = "Information Processing and Management"}

@String{j-INFO-SCI              = "Information Sciences"}

@String{j-INT-ECON-REV          = "International Economic Review"}

@String{j-INT-J-ACCOUNT-INFO-SYS = "International Journal of Accounting
                                  Information Systems"}

@String{j-INT-J-FOUND-COMP-SCI  = "International Journal of Foundations of
                                  Computer Science (IJFCS)"}

@String{j-INT-J-MATH-EDU-SCI-TECH = "International Journal of Mathematical
                                  Education in Science and Technology"}

@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}

@String{j-INT-J-MOD-PHYS-C      = "International Journal of Modern Physics C
                                  [Physics and Computers]"}

@String{j-INT-J-PROD-ECON       = "International Journal of Production
                                  Economics"}

@String{j-INT-J-PURE-APPL-MATH  = "International Journal of Pure and Applied
                                  Mathematics"}

@String{j-INT-J-RES-MARK        = "International Journal of Research in
                                  Marketing"}

@String{j-INT-J-SYST-SCI        = "International Journal of Systems Science"}

@String{j-INT-J-THEOR-PHYS      = "International Journal of Theoretical
                                  Physics"}

@String{j-INTERNET-MATH         = "Internet Mathematics"}

@String{j-IZV-AKAD-NAUK-SSSR-MAT = "Izvestiia Akademii Nauk. USSR Seriia
                                  Matematicheskaia (Moscow)"}

@String{j-J-ACCOUNT-EDUC        = "Journal of Accounting Education"}

@String{j-J-ACCOUNTANCY         = "Journal of Accountancy"}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-AM-SOC-INF-SCI      = "Journal of the American Society for
                                  Information Science"}

@String{j-J-AM-SOC-INF-SCI-TECHNOL = "Journal of the American Society for
                                  Information Science and Technology"}

@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}

@String{j-J-APPL-PROBAB         = "Journal of Applied Probability"}

@String{j-J-APPL-STAT           = "Journal of Applied Statistics"}

@String{j-J-ASSET-MANAGE        = "Journal of Asset Management"}

@String{j-J-CLIN-PSYCHOL        = "Journal of Clinical Psychology"}

@String{j-J-COLLOID-INTERFACE-SCI = "Journal of Colloid and Interface Science"}

@String{j-J-COMB-THEORY-A       = "Journal of Combinatorial Theory (Series A)"}

@String{j-J-CONFL-RESOLUT       = "Journal of Conflict Resolution"}

@String{j-J-DIFFERENCE-EQU-APPL = "Journal of Difference Equations and
                                 Applications"}

@String{j-J-DOC                 = "Journal of Documentation"}

@String{j-J-ECON-DYN-CONTROL    = "Journal of Economic Dynamics and Control"}

@String{j-J-EMPIR-FINANCE       = "Journal of Empirical Finance"}

@String{j-J-EXP-PSYCH-GEN       = "Journal of Experimental Psychology: General"}

@String{j-J-FORENSIC-ACCOUNT    = "Journal of Forensic Accounting"}

@String{j-J-GAMBL-STUD          = "Journal of Gambling Studies"}

@String{j-J-GEN-PSYCH           = "The Journal of General Psychology"}

@String{j-J-HUM-RESOUR          = "Journal of Human Resources"}

@String{j-J-HYDROL              = "Journal of Hydrology"}

@String{j-J-INFO-ORG-SCI        = "Journal of Informational and Organizational
                                  Sciences"}

@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
                                  Cybernetics: EIK"}

@String{j-J-INFO-SCI-PRINCIPLES-PRACTICE = "Journal of Information Science,
                                  Principles and Practice"}

@String{j-J-INFORMETRICS        = "Journal of Informetrics"}

@String{j-J-INT-ECON            = "Journal of International Economics"}

@String{j-J-INT-FINANC-MANAG-ACCOUNT = "Journal of International Financial
                                  Management and Accounting"}

@String{j-J-JPN-INT-ECON        = "Journal of the {Japanese} and International
                                  Economies"}

@String{j-J-MAR-SYST            = "Journal of Marine Systems"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-ARTS           = "Journal of Mathematics and the Arts"}

@String{j-J-MATH-IMAG-VIS       = "Journal of Mathematical Imaging and Vision:
                                  JMIV"}

@String{j-J-MATH-SOC-JPN        = "Journal of the {Mathematical Society of
                                  Japan}"}

@String{j-J-NUMBER-THEORY       = "Journal of Number Theory"}

@String{j-J-PHYS-A              = "Journal of Physics A (Mathematical and
                                  General)"}

@String{j-J-PHYS-SOC-JAP        = "Journal of the Physical Society of Japan"}

@String{j-J-PROD-BRAND-MANAG    = "Journal of Product \& Brand Management"}

@String{j-J-QUANT-CRIMINOL      = "Journal of Quantitative Criminology"}

@String{j-J-QUANT-LINGUISTICS   = "Journal of Quantitative Linguistics"}

@String{j-J-R-STAT-SOC          = "Journal of the Royal Statistical Society"}

@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
                                  Society. Series D (The Statistician)"}

@String{j-J-REG-SCI             = "Journal of Regional Science"}

@String{j-J-STAT-MECH-THEORY-EXP = "Journal of Statistical Mechanics: Theory and
                                  Experiment"}

@String{j-J-STAT-PHYS           = "Journal of Statistical Physics"}

@String{j-J-THEOR-BIOL          = "Journal of Theoretical Biology"}

@String{j-J-URBAN-ECON          = "Journal of Urban Economics"}

@String{j-J-WASH-ACAD-SCI       = "Journal of the Washington Academy of
                                  Sciences"}

@String{j-KNOWL-INFO-SYS        = "Knowledge and Information Systems"}

@String{j-LANG-SCI              = "Language Sciences"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LIBR-TRENDS           = "Library Trends"}

@String{j-MAT-ZAMETKI           = "Matematicheskie Zametki"}

@String{j-MATH-ANN              = "Mathematische Annalen"}

@String{j-MATH-COMP-MODELLING   = "Mathematical and Computer Modelling"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-GAZ              = "The Mathematical Gazette"}

@String{j-MATH-GEOL             = "Mathematical Geology"}

@String{j-MATH-GEOSCI           = "Mathematical Geosciences"}

@String{j-MATH-INTEL            = "The Mathematical Intelligencer"}

@String{j-MATH-MAG              = "Mathematics Magazine"}

@String{j-MATH-NACHR            = "Mathematische Nachrichten"}

@String{j-MATH-NOTES-ACAD-SCI-USSR = "Mathematical Notes of the {Academy of
                                  Sciences of the USSR = Matematicheskie
                                  Zametki}"}

@String{j-MICROELECT-RELIABILITY = "Microelectronics and Reliability"}

@String{j-MOD-PHYS-LETT-A       = "Modern Physics Letters A (MPLA)"}

@String{j-MONAT-MATH            = "Monatshefte f{\"u}r Mathematik"}

@String{j-NATURE                = "Nature"}

@String{j-NEW-J-PHYS            = "New Journal of Physics"}

@String{j-NEW-SCIENTIST         = "New Scientist"}

@String{j-NY-TIMES              = "New York Times"}

@String{j-OPER-SYS-REV          = "Operating Systems Review"}

@String{j-PAP-REG-SCI           = "Papers in Regional Science"}

@String{j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI = "Philosophical
                                  transactions of the Royal Society of
                                  London Series B, Biological sciences"}

@String{j-PHYS-LET-A            = "Physics Letters A"}

@String{j-PHYS-REV              = "Physical Review"}

@String{j-PHYS-REV-A            = "Physical Review A (Atomic, Molecular, and
                                  Optical Physics)"}

@String{j-PHYS-REV-C            = "Physical Review C (Nuclear Physics)"}

@String{j-PHYS-REV-E            = "Physical Review E (Statistical physics,
                                  plasmas, fluids, and related
                                  interdisciplinary topics)"}

@String{j-PHYS-REV-LET          = "Physical Review Letters"}

@String{j-PHYSICA-A             = "Physica A: Statistical Mechanics and its
                                  Applications"}

@String{j-PHYSICA-D             = "Physica. D, Nonlinear phenomena"}

@String{j-PLOS-MED              = "PLoS Medicine"}

@String{j-PLOS-ONE              = "PLoS One"}

@String{j-POLIT-ANAL            = "Political Analysis"}

@String{j-PROB-ENG-INFO-SCI     = "Probability in the Engineering and
                                  Informational Sciences"}

@String{j-PROBAB-SURV           = "Probabability Surveys"}

@String{j-PROBAB-THEORY-RELAT-FIELDS = "Probability Theory and Related Fields"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-AMER-PHIL-SOC    = "Proceedings of the American Philosophical
                                  Society"}

@String{j-PROC-INST-STATIST-MATH = "Proceedings of the Institute of Statistical
                                  Mathematics"}

@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
                                  Sciences of the United States of America"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI = "Proceedings of the Royal
                                  Society A: Mathematical, Physical, \&
                                  Engineering Sciences"}

@String{j-PROC-R-SOC-LOND-SER-B-BIO-SCI = "Proceedings of the Royal Society of
                                  London. Series B. Biological sciences"}

@String{j-PROG-THEOR-PHYS       = "Progress of Theoretical Physics"}

@String{j-PSYCHOL-REP           = "Psychological Reports"}

@String{j-Q-J-ECON              = "The Quarterly Journal of Economics"}

@String{j-RAND-STRUCT           = "Random Structures and Algorithms"}

@String{j-REG-SCI-URBAN-ECON    = "Regional Science and Urban Economics"}

@String{j-RELIABLE-COMPUTING    = "Reliable Computing = Nadezhnye vychisleniia"}

@String{j-REV-INT-ECON          = "Review of International Economics"}

@String{j-REV-MOD-PHYS = "Reviews of Modern Physics"}

@String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"}

@String{j-RUSS-J-MATH-PHYS      = "Russian Journal of Mathematical Physics"}

@String{j-SANKHYA-B             = "Sankhy{\=a} (Indian Journal of Statistics),
                                  Series B. Methodological"}

@String{j-SCI-AMER              = "Scientific American"}

@String{j-SCI-REP               = "Scientific Reports"}

@String{j-SCIENCE               = "Science"}

@String{j-SCIENTOMETRICS        = "Scientometrics"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SIGMETRICS            = "ACM SIGMETRICS Performance Evaluation
                                  Review"}

@String{j-SIGMOD                = "SIGMOD Record (ACM Special Interest Group
                                  on Management of Data)"}

@String{j-SIGNAL-PROCESS-IMAGE-COMMUN = "Signal Processing: Image
                                  Communication"}

@String{j-SIGNIF                = "Significance ({Oxford, England})"}

@String{j-SIGPLAN               = "ACM SIG{\-}PLAN Notices"}

@String{j-SOC-METH-RES          = "Sociological Methods and Research"}

@String{j-SPE                   = "Soft\-ware --- Prac\-tice and Experience"}

@String{j-STAT-PROB-LETT        = "Statistics \& Probability Letters"}

@String{j-STAT-SCI              = "Statistical Science"}

@String{j-STATISTICA-BOLOGNA    = "Statistica (Bologna)"}

@String{j-STOCH-DYNAM           = "Stochastics and Dynamics"}

@String{j-STOCH-PROC-APPL       = "Stochastic Processes and Their Applications"}

@String{j-STUD-HIST-PHILOS-SCI  = "Studies in History and Philosophy of Science
                                  Part {A}"}

@String{j-STUD-LINGUISTICA      = "Studia Linguistica"}

@String{j-SYSTEM                = "System"}

@String{j-TCBB                  = "IEEE\slash ACM Transactions on Computational
                                  Biology and Bioinformatics"}

@String{j-TECHNOMETRICS         = "Technometrics"}

@String{j-TEORET-MATH-FIZ       = "Teoreticheskaya i Matematicheskaya Fizika"}

@String{j-THEOR-COMP-SCI        = "Theoretical Computer Science"}

@String{j-THEORY-PROBAB-APPL    = "Theory of Probability and its Applications"}

@String{j-THEORY-PROBAB-MATH-STAT = "Theory of Probability and Mathematical
                                  Statistics"}

@String{j-TKDD                  = "ACM Transactions on Knowledge Discovery
                                  from Data (TKDD)"}

@String{j-TODS                  = "ACM Transactions on Database Systems"}

@String{j-TOIS                  = "ACM Transactions on Information Systems"}

@String{j-TOS                   = "ACM Transactions on Storage"}

@String{j-TRANS-AM-MATH-SOC     = "Transactions of the American Mathematical
                                  Society"}

@String{j-TRAV-HUM              = "Le Travail Humain"}

@String{j-WALL-ST-J             = "Wall Street Journal"}

@String{j-Z-ANAL-ANWEND         = "{Zeitschrift f{\"u}r Analysis und ihre
                                  Anwendungen}"}

@String{j-Z-ANGE-MATH-MECH      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik}"}

@String{j-Z-NATURFORSCH         = "{Zeitschrift f{\"u}r Naturforschung}"}

@String{j-ZASTOS-MAT            = "Zastosowania Matematyki"}

%%% ====================================================================
%%% Publisher abbreviations:

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-ADAM-HILGER         = "Adam Hilger Ltd."}
@String{pub-ADAM-HILGER:adr     = "Bristol, UK"}

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-BASIC-BOOKS         = "Basic Books"}
@String{pub-BASIC-BOOKS:adr     = "New York, NY, USA"}

@String{pub-BUTTERWORTHS        = "Butterworths"}
@String{pub-BUTTERWORTHS:adr    = "London, UK"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-CLARENDON           = "Clarendon Press"}
@String{pub-CLARENDON:adr       = "Oxford, UK"}

@String{pub-DOVER               = "Dover Publications, Inc."}
@String{pub-DOVER:adr           = "New York, NY, USA"}

@String{pub-ELSEVIER            = "Elsevier"}
@String{pub-ELSEVIER:adr        = "Amsterdam, The Netherlands"}

@String{pub-HARVARD             = "Harvard University Press"}
@String{pub-HARVARD:adr         = "Cambridge, MA, USA"}

@String{pub-HOUGHTON-MIFFLIN   = "Houghton-Mifflin"}
@String{pub-HOUGHTON-MIFFLIN:adr = "Boston, MA, USA"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-MATH-ASSOC-AMER     = "Mathematical Association of America"}
@String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"}

@String{pub-MCGRAW-HILL         = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr     = "New York, NY, USA"}

@String{pub-MIT                 = "MIT Press"}
@String{pub-MIT:adr             = "Cambridge, MA, USA"}

@String{pub-MORGAN-KAUFMANN     = "Morgan Kaufmann Publishers"}
@String{pub-MORGAN-KAUFMANN:adr = "Los Altos, CA 94022, USA"}

@String{pub-NORTH-HOLLAND       = "North-Holland Publishing Co."}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Upper Saddle River, NJ, USA"}

@String{pub-PRINCETON           = "Princeton University Press"}
@String{pub-PRINCETON:adr       = "Princeton, NJ, USA"}

@String{pub-SPIE                = "SPIE Optical Engineering Press"}
@String{pub-SPIE:adr            = "Bellingham, WA, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-U-MICHIGAN          = "University of Michigan Press"}
@String{pub-U-MICHIGAN:adr      = "Ann Arbor, MI, USA"}

@String{pub-W-H-FREEMAN         = "W. H. {Freeman and Company}"}
@String{pub-W-H-FREEMAN:adr     = "New York, NY, USA"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

@String{pub-WORLD-SCI           = "World Scientific Publishing
                                  Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr       = "P. O. Box 128, Farrer Road,
                                  Singapore 9128"}

@String{pub-YALE                = "Yale University Press"}
@String{pub-YALE:adr            = "New Haven, CT, USA"}

%%% ====================================================================
%%% Series abbreviations:

@String{ser-LNAI                = "Lecture Notes in Artificial Intelligence"}

@String{ser-LNCS                = "Lecture Notes in Computer Science"}

@String{ser-LNM                 = "Lecture Notes in Mathematics"}

%%% ====================================================================
%%% Bibliography entries, sorted by year, and then by citation label:

@Article{Aban:2006:PET,
  author =       "Inmaculada B. Aban and Mark M. Meerschaert and Anna K.
                 Panorska",
  title =        "Parameter Estimation for the Truncated {Pareto}
                 Distribution",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "101",
  number =       "473",
  pages =        "270--277",
  month =        mar,
  year =         "2006",
  CODEN =        "JSTNAL",
  DOI =          "http://dx.doi.org/10.1198/016214505000000411",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Thu Aug 26 11:26:31 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/jasa/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Abdel-All:2003:GPP,
  author =       "N. H. Abdel-All and M. A. W. Mahmoud and H. N.
                 Abd-Ellah",
  title =        "Geometrical properties of {Pareto} distribution",
  journal =      j-APPL-MATH-COMP,
  volume =       "145",
  number =       "2--3",
  pages =        "321--339",
  day =          "25",
  month =        dec,
  year =         "2003",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Jan 9 08:41:12 MST 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Abe:2002:STE,
  author =       "Sumiyoshi Abe",
  title =        "Stability of {Tsallis} entropy and instabilities of
                 {R{\'e}nyi} and normalized {Tsallis} entropies: a basis
                 for $q$-exponential distributions",
  journal =      j-PHYS-REV-E,
  volume =       "66",
  number =       "??",
  pages =        "046134",
  day =          "24",
  month =        oct,
  year =         "2002",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.66.046134",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.66.046134",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Abourbih:2010:SSD,
  author =       "Jonathan A. Abourbih and Luke Blaney and Alan Bundy
                 and Fiona McNeill",
  title =        "A Single-Significant-Digit Calculus for Semi-Automated
                 Guesstimation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6173",
  pages =        "354--368",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-14203-1_31",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:43:23 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31",
  acknowledgement = ack-nhfb,
  book-DOI =     "http://dx.doi.org/10.1007/978-3-642-14203-1",
  book-URL =     "http://www.springerlink.com/content/978-3-642-14203-1",
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Abrantes-Metz:2011:TLR,
  author =       "R. M. Abrantes-Metz and S. B. Villas-Boas and G.
                 Judge",
  title =        "Tracking the {Libor} rate",
  journal =      j-APPL-ECON-LETT,
  volume =       "18",
  number =       "10",
  pages =        "893--899",
  month =        "????",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1080/13504851.2010.515197",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Mon Feb 18 18:17:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/13504851.2010.515197",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  keywords =     "Benford's Second-Digit Law",
  remark =       "From the abstract: ``Libor rates depart significantly
                 from the expected Benford reference distribution. This
                 raises potential concerns relative to the unbiased
                 nature of the signals coming from the 16 banks from
                 which the Libor is computed and the usefulness of the
                 Libor as a major economic indicator.''",
}

@Article{Ackermann:2007:DMB,
  author =       "Heiner Ackermann and Alantha Newman and Heiko
                 R{\"o}glin and Berthold V{\"o}cking",
  title =        "Decision-making based on approximate and smoothed
                 {Pareto} curves",
  journal =      j-THEOR-COMP-SCI,
  volume =       "378",
  number =       "3",
  pages =        "253--270",
  day =          "9",
  month =        jun,
  year =         "2007",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Tue Mar 29 08:55:49 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/03043975",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Adamic:2011:CSU,
  author =       "Lada Adamic",
  title =        "Complex systems: Unzipping {Zipf}'s law",
  journal =      j-NATURE,
  volume =       "474",
  number =       "7350",
  pages =        "164--165",
  month =        jun,
  year =         "2011",
  CODEN =        "NATUAS",
  DOI =          "http://dx.doi.org/10.1038/474164a",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Tue Nov 15 09:29:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  onlinedate =   "09 June 2011",
}

@Article{Adhikari:1968:DMS,
  author =       "A. K. Adhikari and B. P. Sarkar",
  title =        "Distribution of most significant digit in certain
                 functions whose arguments are random variables",
  journal =      j-SANKHYA-B,
  volume =       "30",
  number =       "??",
  pages =        "47--58",
  month =        "????",
  year =         "1968",
  CODEN =        "SANBBV",
  ISSN =         "0581-5738",
  ISSN-L =       "0581-5738",
  bibdate =      "Sat Nov 12 16:09:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Article{Adhikari:1969:SRD,
  author =       "A. K. Adhikari",
  title =        "Some results on the distribution of the most
                 significant digit",
  journal =      j-SANKHYA-B,
  volume =       "31",
  number =       "??",
  pages =        "413--420",
  month =        "????",
  year =         "1969",
  CODEN =        "SANBBV",
  ISSN =         "0581-5738",
  ISSN-L =       "0581-5738",
  bibdate =      "Sat Nov 12 16:12:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Article{Aigner:1970:EPL,
  author =       "Dennis J. Aigner and Arthur S. Goldberger",
  title =        "Estimation of {Pareto's Law} from Grouped
                 Observations",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "65",
  number =       "330",
  pages =        "712--723",
  month =        jun,
  year =         "1970",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:44 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314212;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2284582",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Aigner:1972:CEP,
  author =       "Dennis J. Aigner and Arthur S. Goldberger",
  title =        "Corrigenda: Estimation of {Pareto's Law} from Grouped
                 Observations",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "67",
  number =       "337",
  pages =        "252--252",
  month =        mar,
  year =         "1972",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:45 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314217;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2284755",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Ainsworth:2009:QSR,
  author =       "Richard Thompson Ainsworth and Urs Hengartner",
  title =        "{Quebec's Sales Recording Module (SRM)}: Fighting the
                 {Zapper}, {Phantomware}, and Tax Fraud with
                 technology",
  journal =      "Canadian Tax Journal",
  volume =       "57",
  number =       "4",
  pages =        "715--761",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0068-9823",
  ISSN-L =       "0068-9823",
  bibdate =      "Fri Mar 22 08:37:54 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.ctf.ca/ctfweb/Documents/PDF/2009ctj/09ctj4-ainsworth.pdf",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  journal-URL =  "https://www.ctf.ca/ctfweb",
  keywords =     "Benford's Law",
}

@Misc{Alagoz:2010:MDB,
  author =       "Ali Alag{\"o}z and Mustafa Ay",
  title =        "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital
                 Analiz. ({Turkish}) [{Benford Law}-Based Digital
                 Analysis of Accounting Oversight]",
  pages =        "17",
  day =          "8",
  month =        jan,
  year =         "2010",
  bibdate =      "Mon Feb 18 09:19:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf",
  acknowledgement = ack-nhfb,
  language =     "Turkish",
}

@Article{Aldous:2010:WCO,
  author =       "David Aldous and Tung Phan",
  title =        "When Can One Test an Explanation? {Compare} and
                 Contrast {Benford's Law} and the Fuzzy {CLT}",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "3",
  pages =        "221--227",
  month =        aug,
  year =         "2010",
  CODEN =        "ASTAAJ",
  DOI =          "http://dx.doi.org/10.1198/tast.2010.09098",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2757166",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@TechReport{Alexander:2009:RUB,
  author =       "James C. Alexander",
  title =        "Remarks on the use of {Benford's Law}",
  type =         "Working paper",
  institution =  "Department of Mathematics and Cognitive Science, Case
                 Western Reserve University",
  address =      "Cleveland, OH, USA",
  day =          "23",
  month =        nov,
  year =         "2009",
  bibdate =      "Fri Mar 22 08:40:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1505147",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
}

@Article{Allaart:1997:ISC,
  author =       "Pieter C. Allaart",
  title =        "An Invariant-Sum Characterization of {Benford's Law}",
  journal =      j-J-APPL-PROBAB,
  volume =       "34",
  number =       "1",
  pages =        "288--291",
  month =        mar,
  year =         "1997",
  CODEN =        "JPRBAM",
  DOI =          "http://dx.doi.org/10.2307/3215195",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "60E05",
  MRnumber =     "1429075 (98d:60029)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3215195",
  abstract =     "The accountant Nigrini remarked that in tables of data
                 distributed according to Benford's law, the sum of all
                 elements with first digit $ d (d = 1, 2, \ldots, 9) $
                 is approximately constant. In this note, a mathematical
                 formulation of Nigrini's observation is given and it is
                 shown that Benford's law is the unique probability
                 distribution such that the expected sum of all elements
                 with first digits $ d_1, \ldots, d_k $ is constant for
                 every fixed $k$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@InProceedings{Altamirano:2009:GTU,
  author =       "C. Altamirano and A. Robledo",
  editor =       "J. Zhou",
  booktitle =    "Complex Sciences",
  title =        "Generalized Thermodynamics Underlying the Laws of
                 {Zipf} and {Benford}",
  volume =       "5",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "2232--??",
  year =         "2009",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-02469-6_100",
  ISBN =         "3-642-02468-8",
  ISBN-13 =      "978-3-642-02468-9",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A",
  acknowledgement = ack-nhfb,
}

@Article{Altamirano:2010:PTS,
  author =       "Carlo Altamirano and Alberto Robledo",
  title =        "Possible thermodynamic structure underlying the laws
                 of {Zipf} and {Benford}",
  journal =      "ArXiv e-prints",
  day =          "10",
  month =        aug,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:12:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1008.1614",
  abstract =     "We show that the laws of Zipf and Benford, obeyed by
                 scores of numerical data generated by many and diverse
                 kinds of natural phenomena and human activity are
                 related to the focal expression of a generalized
                 thermodynamic structure. This structure is obtained
                 from a deformed type of statistical mechanics that
                 arises when configurational phase space is incompletely
                 visited in a severe way. Specifically, the restriction
                 is that the accessible fraction of this space has
                 fractal properties. The focal expression is an
                 (incomplete) Legendre transform between two entropy (or
                 Massieu) potentials that when particularized to first
                 digits leads to a previously existing generalization of
                 Benford's law. The inverse functional of this
                 expression leads to Zipf's law; but it naturally
                 includes the bends or tails observed in real data for
                 small and large rank. Remarkably, we find that the
                 entire problem is analogous to the transition to chaos
                 via intermittency exhibited by low-dimensional
                 nonlinear maps. Our results also explain the generic
                 form of the degree distribution of scale-free
                 networks.",
  acknowledgement = ack-nhfb,
  remark =       "To be published in European Physical Journal B.",
}

@Article{Altamirano:2011:PTS,
  author =       "C. Altamirano and A. Robledo",
  title =        "Possible thermodynamic structure underlying the laws
                 of {Zipf} and {Benford}",
  journal =      j-EUR-PHYS-J-B,
  volume =       "81",
  number =       "3",
  pages =        "345--351",
  month =        jun,
  year =         "2011",
  CODEN =        "EPJBFY",
  DOI =          "http://dx.doi.org/10.1140/epjb/e2011-10968-5",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Mon Nov 14 17:53:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011EPJB...81..345A",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1008.1614",
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
  primaryclass = "cond-mat.stat-mech",
}

@Article{Alvarez-Ramirez:2003:ZMS,
  author =       "Jose Alvarez-Ramirez and Monica Meraz and Gustavo
                 Gallegos",
  title =        "{Zipf--Mandelbrot} scaling law for world track
                 records",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "3--4",
  pages =        "545--560",
  day =          "15",
  month =        oct,
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(03)00579-X",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037843710300579X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Amin:2007:TVA,
  author =       "Zeinab H. Amin",
  title =        "Tests for the Validity of the Assumption that the
                 Underlying Distribution of Life is {Pareto}",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "2",
  pages =        "195--201",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Book{Anastasi:2003:NFI,
  author =       "Joe Anastasi",
  title =        "The new forensics: investigating corporate fraud and
                 the theft of intellectual property",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 270",
  year =         "2003",
  ISBN =         "0-471-26994-8 (hardcover)",
  ISBN-13 =      "978-0-471-26994-6 (hardcover)",
  LCCN =         "HV8079.W47 A5 2003",
  bibdate =      "Tue Nov 22 11:42:36 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/wiley044/2003001697.html;
                 http://www.loc.gov/catdir/description/wiley037/2003001697.html;
                 http://www.loc.gov/catdir/toc/wiley031/2003001697.html",
  acknowledgement = ack-nhfb,
  remark =       "Brief mention of Benford's Law on pp. 184--185.",
  subject =      "white collar crime investigation; data processing;
                 case studies; fraud investigation; forensic accounting;
                 computer security",
}

@Article{Anderson:2009:CRC,
  author =       "Thomas Anderson",
  title =        "Conference reviewing considered harmful",
  journal =      j-OPER-SYS-REV,
  volume =       "43",
  number =       "2",
  pages =        "108--116",
  month =        apr,
  year =         "2009",
  CODEN =        "OSRED8",
  DOI =          "http://doi.acm.org/10.1145/1531793.1531815",
  ISSN =         "0163-5980 (print), 1943-586X (electronic)",
  ISSN-L =       "0163-5980",
  bibdate =      "Thu Apr 23 19:43:22 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "This paper develops a model of computer systems
                 research to help prospective authors understand the
                 often obscure workings of conference program
                 committees. We present data to show that the
                 variability between reviewers is often the dominant
                 factor as to whether a paper is accepted. We argue that
                 paper merit is likely to be Zipf distributed, making it
                 inherently difficult for program committees to
                 distinguish between most papers. We use game theory to
                 show that with noisy reviews and Zipf merit, authors
                 have an incentive to submit papers too early and too
                 often. These factors make conference reviewing, and
                 systems research as a whole, less efficient and less
                 effective. We describe some recent changes in
                 conference design to address these issues, and we
                 suggest some further potential improvements.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGOPS Operating Systems Review",
}

@Article{Anderson:2010:BLC,
  author =       "Theresa Anderson and Larry Rolen and Ruth Stoehr",
  title =        "{Benford's} Law For Coefficients of Modular Forms and
                 Partition Functions",
  journal =      "ArXiv e-prints",
  day =          "3",
  month =        sep,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:10:51 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1009.0780",
  abstract =     "Here we prove that Benford's law holds for
                 coefficients of an infinite class of modular forms.
                 Expanding the work of Bringmann and Ono on exact
                 formulas for harmonic Maass forms, we derive the
                 necessary asymptotics. This implies that the
                 unrestricted partition function $ p(n) $, as well as
                 other natural partition functions, satisfy Benford's
                 law.",
  acknowledgement = ack-nhfb,
  pagecount =    "10",
}

@Article{Anderson:2011:BLC,
  author =       "Theresa C. Anderson and Larry Rolen and Ruth Stoehr",
  title =        "{Benford}'s law for coefficients of modular forms and
                 partition functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "139",
  number =       "5",
  pages =        "1533--1541",
  year =         "2011",
  CODEN =        "PAMYAR",
  DOI =          "http://dx.doi.org/10.1090/S0002-9939-2010-10577-4",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "11F12 (11F20 11P83)",
  MRnumber =     "2763743",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@Article{Andrew:2011:OBM,
  author =       "Alex M. Andrew",
  title =        "Obituary: {Beno{\^\i}t Mandelbrot: 20 November
                 1924--14 October 2010}",
  journal =      "Kybernetes",
  volume =       "40",
  number =       "1--2",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "KBNTA3",
  ISSN =         "0368-492X (print), 1758-7883 (electronic)",
  ISSN-L =       "0368-492X",
  bibdate =      "Fri Nov 25 07:32:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://en.wikipedia.org/wiki/ernst_von_glasersfeld;
                 http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf;
                 http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825;
                 http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary;
                 http://www.math.yale.edu/mandelbrot/;
                 http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:1932:FL,
  author =       "Anonymous",
  title =        "Fishpole Lamp",
  howpublished = "Web site",
  day =          "30",
  month =        apr,
  year =         "1932",
  bibdate =      "Sat Feb 23 14:52:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This Web site reports that General Electric researcher
                 Frank Benford invented the electric light pointer, the
                 forerunner of the modern laser pointer.",
  URL =          "http://scienceservice.si.edu/pages/012020.htm",
  acknowledgement = ack-nhfb,
  remark =       "CD 2478048, E\&MP12.020, Electric Appliances \
                 Apparatus.",
}

@Article{Anonymous:1950:BRZ,
  author =       "Anonymous",
  title =        "Book review: {Zipf, George K., \booktitle{Human
                 behavior and the principle of least effort}. Cambridge,
                 (Mass.): Addison-Wesley, 1949, pp. 573}",
  journal =      j-J-CLIN-PSYCHOL,
  volume =       "6",
  number =       "3",
  pages =        "306--306",
  year =         "1950",
  CODEN =        "JCPYAO",
  DOI =          "http://dx.doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO;2-7",
  ISSN =         "0021-9762 (print), 1097-4679 (electronic)",
  ISSN-L =       "0021-9762",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Psychology",
}

@Article{Anonymous:1993:WFR,
  author =       "Anonymous",
  title =        "Why failure rates observe {Zipf}'s law in operational
                 software: {M. Trachtenberg. IEEE Transactions on
                 Reliability, {\bf 41}(3), 386 (1992)}",
  journal =      j-MICROELECT-RELIABILITY,
  volume =       "33",
  number =       "13",
  pages =        "2062--2062",
  month =        oct,
  year =         "1993",
  CODEN =        "MCRLAS",
  DOI =          "http://dx.doi.org/10.1016/0026-2714(93)90406-O",
  ISSN =         "0026-2714 (print), 1872-941X (electronic)",
  ISSN-L =       "0026-2714",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002627149390406O",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Zipf's Law",
}

@Article{Anonymous:2002:ZLM,
  author =       "Anonymous",
  title =        "{Zipf}'s law and maximum sustainable growth",
  journal =      j-STAT-PROB-LETT,
  volume =       "56",
  number =       "2",
  pages =        "??--??",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "SPLTDC",
  DOI =          "http://dx.doi.org/10.1016/j.jedc.2013.02.004",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165188913000341",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Zipf's Law",
  onlinedate =   "19 February 2013",
}

@Article{Anonymous:2005:UZL,
  author =       "Anonymous",
  title =        "The use of {Zipf}'s law in animal communication
                 analysis",
  journal =      j-ANIM-BEHAV,
  volume =       "69",
  number =       "1",
  pages =        "??--??",
  day =          "20",
  month =        jan,
  year =         "2005",
  CODEN =        "ANBEA8",
  DOI =          "http://dx.doi.org/10.1016/j.anbehav.2004.08.004",
  ISSN =         "0003-3472 (print), 1095-8282 (electronic)",
  ISSN-L =       "0003-3472",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0003347204003471",
  acknowledgement = ack-nhfb,
  fjournal =     "Animal Behaviour",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00033472",
  keywords =     "Zipf's Law",
}

@Misc{Anonymous:2007:ZL,
  author =       "Anonymous",
  key =          "Zipf's Law",
  title =        "{Zipf}'s law",
  year =         "2007",
  bibdate =      "Sat Jan 26 12:46:16 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/datacompression.bib",
  URL =          "http://en.wikipedia.org/wiki/Zipf's_law",
  acknowledgement = ack-ds,
  lastaccess =   "27 January 2013",
  rawdata =      "Zipf's Law (2007)
                 |http://en.wikipedia.org/wiki/Zipf's_law|",
}

@Article{Anonymous:2012:SB,
  author =       "Anonymous",
  title =        "The scam busters",
  journal =      j-ECONOMIST,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        dec,
  year =         "2012",
  CODEN =        "EONOEH",
  ISSN =         "0013-0613 (print), 1476-8860 (electronic)",
  ISSN-L =       "0013-0613",
  bibdate =      "Mon Feb 18 19:01:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.economist.com/news/finance-and-economics/21568364-how-antitrust-economists-are-getting-better-spotting-cartels-scam-busters",
  acknowledgement = ack-nhfb,
  fjournal =     "The Economist",
  keywords =     "Benford's Law",
}

@Article{Antonini:1991:NUD,
  author =       "Rita Giuliano Antonini",
  title =        "On the Notion of Uniform Distribution Mod $1$",
  journal =      j-FIB-QUART,
  volume =       "29",
  number =       "3",
  pages =        "230--234",
  month =        aug,
  year =         "1991",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:01:34 MDT 2011",
  bibsource =    "http://www.fq.math.ca/29-3.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/29-3/antonini.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
  keywords =     "Benford's Law",
}

@Article{Antonini:2005:RSC,
  author =       "Rita Giuliano Antonini and Georges Grekos",
  title =        "Regular sets and conditional density: an extension of
                 {Benford}'s law",
  journal =      j-COLLOQ-MATH,
  volume =       "103",
  number =       "2",
  pages =        "173--192",
  year =         "2005",
  CODEN =        "CQMAAQ",
  DOI =          "http://dx.doi.org/10.4064/cm103-2-3",
  ISSN =         "0010-1354 (print), 1730-6302 (electronic)",
  ISSN-L =       "0010-1354",
  MRclass =      "11B05 (11K99)",
  MRnumber =     "2197847 (2006j:11012)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1092.11009",
  acknowledgement = ack-nhfb,
  fjournal =     "Colloquium Mathematicum",
  keywords =     "asymptotic density; Benford's law; conditional
                 density; first digit problem; logarithmic density;
                 regular set; regular varying function",
  ZMclass =      "11B05 (Topology etc. of sets of numbers); 11K99
                 (Probabilistic theory)",
}

@Article{Aono:2008:ISO,
  author =       "June Y. Aono and Liming Guan",
  title =        "The impact of {Sarbanes--Oxley} act on cosmetic
                 earnings management",
  journal =      "Research in Accounting Regulation",
  volume =       "20",
  number =       "??",
  pages =        "205--215",
  month =        oct,
  year =         "2008",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/S1052-0457(07)00212-3",
  ISSN =         "1052-0457",
  ISSN-L =       "1052-0457",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1052045707002123",
  acknowledgement = ack-nhfb,
  fjournal =     "Research in Accounting Regulation",
  keywords =     "Benford's Law",
}

@Article{Aoyama:2004:KDP,
  author =       "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma",
  title =        "Kinematics and dynamics of {Pareto--Zipf}'s law and
                 {Gibrat}'s law",
  journal =      j-PHYSICA-A,
  volume =       "344",
  number =       "1--2",
  pages =        "117--121",
  day =          "1",
  month =        dec,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2004.06.099",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437104009185",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Archambault:2011:EMA,
  author =       "J. Archambault and M. Archambault",
  title =        "Earnings management among firms during the pre-{SEC}
                 era: a {Benford}'s law analysis",
  journal =      j-ACCOUNT-HIST-J,
  volume =       "38",
  number =       "2",
  pages =        "145--170",
  month =        "????",
  year =         "2011",
  ISSN =         "0148-4184",
  ISSN-L =       "0148-4184",
  bibdate =      "Mon Feb 18 11:32:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Accounting Historians Journal",
  journal-URL =  "http://www.jstor.org/action/showPublication?journalCode=accohistjour;
                 http://www.aahhq.org/",
  remark =       "JSTOR has a 3-year moving wall, so this article is not
                 yet in that archive; the publisher's Web site is poor,
                 and I cannot find the article there.",
}

@Article{Arnold:1989:BEP,
  author =       "Barry C. Arnold and S. James Press",
  title =        "{Bayesian} estimation and prediction for {Pareto}
                 data",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "84",
  number =       "408",
  pages =        "1079--1084",
  month =        "????",
  year =         "1989",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62F15 (62F10)",
  MRnumber =     "92f:62034",
  bibdate =      "Mon May 5 12:36:01 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Book{Arthur:1994:IRP,
  author =       "W. Brian Arthur",
  title =        "Increasing returns and path dependence in the
                 economy",
  publisher =    pub-U-MICHIGAN,
  address =      pub-U-MICHIGAN:adr,
  pages =        "xx + 201",
  year =         "1994",
  ISBN =         "0-472-09496-3 , 0-472-06496-7 (paperback)",
  ISBN-13 =      "978-0-472-09496-7, 978-0-472-06496-0 (paperback)",
  LCCN =         "HD69.S5 A77 1994",
  bibdate =      "Wed Feb 27 07:08:40 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With a foreword by Kenneth J. Arrow.",
  series =       "Economics, cognition, and society",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Economies of scale; Mathematical models; Economic
                 development; Economics, Mathematical",
}

@Article{Auerbach:1913:GBG,
  author =       "Felix Auerbach",
  title =        "{Das Gesetz der Bev{\"o}lkerungskonzentration}.
                 ({German}) [{The} law of population concentration]",
  journal =      "{Petermann's Geographische Mitteilungen}",
  volume =       "59",
  number =       "1",
  pages =        "74--76",
  month =        "????",
  year =         "1913",
  CODEN =        "PGGMA3",
  ISSN =         "0031-6229",
  ISSN-L =       "0031-6229",
  bibdate =      "Thu Nov 24 10:49:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper is reported in \cite{Newman:2005:PLP} to be
                 the first discovery of {\em Zipf's Law\/} in connection
                 with city populations (see \cite{Zipf:1932:SSP}). See
                 also \cite{Estoup:1916:GSM}.",
  URL =          "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122",
  acknowledgement = ack-nhfb,
  ajournal =     "Petermanns Geogr. Mitteilung",
  ajournal-2 =   "Petermanns Geogr. Mitt.",
  language =     "German",
}

@Article{Ausloos:1999:PMK,
  author =       "M. Ausloos and K. Ivanova",
  title =        "Precise $ (m, k) $-{Zipf} diagram analysis of
                 mathematical and financial time series when $ m = 6 $,
                 $ k = 2 $",
  journal =      j-PHYSICA-A,
  volume =       "270",
  number =       "3--4",
  pages =        "526--542",
  day =          "15",
  month =        aug,
  year =         "1999",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(99)00178-8",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437199001788",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Ausloos:2003:SIZ,
  author =       "M. Ausloos and Ph. Bronlet",
  title =        "Strategy for investments from {Zipf} law(s)",
  journal =      j-PHYSICA-A,
  volume =       "324",
  number =       "1--2",
  pages =        "30--37",
  day =          "1",
  month =        jun,
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(02)01845-9",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B82",
  MRnumber =     "2030919",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "International Econophysics Conference IEC2002 (Bali)",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437102018459",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Axtell:2001:ZDU,
  author =       "R. L. Axtell",
  title =        "{Zipf} Distribution of {U.S.} Firm Sizes",
  journal =      j-SCIENCE,
  volume =       "293",
  number =       "5536",
  pages =        "1818--1820",
  day =          "7",
  month =        sep,
  year =         "2001",
  CODEN =        "SCIEAS",
  DOI =          "http://dx.doi.org/10.1126/science.1062081",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Wed Feb 27 06:38:34 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/293/5536/1818",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "Zipf's Law",
}

@Article{AyllonBurguillo:1999:PDS,
  author =       "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera
                 Dom{\'\i}nguez}",
  title =        "El primer d{\'\i}gito significativo. ({Spanish}) [The
                 first significant digit]",
  journal =      "{Epsilon}: Revista de la {Sociedad Andaluza de
                 Educaci{\'o}n Matem{\'a}tica ``Thales''}",
  volume =       "15",
  number =       "3(45)",
  pages =        "339--352",
  month =        "????",
  year =         "1999",
  ISSN =         "1131-9321",
  ISSN-L =       "1131-9321",
  bibdate =      "Sat Feb 16 14:32:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "MATHEDUC.02332710",
  acknowledgement = ack-nhfb,
  ajournal =     "{Rev. Epsil{\'o}n SAEM `Thales'}",
  journal-URL =  "http://thales.cica.es/epsilon/;
                 http://dialnet.unirioja.es/servlet/revista?codigo=504",
  language =     "Spanish",
  msc2010 =      "K60xx",
  remark =       "Reported in \cite{Torres:2007:HDN} to contain an
                 extensive bibliography on Benford's Law. The publisher
                 does not have issues before 2003, and no electronic
                 copy has yet been found on the Internet. Attempts to
                 get this paper via Interlibrary Loan failed on the
                 grounds that ``We are unable to verify any owning
                 libraries within the United States or those that we
                 have ILL privileges.''",
  xxauthor =     "M. P. Dominguez and J. D. A. Burguillo",
  xxauthor =     "Manuel {Perera Dom{\'\i}nguez} and Juan David
                 {Ayll{\'o}n Burguillo}",
}

@Article{Bach:1998:EPM,
  author =       "Eric Bach",
  title =        "Efficient prediction of {Marsaglia--Zaman} random
                 number generators",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "44",
  number =       "3",
  pages =        "1253--1257",
  year =         "1998",
  CODEN =        "IETTAW",
  DOI =          "http://dx.doi.org/10.1109/18.669305",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  MRclass =      "65C10",
  MRnumber =     "99b:65007",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  ZMnumber =     "0915.65003",
  abstract =     "This paper presents two properties of the random
                 number generator by {\it G. Marsaglia} and {\it A.
                 Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
                 0733.65005)]. First, it is shown that its successive
                 digits are digits of certain rational $b$-adic numbers.
                 Then, an efficient algorithm is derived to predict an
                 unknown pseudorandom sequence of this type. Two
                 examples of the prediction are given.",
  acknowledgement = ack-nhfb,
  classmath =    "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc.",
  fjournal =     "IEEE Transactions on Information Theory",
  keywords =     "$b$-adic number; algorithm; continued fraction;
                 pseudo-random number generator",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@Article{Bachmann:2010:APC,
  author =       "Val{\'e}rie Bachmann and Martin H. Fischer and
                 Hans-Peter Landolt and Peter Brugger",
  title =        "Asymmetric prefrontal cortex functions predict
                 asymmetries in number space",
  journal =      j-BRAIN-COGN,
  volume =       "74",
  number =       "3",
  pages =        "306--311",
  month =        dec,
  year =         "2010",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/j.bandc.2010.08.011",
  ISSN =         "0278-2626 (print), 1090-2147 (electronic)",
  ISSN-L =       "0278-2626",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0278262610001272",
  acknowledgement = ack-nhfb,
  fjournal =     "Brain and Cognition",
  keywords =     "Benford's Law; small-number bias (SNB); Spatial
                 Numerical Association of Response Codes (SNARC)
                 effect",
}

@Article{Baek:2011:ZLU,
  author =       "Seung Ki Baek and Sebastian Bernhardsson and Petter
                 Minnhagen",
  title =        "{Zipf}'s law unzipped",
  journal =      j-NEW-J-PHYS,
  volume =       "13",
  number =       "4",
  pages =        "043004",
  month =        "????",
  year =         "2011",
  CODEN =        "NJOPFM",
  DOI =          "http://dx.doi.org/10.1088/1367-2630/13/4/043004",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Tue Nov 15 09:32:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://iopscience.iop.org/1367-2630/13/4/043004",
  abstract =     "Why does Zipf's law give a good description of data
                 from seemingly completely unrelated phenomena? Here it
                 is argued that the reason is that they can all be
                 described as outcomes of a ubiquitous random group
                 division: the elements can be citizens of a country and
                 the groups family names, or the elements can be all the
                 words making up a novel and the groups the unique
                 words, or the elements could be inhabitants and the
                 groups the cities in a country and so on. A random
                 group formation (RGF) is presented from which a
                 Bayesian estimate is obtained based on minimal
                 information: it provides the best prediction for the
                 number of groups with $k$ elements, given the total
                 number of elements, groups and the number of elements
                 in the largest group. For each specification of these
                 three values, the RGF predicts a unique group
                 distribution $ N(k) \propto \exp ( - b k) / k^\gamma $,
                 where the power-law index $ \gamma $ is a unique
                 function of the same three values. The universality of
                 the result is made possible by the fact that no
                 system-specific assumptions are made about the
                 mechanism responsible for the group division. The
                 direct relation between $ \gamma $ and the total number
                 of elements, groups and the number of elements in the
                 largest group is calculated. The predictive power of
                 the RGF model is demonstrated by direct comparison with
                 data from a variety of systems. It is shown that $
                 \gamma $ usually takes values in the interval $ 1 \leq
                 \gamma \leq 2 $ and that the value for a given
                 phenomenon depends in a systematic way on the total
                 size of the dataset. The results are put in the context
                 of earlier discussions on Zipf's and Gibrat's laws, $
                 N(k) \propto k^{-2} $ and the connection between growth
                 models and RGF is elucidated.",
  acknowledgement = ack-nhfb,
  fjournal =     "New Journal of Physics",
  pagecount =    "21",
}

@Article{Bak:1987:SOC,
  author =       "Per Bak and Chao Tang and Kurt Wiesenfeld",
  title =        "Self-organized criticality: An explanation of the $ 1
                 / f $ noise",
  journal =      j-PHYS-REV-LET,
  volume =       "59",
  number =       "4",
  pages =        "381--384",
  month =        jul,
  year =         "1987",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.59.381",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Feb 28 10:54:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.59.381",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Book{Bak:1996:HNW,
  author =       "Per Bak",
  title =        "How nature works: the science of self-organized
                 criticality",
  publisher =    "Copernicus",
  address =      "New York, NY, USA",
  pages =        "xiii + 212 + 8",
  year =         "1996",
  ISBN =         "0-387-94791-4 (hardcover)",
  ISBN-13 =      "978-0-387-94791-4 (hardcover)",
  LCCN =         "QC173.4.C74 B34 1996",
  bibdate =      "Thu Nov 24 13:34:22 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Critical phenomena (Physics); Complexity (Philosophy);
                 Physics; Philosophy",
}

@Article{Bakulina:2007:AZL,
  author =       "M. P. Bakulina",
  title =        "Application of {Zipf}'s law for text compression",
  journal =      "Diskretn. Anal. Issled. Oper. Ser. 2",
  volume =       "14",
  number =       "2",
  pages =        "3--13",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1560-9901",
  ISSN-L =       "1560-9901",
  MRclass =      "94A15",
  MRnumber =     "2542308 (2010i:94076)",
  MRreviewer =   "I. Vajda",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}.
                 Seriya 2",
}

@Article{Balanzario:2010:SCB,
  author =       "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz",
  title =        "Sufficient conditions for {Benford}'s law",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "23--24",
  pages =        "1713--1719",
  day =          "1--15",
  month =        dec,
  year =         "2010",
  CODEN =        "SPLTDC",
  DOI =          "http://dx.doi.org/10.1016/j.spl.2010.07.014",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "62E10 (62E17)",
  MRnumber =     "2734233 (2011i:62019)",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@TechReport{Balanzario:2012:BLM,
  author =       "E. P. Balanzario",
  title =        "{Benford}'s law for mixtures",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2012",
  bibdate =      "Mon Feb 18 19:02:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Balaz:2010:BLD,
  author =       "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch",
  title =        "{Benford}'s law and distribution functions of
                 sequences in $ (0, 1) $",
  journal =      j-MATH-NOTES-ACAD-SCI-USSR,
  volume =       "88",
  number =       "3--4",
  pages =        "449--463",
  month =        oct,
  year =         "2010",
  CODEN =        "MTHNB2",
  DOI =          "http://dx.doi.org/10.1134/S0001434610090178",
  ISSN =         "0001-4346 (print), 1573-8876 (electronic)",
  ISSN-L =       "0001-4346",
  bibdate =      "Fri Nov 25 10:52:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1134%2FS0001434610090178",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Notes of the {Academy of Sciences of the
                 USSR = Matematicheskie Zametki}",
}

@Article{Balazh:2010:BLD,
  author =       "V. Balazh and K. Nagasaka and O. Shtraukh",
  title =        "{Benford}'s law and distribution functions of
                 sequences in {$ (0, 1) $}",
  journal =      j-MAT-ZAMETKI,
  volume =       "88",
  number =       "4",
  pages =        "485--501",
  year =         "2010",
  DOI =          "http://dx.doi.org/10.1134/S0001434610090178",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "11K06 (60E05)",
  MRnumber =     "2882211",
  MRreviewer =   "Michael Drmota",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Book{Baldi:2003:MIW,
  author =       "Pierre Baldi and Paolo Frasconi and Padhraic Smyth",
  title =        "Modeling the {Internet} and the {Web}: probabilistic
                 methods and algorithms",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 285",
  year =         "2003",
  ISBN =         "0-470-86492-3 (e-book), 0-470-84906-1",
  ISBN-13 =      "978-0-470-86492-0 (e-book), 978-0-470-84906-4",
  LCCN =         "TK5105.875.I57 B35 2003eb",
  bibdate =      "Fri Jun 3 10:03:23 MDT 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/pagerank.bib",
  acknowledgement = ack-nhfb,
  subject =      "Internet; Mathematical models; Telecommunication;
                 Traffic; World Wide Web; Cyberspace; Probabilities;
                 Computers; Web; General; Networking; Intranets and
                 Extranets",
  tableofcontents = "Mathematical Background \\
                 Probability and Learning from a Bayesian Perspective
                 \\
                 Parameter Estimation from Data \\
                 Basic principles \\
                 A simple die example \\
                 Mixture Models and the Expectation Maximization
                 Algorithm \\
                 Graphical Models \\
                 Bayesian networks \\
                 Belief propagation \\
                 Learning directed graphical models from data \\
                 Classification \\
                 Clustering \\
                 Power-Law Distributions \\
                 Scale-free properties (80/20 rule) \\
                 Applications to Languages: Zipf's and Heaps' Laws \\
                 Origin of power-law distributions and Fermi's model \\
                 Basic WWW Technologies \\
                 Web Documents \\
                 SGML and HTML \\
                 General structure of an HTML document \\
                 Links \\
                 Resource Identifiers: URI, URL, and URN \\
                 Protocols \\
                 Reference models and TCP/IP \\
                 The domain name system \\
                 The Hypertext Transfer Protocol \\
                 Programming examples \\
                 Log Files \\
                 Search Engines \\
                 Coverage \\
                 Basic crawling \\
                 Web Graphs \\
                 Internet and Web Graphs \\
                 Power-law size \\
                 Power-law connectivity \\
                 Small-world networks \\
                 Power law of PageRank \\
                 The bow-tie structure \\
                 Generative Models for the Web Graph and Other Networks
                 \\
                 Web page growth \\
                 Lattice perturbation models: between order and disorder
                 \\
                 Preferential attachment models, or the rich get richer
                 \\
                 Copy models \\
                 PageRank models \\
                 Applications \\
                 Distributed search algorithms \\
                 Subgraph patterns and communities \\
                 Robustness and vulnerability \\
                 Notes and Additional Technical References \\
                 Text Analysis \\
                 Indexing \\
                 Compression techniques \\
                 Lexical Processing \\
                 Tokenization",
}

@Article{Banks:1974:AMN,
  author =       "William P. Banks and David K. Hill",
  title =        "The apparent magnitude of number scaled by random
                 production",
  journal =      j-J-EXP-PSYCH-GEN,
  volume =       "102",
  number =       "2",
  pages =        "353--376",
  month =        feb,
  year =         "1974",
  CODEN =        "JPGEDD",
  DOI =          "http://psycnet.apa.org/doi/10.1037/h0035850",
  ISSN =         "0096-3445 (print), 1939-2222 (electronic)",
  ISSN-L =       "0096-3445",
  bibdate =      "Fri Feb 15 06:32:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://psycnet.apa.org/journals/xge/102/2/353/;
                 http://psycnet.apa.org/psycinfo/1974-24305-001",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Experimental Psychology: General",
}

@Article{Banks:2013:BLM,
  author =       "David G. Banks",
  title =        "{Benford's Law} Made Easy: Common Software Eases use
                 of Fraud Search Theorem",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2013",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:11:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294968485",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Article{Barabasi:1999:ESR,
  author =       "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka
                 Albert",
  title =        "Emergence of scaling in random networks",
  journal =      j-SCIENCE,
  volume =       "286",
  number =       "5439",
  pages =        "509--512",
  day =          "15",
  month =        oct,
  year =         "1999",
  CODEN =        "SCIEAS",
  DOI =          "http://dx.doi.org/10.1126/science.286.5439.509",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Tue Nov 15 09:57:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/286/5439/509",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "power-law distribution; Zipf's Law",
}

@Article{Barlow:1985:RED,
  author =       "J. L. Barlow and E. H. Bareiss",
  title =        "On Roundoff Error Distributions in Floating Point and
                 Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "325--347",
  month =        dec,
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "87c:65045",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Pennsylvania State Univ, Computer Science Dep,
                 University Park, PA, USA",
  affiliationaddress = "USA",
  classification = "723",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer metatheory; floating
                 point arithmetic; logarithmic arithmetic; roundoff
                 error distributions",
}

@Misc{Barnes:2011:LCS,
  author =       "K. Barnes",
  title =        "Letter to {China Shen Zhou Mining and Resources (AMEX:
                 SHZ)} current shareholders and potential investors from
                 {Absaroka Capital}",
  howpublished = "Absaroka Capital Management, LLP, Wyoming, USA.",
  year =         "2011",
  bibdate =      "Fri Mar 22 08:42:58 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Baskerville:2006:SEM,
  author =       "Kim Baskerville and Maya Paczuski",
  title =        "Subgraph ensembles and motif discovery using an
                 alternative heuristic for graph isomorphism",
  journal =      j-PHYS-REV-E,
  volume =       "74",
  number =       "??",
  pages =        "051903",
  day =          "3",
  month =        nov,
  year =         "2006",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.74.051903",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.74.051903",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Baskerville:2007:GAS,
  author =       "Kim Baskerville and Peter Grassberger and Maya
                 Paczuski",
  title =        "Graph animals, subgraph sampling, and motif search in
                 large networks",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  number =       "??",
  pages =        "036107",
  day =          "11",
  month =        sep,
  year =         "2007",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.76.036107",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.76.036107",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Battersby:2009:SAH,
  author =       "Stephen Battersby",
  title =        "Statistical analyses hint at fraud in {Iranian}
                 election",
  journal =      j-NEW-SCIENTIST,
  volume =       "202",
  number =       "2714",
  pages =        "10--??",
  day =          "24",
  month =        jun,
  year =         "2009",
  CODEN =        "NWSCAL",
  DOI =          "http://dx.doi.org/10.1016/S0262-4079(09)61682-1",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262407909616821",
  acknowledgement = ack-nhfb,
  fjournal =     "The New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law",
  xxISSN =       "0262-4079, 0028-6664",
}

@Article{Batty:2008:PSS,
  author =       "Michael Batty",
  title =        "Perspective: The Size, Scale, and Shape of Cities",
  journal =      j-SCIENCE,
  volume =       "318",
  number =       "5864",
  pages =        "769--771",
  day =          "8",
  month =        feb,
  year =         "2008",
  CODEN =        "SCIEAS",
  DOI =          "http://dx.doi.org/10.1126/science.1151419",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Wed Feb 27 06:02:28 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/319/5864/769.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "200 tallest buildings in world; US cities of one
                 million (or more) population; Zipf's law",
}

@TechReport{Bauer:2009:DDF,
  author =       "J. Bauer and J. Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford's
                 Law} on Regression Tables",
  type =         "Report",
  number =       "??",
  institution =  "Institute of Sociology, LMU Munich",
  address =      "Munich, Germany",
  month =        "????",
  year =         "2009",
  bibdate =      "Fri Nov 18 11:46:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Bauer:2010:DDF,
  author =       "J. Bauer and J. Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford's
                 Law} on Regression Tables",
  type =         "Report",
  institution =  "Institute of Sociology,
                 Ludwig-Maximilians-Universit{\"a}t",
  address =      "M{\"u}nchen, Germany",
  pages =        "????",
  year =         "2010",
  bibdate =      "Tue Nov 22 21:15:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bauer:2011:DDF,
  author =       "Johannes Bauer and Jochen Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford?s
                 Law} on Regression Tables",
  journal =      "Journal of Economics and Statistics (Jahrb{\"u}cher
                 f{\"u}r National{\"o}konomie und Statistik)",
  volume =       "231",
  number =       "5--6",
  pages =        "733--748",
  month =        nov,
  year =         "2011",
  DOI =          "????",
  bibdate =      "Mon Feb 18 18:18:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ideas.repec.org/a/jns/jbstat/v231y2011i5-6p733-748.html",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/",
}

@Article{Bawden:2011:BMS,
  author =       "David Bawden",
  title =        "{Beno{\^\i}t Mandelbrot} and the self-similarity of
                 information",
  journal =      j-J-DOC,
  volume =       "67",
  number =       "2",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "JDOCAS",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:40:34 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Beber:2010:WNS,
  author =       "Bernd Beber and Alexandria Scacco",
  title =        "What the Numbers Say: a Digit-Based Test for Election
                 Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "20",
  number =       "2",
  pages =        "211--234",
  month =        "Spring",
  year =         "2010",
  DOI =          "http://dx.doi.org/10.1093/pan/mps003",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Mon Feb 18 17:29:42 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pan.oxfordjournals.org/content/20/2/211.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  keywords =     "Benford's Law",
}

@Article{Becker:2011:BLC,
  author =       "T. Becker and A. Greaves-Tunnell and S. J. Miller and
                 R. Ronan and F. W. Strauch",
  title =        "{Benford's Law} and Continuous Dependent Random
                 Variables",
  journal =      "ArXiv e-prints",
  month =        nov,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 17:50:20 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B;
                 http://arxiv.org/abs/1111.0568",
  abstract =     "Many systems exhibit a digit bias. For example, the
                 first digit base 10 of the Fibonacci numbers, or of $
                 2^n $, equals 1 not 10\% or 11\% of the time, as one
                 would expect if all digits were equally likely, but
                 about 30\% of the time. This phenomenon, known as
                 Benford's Law, has many applications, ranging from
                 detecting tax fraud for the IRS to analyzing round-off
                 errors in computer science.\par

                 The central question is determining which data sets
                 follow Benford's law. Inspired by natural processes
                 such as particle decay, our work examines models for
                 the decomposition of conserved quantities. We prove
                 that in many instances the distribution of lengths of
                 the resulting pieces converges to Benford behavior as
                 the number of divisions grow. The main difficulty is
                 that the resulting random variables are dependent,
                 which we handle by a careful analysis of the
                 dependencies and tools from Fourier analysis to obtain
                 quantified convergence rates.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1111.0568",
  keywords =     "Mathematics - Probability, 11K06, 60A10 (primary),
                 60E10 (secondary)",
  primaryclass = "math.PR",
}

@Article{Beirlant:1996:TIE,
  author =       "Jan Beirlant and Petra Vynckier and Jozef L. Teugels",
  title =        "Tail Index Estimation, {Pareto} Quantile Plots, and
                 Regression Diagnostics",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "91",
  number =       "436",
  pages =        "1659--??",
  month =        "????",
  year =         "1996",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Mon May 5 08:26:17 MDT 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Belevitch:1988:PQD,
  author =       "Vitold Belevitch",
  title =        "{{\`A}} propos de la queue de la distribution de
                 {Zipf}. ({French}) [{On} the tail of the {Zipf}
                 distribution]",
  journal =      "Ann. Soc. Sci. Bruxelles S{\'e}r. I",
  volume =       "102",
  number =       "3",
  pages =        "73--85 (1989)",
  year =         "1988",
  CODEN =        "ASSBAH",
  ISSN =         "0037-959X",
  ISSN-L =       "0037-959X",
  MRclass =      "92A90",
  MRnumber =     "1016850 (90g:92114)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales de la Societ{\'e} Scientifique de Bruxelles.
                 S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques
                 et Physiques",
  language =     "French",
}

@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X",
  ISSN-L =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See comments about Benford's biased rounding practices
                 \cite{Diaconis:1979:RP}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
  ZMnumber =     "JFM 64.0555.03; Zbl 0018.26502",
  abstract =     "It has been observed that the first pages of a table
                 of common logarithms show more wear than do the last
                 pages, indicating that more used numbers begin with the
                 digit 1 than with the digit 9. A compilation of some
                 20,000 first digits taken from widely divergent sources
                 shows that there is a logarithmic distribution of first
                 digits when the numbers are composed of four or more
                 digits. An analysis of the numbers from different
                 sources shows that the numbers taken from unrelated
                 subjects, such as a group of newspaper items, show a
                 much better agreement with a logarithmic distribution
                 than do numbers from mathematical tabulations or other
                 formal data. There is here the peculiar fact that
                 numbers that individually are without relationship are,
                 when considered in large groups, in good agreement with
                 a distribution law---hence the name ``Anomalous
                 Numbers.''\par

                 A further analysis of the data shows a strong tendency
                 for bodies of numerical data to fall into geometric
                 series. If the series is made up of numbers containing
                 three or more digits the first digits form a
                 logarithmic series. If the numbers contain only single
                 digits the geometric relation still holds but the
                 simple logarithmic relation no longer applies.\par

                 An equation is given showing the frequencies of first
                 digits in the different orders of numbers 1 to 10, 10
                 to 100, etc.\par

                 The equation also gives the frequency of digits in the
                 second, third + place of a multi-digit number, and it
                 is shown that the same law applies to
                 reciprocals.\par

                 There are many instances showing that the geometric
                 series, or the logarithmic law, has long been
                 recognized as a common phenomenon in factual literature
                 and in the ordinary affairs of life. The wire gauge and
                 drill gauge of the mechanic, the magnitude scale of the
                 astronomer and the sensory response curves of the
                 psychologist are all particular examples of a
                 relationship that seems to extend to all human affairs.
                 The Law of Anomalous Numbers is thus a general
                 probability law of widespread application.",
  acknowledgement = ack-nhfb,
  author-dates = "1883--December 4, 1948",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From \cite{Logan:1978:FDP}: ``Benford's paper was
                 published in 1938 in a journal of rather limited
                 circulation and not usually read by mathematicians. It
                 so happened that it was immediately followed in the
                 same issue by a physics paper which became of some
                 importance for secret nuclear work during World War II
                 [H. A. Bethe, M. E. Rose, and L. P. Smith, `The
                 Multiple Scattering of Electrons', Proc. Amer. Phil.
                 Soc. 78(4), 573--585 (1938)]. That is why Benford's
                 paper caught the attention of physicists in the early
                 1940's and was much discussed. This led to the notes in
                 Nature by Goudsmit and Furry [3] and Furry and Hurwitz
                 [4] containing an effort to explain Benford's law. We
                 considered it at that time merely a welcome diversion
                 and did not expect that over thirty papers would be
                 devoted to this subject in subsequent years.'' The 2006
                 bibliography \cite{Hurlimann:2006:BLB} cites 325
                 publications about Benford's Law.",
  xxURL =        "http://en.wikipedia.org/wiki/Frank_Benford",
}

@Article{Benford:1943:PAG,
  author =       "Frank Benford",
  title =        "The Probable Accuracy of the General Physical
                 Constants",
  journal =      j-PHYS-REV,
  volume =       "63",
  number =       "5--6",
  pages =        "212--212",
  month =        mar,
  year =         "1943",
  CODEN =        "PHRVAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRev.63.212",
  ISSN =         "0031-899X (print), 1536-6065 (electronic)",
  ISSN-L =       "0031-899X",
  bibdate =      "Mon Nov 21 21:52:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRev.63.212",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review",
  journal-URL =  "http://prola.aps.org/browse/PR",
}

@Article{Benguigui:2007:DMC,
  author =       "Lucien Benguigui and Efrat Blumenfeld-Lieberthal",
  title =        "A dynamic model for city size distribution beyond
                 {Zipf}'s law",
  journal =      j-PHYSICA-A,
  volume =       "384",
  number =       "2",
  pages =        "613--627",
  day =          "15",
  month =        oct,
  year =         "2007",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2007.05.059",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437107006061",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@InProceedings{Bennett:1975:SDI,
  author =       "John M. Bennett",
  booktitle =    "Int. Comput. Symp. 1975, Proc., Antibes, (1975)",
  title =        "Storage design for information retrieval: {Scarrott}'s
                 conjecture and {Zipf}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "233--237",
  year =         "1975",
  bibdate =      "Sat Nov 12 10:49:15 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0322.68068",
  acknowledgement = ack-nhfb,
  classmath =    "68P20 (Information storage and retrieval) 68N01
                 (General)",
}

@Article{Bennett:1984:ZLS,
  author =       "J. M. Bennett",
  title =        "{Zipf's Law}, Structured Programming and Creativity",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "16",
  number =       "4",
  pages =        "122--129",
  year =         "1984",
  CODEN =        "ACMJB2",
  ISSN =         "0004-8917",
  ISSN-L =       "0004-8917",
  bibdate =      "Fri Mar 9 17:59:26 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "As software projects increase in size, the effort
                 required to implement them increases at a greater rate.
                 The use of higher level languages and adherence to
                 various rules of ``good programming practice'' appear
                 to help only marginally in reducing the impact of this
                 non-linear effect, and progress can only be made by
                 calling on techniques for managing complexity which
                 have emerged in other fields. Hierarchical structures
                 are discussed with particular reference to software as
                 is the effect which appears to be common to a wide
                 range of human activities, and which is known as Zipf's
                 law. The effects of variation in individual programming
                 skills, the roles of creativity, invention and
                 innovation and lessons to be learned from case studies
                 of past failure are also examined.",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Computer Journal",
  keywords =     "creativity; innovation; invention; large software
                 projects; project failures; structured programming;
                 Zipf's law",
}

@TechReport{Berger:2003:BLP,
  author =       "Arno Berger",
  title =        "{Benford}'s law in power-like nonautonomous dynamical
                 systems",
  type =         "Preprint",
  institution =  "Vienna University of Technology",
  address =      "Vienna, Austria",
  year =         "2003",
  bibdate =      "Sat Feb 16 17:18:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Berger:2004:DDU,
  author =       "A. Berger",
  title =        "Dynamics and digits: on the ubiquity of {Benford's
                 Law}",
  type =         "Preprint",
  institution =  "Institute of Mechanics, Vienna University of
                 Technology",
  address =      "Vienna, Austria",
  pages =        "3",
  day =          "19",
  month =        nov,
  year =         "2004",
  bibdate =      "Sat Feb 16 17:20:58 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2005:BLP,
  author =       "Arno Berger",
  title =        "{Benford}'s law in power-like dynamical systems",
  journal =      j-STOCH-DYNAM,
  volume =       "5",
  number =       "4",
  pages =        "587--607",
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1142/S0219493705001602",
  ISSN =         "0219-4937",
  ISSN-L =       "0219-4937",
  MRclass =      "37B55 (11K06 37A50 37E05)",
  MRnumber =     "2185507 (2008i:37029)",
  MRreviewer =   "Peter Raith",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Stoch. Dyn.",
  fjournal =     "Stochastics and Dynamics",
}

@InCollection{Berger:2005:DDU,
  author =       "A. Berger",
  booktitle =    "{EQUADIFF} 2003",
  title =        "Dynamics and digits: on the ubiquity of {Benford}'s
                 law",
  publisher =    "World Sci. Publ., Hackensack, NJ",
  pages =        "693--695",
  year =         "2005",
  DOI =          "http://dx.doi.org/10.1142/9789812702067_0115",
  MRclass =      "37A45 (11K55)",
  MRnumber =     "2185113",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2005:MDD,
  author =       "Arno Berger",
  title =        "Multi-dimensional dynamical systems and {Benford}'s
                 law",
  journal =      j-DISCRETE-CONTIN-DYN-SYST,
  volume =       "13",
  number =       "1",
  pages =        "219--237",
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.3934/dcds.2005.13.219",
  ISSN =         "1078-0947 (print), 1553-5231 (electronic)",
  ISSN-L =       "1078-0947",
  MRclass =      "37A45 (11K36 28D05 37A50 60F05)",
  MRnumber =     "2128801 (2005m:37016)",
  MRreviewer =   "Reinhard Winkler",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete and Continuous Dynamical Systems. Series A",
}

@Article{Berger:2005:ODD,
  author =       "Arno Berger and Leonid A. Bunimovich and Theodore P.
                 Hill",
  title =        "One-dimensional dynamical systems and {Benford}'s
                 law",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "357",
  number =       "1",
  pages =        "197--219",
  year =         "2005",
  CODEN =        "TAMTAM",
  DOI =          "http://dx.doi.org/10.1090/S0002-9947-04-03455-5",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "37A45 (11K06 37A50 37E05 60F05 82B05)",
  MRnumber =     "2098092 (2005m:37017)",
  MRreviewer =   "Peter Raith",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
}

@Article{Berger:2007:DMN,
  author =       "A. Berger and S. Siegmund",
  title =        "On the distribution of mantissae in nonautonomous
                 difference equations",
  journal =      j-J-DIFFERENCE-EQU-APPL,
  volume =       "13",
  number =       "8--9",
  pages =        "829--845",
  month =        "????",
  year =         "2007",
  CODEN =        "JDEAEA",
  DOI =          "http://dx.doi.org/10.1080/10236190701388039",
  ISSN =         "1023-6198 (print), 1563-5120 (electronic)",
  ISSN-L =       "1023-6198",
  MRclass =      "37A45 (37B55 39A11)",
  MRnumber =     "2343033 (2008j:37010)",
  MRreviewer =   "Reinhard Winkler",
  bibdate =      "Tue Feb 19 09:37:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Second Memorial Issue in Honour of Bernd Aulbach.",
  URL =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Difference Equations and Applications",
  journal-URL =  "http://www.informaworld.com/1023-6198",
}

@Article{Berger:2007:NMO,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "{Newton}'s Method Obeys {Benford}'s Law",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "114",
  number =       "7",
  pages =        "588--601",
  month =        aug # "\slash " # sep,
  year =         "2007",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65G50 (37N30)",
  MRnumber =     "2341322 (2008h:65016)",
  MRreviewer =   "Uwe Sch{\"a}fer",
  bibdate =      "Mon Jan 30 12:00:29 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i27642270;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/27642274",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@TechReport{Berger:2009:BOB,
  author =       "A. Berger and T. P. Hill",
  title =        "{Benford} Online Bibliography",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  year =         "2009",
  bibdate =      "Sat Nov 12 16:48:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.benfordonline.net",
  acknowledgement = ack-nhfb,
  remark =       "According to \cite{Berger:2011:BLS}, the authors'
                 online bibliography contains more than 600
                 references.",
}

@TechReport{Berger:2010:FFFa,
  author =       "A. Berger and T. P. Hill",
  title =        "Fundamental Flaws in {Feller}'s Classical Derivation
                 of {Benford's Law}",
  type =         "Preprint",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "8",
  year =         "2010",
  bibdate =      "Mon Feb 18 17:31:57 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf",
  abstract =     "Feller's classic text \booktitle{An Introduction to
                 Probability Theory and its Applications}
                 \cite{Feller:1968:IPT} contains a derivation of the
                 well known significant-digit law called Benford's law.
                 More specifically, Feller gives a sufficient condition
                 (`large spread') for a random variable $X$ to be
                 approximately Benford distributed, that is, for $
                 \log_{10} X $ to be approximately uniformly distributed
                 modulo one. This note shows that the large-spread
                 derivation, which continues to be widely cited and
                 used, contains serious basic errors. Concrete examples
                 and a new inequality clearly demonstrate that large
                 spread (or large spread on a logarithmic scale) does
                 not imply that a random variable is approximately
                 Benford distributed, for any reasonable definition of
                 `spread' or measure of dispersion.",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2010:FFFb,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "Fundamental Flaws in {Feller}'s Classical Derivation
                 of {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 18:23:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B;
                 http://arxiv.org/abs/1005.2598",
  abstract =     "Feller's classic text \booktitle{An Introduction to
                 Probability Theory and its Applications}
                 \cite{Feller:1968:IPT} contains a derivation of the
                 well known significant-digit law called Benford's law.
                 More specifically, Feller gives a sufficient condition
                 (`large spread') for a random variable $X$ to be
                 approximately Benford distributed, that is, for $
                 \log_{10}X $ to be approximately uniformly distributed
                 modulo one. This note shows that the large-spread
                 derivation, which continues to be widely cited and
                 used, contains serious basic errors. Concrete examples
                 and a new inequality clearly demonstrate that large
                 spread (or large spread on a logarithmic scale) does
                 not imply that a random variable is approximately
                 Benford distributed, for any reasonable definition of
                 `spread' or measure of dispersion",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1005.2598",
  keywords =     "Mathematics - Probability, Mathematics - Statistics,
                 62Axx",
  primaryclass = "math.PR",
}

@TechReport{Berger:2010:LSD,
  author =       "A. Berger",
  title =        "Large Spread Does Not Imply {Benford's Law}",
  type =         "Preprint",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  year =         "2010",
  bibdate =      "Sat Nov 12 16:46:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.math.ualberta.ca/~aberger/Publications.html",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2011:BLS,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "{Benford}'s law strikes back: no simple explanation in
                 sight for mathematical gem",
  journal =      j-MATH-INTEL,
  volume =       "33",
  number =       "1",
  pages =        "85--91",
  month =        mar,
  year =         "2011",
  CODEN =        "MAINDC",
  DOI =          "http://dx.doi.org/10.1007/s00283-010-9182-3",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "62A99 (60E05)",
  MRnumber =     "2774458",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See letter \cite{Hill:2011:LEB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
}

@Article{Berger:2011:BTB,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "A basic theory of {Benford's Law}",
  journal =      j-PROBAB-SURV,
  volume =       "8",
  pages =        "1--126",
  year =         "2011",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1214/11-PS175",
  ISSN =         "1549-5787",
  ISSN-L =       "1549-5787",
  bibdate =      "Tue Nov 15 11:07:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.ps/1311860830",
  abstract =     "Drawing from a large, diverse body of work, this
                 survey presents a comprehensive and unified
                 introduction to the mathematics underlying the
                 prevalent logarithmic distribution of significant
                 digits and significands, often referred to as {\em
                 Benford's Law\/} (BL) or, in a special case, as the
                 {\em First Digit Law}. The invariance properties that
                 characterize BL are developed in detail. Special
                 attention is given to the emergence of BL in a wide
                 variety of deterministic and random processes. Though
                 mainly expository in nature, the article also provides
                 strengthened versions of, and simplified proofs for,
                 many key results in the literature. Numerous intriguing
                 problems for future research arise naturally.",
  acknowledgement = ack-nhfb,
  fjournal =     "Probabability Surveys",
  keywords =     "base-invariance; Benford's Law; difference equation;
                 mixture of distributions; random probability measure;
                 scale-invariance; shadowing; significant digits;
                 sum-invariance; uniform distribution mod 1",
}

@Article{Berger:2011:FSM,
  author =       "Arno Berger and Theodore P. Hill and Bahar Kaynar and
                 Ad Ridder",
  title =        "Finite-state {Markov} Chains Obey {Benford's Law}",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "32",
  number =       "3",
  pages =        "665--684",
  month =        "????",
  year =         "2011",
  CODEN =        "SJMAEL",
  DOI =          "http://dx.doi.org/10.1137/100789890",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Wed Aug 24 11:18:18 MDT 2011",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "July 21, 2011",
}

@Article{Berger:2011:SDP,
  author =       "Arno Berger",
  title =        "Some dynamical properties of {Benford} sequences",
  journal =      j-J-DIFFERENCE-EQU-APPL,
  volume =       "17",
  number =       "2",
  pages =        "137--159",
  year =         "2011",
  CODEN =        "JDEAEA",
  DOI =          "http://dx.doi.org/10.1080/10236198.2010.549012",
  ISSN =         "1023-6198 (print), 1563-5120 (electronic)",
  ISSN-L =       "1023-6198",
  MRclass =      "37A45 (11K06 37Bxx)",
  MRnumber =     "2783341",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Difference Equ. Appl.",
  fjournal =     "Journal of Difference Equations and Applications",
  journal-URL =  "http://www.informaworld.com/1023-6198",
}

@InProceedings{Berinde:2009:SOH,
  author =       "Radu Berinde and Graham Cormode and Piotr Indyk and
                 Martin J. Strauss",
  title =        "Space-optimal heavy hitters with strong error bounds",
  crossref =     "Paredaens:2009:PTE",
  pages =        "157--166",
  year =         "2009",
  DOI =          "http://doi.acm.org/10.1145/1559795.1559819",
  bibdate =      "Thu Jul 2 14:05:34 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "The problem of finding heavy hitters and approximating
                 the frequencies of items is at the heart of many
                 problems in data stream analysis. It has been observed
                 that several proposed solutions to this problem can
                 outperform their worst-case guarantees on real data.
                 This leads to the question of whether some stronger
                 bounds can be guaranteed. We answer this in the
                 positive by showing that a class of `counter-based
                 algorithms' (including the popular and very
                 space-efficient FREQUENT and SPACESAVING algorithms)
                 provide much stronger approximation guarantees than
                 previously known. Specifically, we show that errors in
                 the approximation of individual elements do not depend
                 on the frequencies of the most frequent elements, but
                 only on the frequency of the remaining `tail.' This
                 shows that counter-based methods are the most
                 space-efficient (in fact, space-optimal) algorithms
                 having this strong error bound.\par

                 This tail guarantee allows these algorithms to solve
                 the `sparse recovery' problem. Here, the goal is to
                 recover a faithful representation of the vector of
                 frequencies, $f$. We prove that using space $ O(k) $,
                 the algorithms construct an approximation $ f* $ to the
                 frequency vector $f$ so that the L1 error $ ||f -
                 f*||_1 $ is close to the best possible error $ \hbox
                 {min}_{f_2} || f_2 - f ||_1 $, where $f$ 2 ranges over
                 all vectors with at most $k$ non-zero entries. This
                 improves the previously best known space bound of about
                 $ O(k \log n) $ for streams without element deletions
                 (where $n$ is the size of the domain from which stream
                 elements are drawn). Other consequences of the tail
                 guarantees are results for skewed (Zipfian) data, and
                 guarantees for accuracy of merging multiple summarized
                 streams.",
  acknowledgement = ack-nhfb,
  keywords =     "frequency estimation; heavy hitters; streaming
                 algorithms",
}

@Article{Bernhardsson:2011:PPM,
  author =       "Sebastian Bernhardsson and Seung Ki Baek and Petter
                 Minnhagen",
  title =        "A paradoxical property of the monkey book",
  journal =      j-J-STAT-MECH-THEORY-EXP,
  volume =       "2011",
  number =       "??",
  pages =        "P07013",
  month =        jul,
  year =         "2011",
  CODEN =        "JSMTC6",
  DOI =          "http://dx.doi.org/10.1088/1742-5468/2011/07/P07013",
  ISSN =         "1742-5468",
  ISSN-L =       "1742-5468",
  bibdate =      "Mon Nov 21 21:57:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1103.2681;
                 http://iopscience.iop.org/1742-5468/2011/07/P07013/",
  abstract =     "A `monkey book' is a book consisting of a random
                 sequence of letters and blanks, where a group of
                 letters surrounded by two blanks is defined as a word.
                 We compare the statistics of the word distribution for
                 a monkey book to real books. It is shown that the word
                 distribution statistics for the monkey book is
                 different and quite distinct from a typical real book.
                 In particular, the monkey book obeys Heaps' power law
                 to an extraordinarily good approximation, in contrast
                 to the word distributions for real books, which deviate
                 from Heaps' law in a characteristic way. This
                 discrepancy is traced to the different properties of a
                 `spiked' distribution and its smooth envelope. The
                 somewhat counter-intuitive conclusion is that a `monkey
                 book' obeys Heaps' power law precisely because its
                 word-frequency distribution is not a smooth power law,
                 contrary to the expectation based on simple
                 mathematical arguments that if one is a power law, so
                 is the other.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Mechanics: Theory and
                 Experiment",
  keywords =     "Heaps' Law",
}

@Article{Bernik:2007:BLA,
  author =       "V. I. Bernik and N. I. Kalosha",
  title =        "{Benford}'s law and the approximation of logarithms of
                 natural numbers by rational numbers",
  journal =      "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser.
                 F{\=\i}z.-Mat. Navuk",
  volume =       "??",
  number =       "3",
  pages =        "68--73, 127",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0002-3574",
  ISSN-L =       "0002-3574",
  MRclass =      "11J83 (11A63 11K36)",
  MRnumber =     "2398318 (2008j:11084)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Vests{\=\i} Natsyyanal\cprime na{\u\i}
                 Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya
                 F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya
                 Natsional\cprime no{\u\i} Akademii Nauk Belarusi.
                 Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the
                 National Academy of Sciences of Belarus. Physics and
                 Mathematics Series",
}

@Article{Berton:1995:HGT,
  author =       "L. Berton",
  title =        "He's Got their Number. {Scholar} Uses Math to Foil
                 Financial Fraud",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        jul,
  year =         "1995",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  ISSN-L =       "0099-9660",
  bibdate =      "Sat Dec 10 11:17:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wall Street Journal",
}

@Article{Bethe:1938:MSE,
  author =       "H. A. Bethe and M. E. Rose and L. P. Smith",
  title =        "The Multiple Scattering of Electrons",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "573--585",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X",
  ISSN-L =       "0003-049X",
  bibdate =      "Wed Nov 23 14:27:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper, which immediately follows Benford's
                 \cite{Benford:1938:LAN} in this journal issue, is
                 reported in \cite[p. 197]{Logan:1978:FDP} to have been
                 of considerable interest to scientists involved in
                 secret nuclear physics work in World War II. That is
                 how Benford's paper ``in a journal of rather limited
                 circulation and not usually read by mathematicians''
                 came to be noticed by physicists.",
  URL =          "http://www.jstor.org/stable/984803",
  acknowledgement = ack-nhfb,
  author-dates = "Hans Albrecht Bethe (1906--2005)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  remark =       "Biography supplement in \cite{Lee:2007:HAB} has this
                 as Proc. Am. Philos. Soc., 89, 373--383 (1938), but
                 that seems to be wrong: check??",
}

@InProceedings{Bhattacharya:2002:KBT,
  author =       "S. Bhattacharya",
  editor =       "????",
  booktitle =    "9th World Congress of Accounting Historians, Deakin
                 University, Melbourne, Australia July 30--August 3,
                 2002",
  title =        "From {Kautilya} to {Benford} --- Trends in Forensic
                 and Investigative Accounting",
  publisher =    "Accounting Association of Australia and New Zealand",
  address =      "????",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:22:29 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://ach.sagepub.com/",
  remark =       "I cannot find the published proceedings in online
                 catalogs or bookstores, or in the Deakin University
                 library catalogs. Where only selected papers published
                 from the conference in the journal Accounting
                 History??",
  review-doi =   "http://dx.doi.org/10.1177/103237320200700207",
  review-url =   "http://dro.deakin.edu.au/view/DU:30012663;
                 http://www.highbeam.com/doc/1G1-97484707.html",
}

@Article{Bhattacharya:2005:CPA,
  author =       "Sukanto Bhattacharya and Kuldeep Kumar and Florentin
                 Smarandache",
  title =        "Conditional probability of actually detecting a
                 financial fraud --- a neutrosophic extension to
                 {Benford}'s law",
  journal =      "International Journal of Applied Mathematics",
  volume =       "17",
  number =       "1",
  pages =        "7--14",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "1311-1728",
  MRclass =      "62G10 (91B28)",
  MRnumber =     "2170667",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math/0504520",
  abstract =     "This study actually draws from and builds on an
                 earlier paper (Kumar and Bhattacharya, 2002). Here we
                 have basically added a neutrosophic dimension to the
                 problem of determining the conditional probability that
                 a financial fraud has been actually committed, given
                 that no Type I error occurred while rejecting the null
                 hypothesis H0: The observed first-digit frequencies
                 approximate a Benford distribution; and accepting the
                 alternative hypothesis H1: The observed first-digit
                 frequencies do not approximate a Benford distribution.
                 We have also suggested a conceptual model to implement
                 such a neutrosophic fraud detection system.",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Appl. Math.",
  fjournal =     "International Journal of Applied Mathematics",
}

@Article{Bhattacharya:2008:FAB,
  author =       "S. Bhattacharya and K. Kumar",
  title =        "Forensic Accounting and {Benford's Law} [In the
                 Spotlight]",
  journal =      j-IEEE-SIGNAL-PROCESS-MAG,
  volume =       "25",
  number =       "2",
  pages =        "152--150",
  month =        mar,
  year =         "2008",
  CODEN =        "ISPRE6",
  DOI =          "http://dx.doi.org/10.1109/MSP.2007.914724",
  ISSN =         "1053-5888 (print), 1558-0792 (electronic)",
  ISSN-L =       "1053-5888",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008ISPM...25..152B",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE signal processing magazine",
}

@Article{Bhattacharya:2011:ABA,
  author =       "Sukanto Bhattacharya and Dongming Xu and Kuldeep
                 Kumar",
  title =        "An {ANN}-based auditor decision support system using
                 {Benford}'s law",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "3",
  pages =        "576--584",
  month =        feb,
  year =         "2011",
  CODEN =        "DSSYDK",
  DOI =          "http://dx.doi.org/10.1016/j.dss.2010.08.011",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923610001351",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law",
}

@Article{Bhattacharyya:2005:COP,
  author =       "P. Bhattacharyya and A. Chatterjee and B. K.
                 Chakrabarti",
  title =        "A common origin of the power law distributions in
                 models of market and earthquake",
  journal =      "ArXiv e-prints",
  year =         "2005",
  bibdate =      "Sat Feb 16 17:25:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/physics/0510038",
  acknowledgement = ack-nhfb,
}

@Article{Billera:1976:PSC,
  author =       "Louis J. Billera and Robert E. Bixby",
  title =        "{Pareto} Surfaces of Complexity $1$",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "1",
  pages =        "81--89",
  month =        jan,
  year =         "1976",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Dept. of Math., Cornell Univ., Ithaca, NY, USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "1-commodity representation; attainable sets;
                 complexity 1; game theory; graph theory; Pareto
                 surfaces; set theory",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Blackwell:1954:TGS,
  author =       "David Blackwell and Meyer A. Girshick",
  title =        "Theory of Games and Statistical Decisions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 355",
  year =         "1954",
  LCCN =         "QA269 .B5",
  bibdate =      "Mon Nov 14 10:04:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://catalog.hathitrust.org/Record/000577721",
  acknowledgement = ack-nhfb,
  author-dates = "David Blackwell (1919--2010)",
  keywords =     "Benford's Law",
  remark =       "Brief mention of Benford's Law on page 74, problem
                 2.7.2 (??).",
}

@Article{Blank:2000:PLC,
  author =       "Aharon Blank and Sorin Solomon",
  title =        "Power laws in cities population, financial markets and
                 {Internet} sites (scaling in systems with a variable
                 number of components)",
  journal =      j-PHYSICA-A,
  volume =       "287",
  number =       "1--2",
  pages =        "279--288",
  day =          "15",
  month =        nov,
  year =         "2000",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(00)00464-7",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 06:24:21 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437100004647",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Blasius:2009:ZLP,
  author =       "Bernd Blasius and Ralf T{\"o}njes",
  title =        "{Zipf's Law} in the Popularity Distribution of Chess
                 Openings",
  journal =      j-PHYS-REV-LET,
  volume =       "103",
  number =       "21",
  pages =        "218701",
  day =          "16",
  month =        nov,
  year =         "2009",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.103.218701",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "4",
}

@Article{Block:2010:GEB,
  author =       "Henry W. Block and Thomas H. Savits",
  title =        "A General Example for {Benford} Data",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "4",
  pages =        "335--339",
  month =        nov,
  year =         "2010",
  CODEN =        "ASTAAJ",
  DOI =          "http://dx.doi.org/10.1198/tast.2010.09169",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2758565",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Benford's Law deals, among other things, with the
                 proportion of numbers whose first significant digit is
                 a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first
                 significant digit $1$ ) in a variety of datasets. In
                 these datasets, which arise in various compendiums or
                 as mixtures of various sets of numbers, the proportion
                 of numbers with first significant digit one is $ 0.3010
                 $ which is much higher than the commonsense value of $
                 1 / 9 $. The reasons for this occurrence have been
                 elusive. Mathematical attempts to explain this
                 phenomenon have been relatively fruitless. Methods
                 involving probability have been somewhat more
                 successful. In this article we give some simple reasons
                 for this occurrence and also give an example of a
                 general mixture of distributions which exactly
                 satisfies this Law. Various other examples and
                 counterexamples are also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Blum:1970:SID,
  author =       "M. Blum",
  title =        "On the Sums of Independently Distributed {Pareto}
                 Variates",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "19",
  number =       "1",
  pages =        "191--198",
  month =        jul,
  year =         "1970",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
}

@Article{Bohachevsky:2006:DBL,
  author =       "Ihor O. Bohachevsky and Mark E. Johnson and Myron L.
                 Stein",
  title =        "A derivation of {Benford}'s law",
  journal =      j-AM-J-MATH-MANAGE-SCI,
  volume =       "26",
  number =       "3--4",
  pages =        "355--370",
  year =         "2006",
  CODEN =        "AMMSDX",
  ISSN =         "0196-6324",
  ISSN-L =       "0196-6324",
  MRclass =      "60E99 (11K36)",
  MRnumber =     "2312400 (2008h:60062)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematical and Management
                 Sciences",
}

@Book{Bologna:1995:FAF,
  author =       "Jack Bologna and Robert J. Lindquist",
  title =        "Fraud auditing and forensic accounting: new tools and
                 techniques",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xv + 249",
  year =         "1995",
  ISBN =         "0-471-10646-1 (hardcover)",
  ISBN-13 =      "978-0-471-10646-3 (hardcover)",
  LCCN =         "HV8079.W47 B65 1995",
  bibdate =      "Tue Nov 22 10:31:53 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/wiley042/95005510.html;
                 http://www.loc.gov/catdir/description/wiley033/95005510.html;
                 http://www.loc.gov/catdir/toc/onix04/95005510.html",
  acknowledgement = ack-nhfb,
  remark =       "This book does not discuss Benford's Law, but may be
                 helpful background for application of that law to the
                 detection of fraud.",
  subject =      "white collar crime investigation; United States;
                 forensic accounting; fraud investigation",
}

@Article{Bolton:2002:SFD,
  author =       "Richard J. Bolton and David J. Hand",
  title =        "Statistical Fraud Detection: A Review",
  journal =      j-STAT-SCI,
  volume =       "17",
  number =       "3",
  pages =        "235--255",
  month =        aug,
  year =         "2002",
  CODEN =        "STSCEP",
  ISSN =         "0883-4237",
  ISSN-L =       "0883-4237",
  bibdate =      "Fri May 30 12:48:50 MDT 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/statsci.bib",
  URL =          "http://projecteuclid.org/euclid.ss/1042727940",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science",
  journal-URL =  "http://projecteuclid.org/all/euclid.ss",
}

@Article{Bonache:2010:DFL,
  author =       "A. B. Bonache and K. Moris and J. Maurice",
  title =        "{D}{\'e}tection de fraudes et loi de {Benford}:
                 Quelques risques associ{\'e}s. ({French}) [{Fraud}
                 detection and {Benford}'s law: Some risks]",
  journal =      "Revue Fran{\c{c}}aise de Comptabilit{\'e}",
  volume =       "??",
  number =       "431",
  pages =        "24--27",
  month =        apr,
  year =         "2010",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "0484-8764",
  ISSN-L =       "0484-8764",
  bibdate =      "Mon Feb 18 17:33:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.experts-comptables.fr/csoec/Publications/RFC",
  language =     "French",
}

@Article{Boring:1920:LNL,
  author =       "Edwin G. Boring",
  title =        "The Logic of the Normal Law of Error in Mental
                 Measurement",
  journal =      j-AMER-J-PSYCHOLOGY,
  volume =       "31",
  number =       "1",
  pages =        "1--33",
  month =        jan,
  year =         "1920",
  CODEN =        "AJPCAA",
  ISSN =         "0002-9556 (print), 1939-8298 (electronic)",
  ISSN-L =       "0002-9556",
  bibdate =      "Thu Dec 01 21:35:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/1413989",
  acknowledgement = ack-nhfb,
  fjournal =     "The American journal of psychology",
  remark =       "A citation search in Google Scholar on 1-Dec-2011
                 found this article as the only one citing Newcomb's
                 work \cite{Newcomb:1881:NFU} before it was brought to
                 wider view by Raimi's frequently-cited paper
                 \cite{Raimi:1976:FDP}. Boring's article has only brief
                 mention of Newcomb's work, and then solely in
                 connection with the believed randomness of digits of
                 transcendental numbers.",
}

@Article{Boroda:1984:ZML,
  author =       "M. G. Boroda and A. A. Polikarpov",
  title =        "The {Zipf--Mandelbrot} law and units of different
                 levels of text organization",
  journal =      "Tartu Riikl. {\"U}l. Toimetised",
  volume =       "??",
  number =       "689",
  pages =        "35--60",
  year =         "1984",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "92A25",
  MRnumber =     "781731 (86c:92030)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
                 Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
                 et Commentationes Universitatis Tartuensis",
}

@Article{Bose:2011:QMD,
  author =       "Indranil Bose and Selwyn Piramuthu and Michael J.
                 Shaw",
  title =        "Quantitative methods for Detection of Financial
                 Fraud",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "3",
  pages =        "557--558",
  month =        feb,
  year =         "2011",
  CODEN =        "DSSYDK",
  DOI =          "http://dx.doi.org/10.1016/j.dss.2010.08.005",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923610001296",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law",
}

@Article{Boyle:1994:AFS,
  author =       "Jeff Boyle",
  title =        "An application of {Fourier} series to the most
                 significant digit problem",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "9",
  pages =        "879--886",
  month =        nov,
  year =         "1994",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "60F99",
  MRnumber =     "1 300 493",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Bradford:1934:SIS,
  author =       "Samuel C. Bradford",
  title =        "Sources of Information on Specific Subjects",
  journal =      "Engineering: An Illustrated Weekly Journal (London)",
  volume =       "137",
  number =       "??",
  pages =        "85--86",
  day =          "26",
  month =        jan,
  year =         "1934",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 25 11:47:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper (reprinted in \cite{Bradford:1985:SIS})
                 introduces an observation later known as Bradford's
                 Law: there are exponentially-diminishing returns of
                 extending a search for references in journals.",
  URL =          "http://en.wikipedia.org/wiki/Bradford%27s_law",
  acknowledgement = ack-nhfb,
}

@Article{Bradford:1985:SIS,
  author =       "Samuel C. Bradford",
  title =        "Sources of Information on Specific Subjects",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "10",
  number =       "4",
  pages =        "173--180",
  month =        oct,
  year =         "1985",
  CODEN =        "JISCDI",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Fri Nov 25 11:49:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprint of \cite{Bradford:1934:SIS}, the source of
                 Bradford's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
}

@Article{Bradley:2009:WBL,
  author =       "Jonathan R. Bradley and David L. Farnsworth",
  title =        "What Is {Benford's Law}?",
  journal =      "Teaching Statistics",
  volume =       "31",
  number =       "1",
  pages =        "2--6",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1111/j.1467-9639.2009.00347.x",
  ISSN =         "0141-982X (print), 1467-9639 (electronic)",
  ISSN-L =       "0141-982X",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Class activity; First significant digit; Goodness of
                 fit; Teaching",
  onlinedate =   "6 Jan 2009",
}

@Article{Brady:1978:MBL,
  author =       "W. G. Brady",
  title =        "More on {Benford}'s Law",
  journal =      j-FIB-QUART,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        feb,
  year =         "1978",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:24 MDT 2011",
  bibsource =    "http://www.fq.math.ca/16-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@InCollection{Brahler:2010:EMS,
  author =       "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena
                 Emke",
  booktitle =    "{Ilmenauer Schriften zur Betriebswirtschaftslehre}.
                 ({German}) [{Illmenauer} writings on economics]",
  title =        "{Der Einsatz mathematisch-statistischer Methoden in
                 der digitalen Betriebspr{\"u}fung}. ({German}) [{The}
                 use of mathematical and statistical methods in the
                 digital audit]",
  volume =       "4/2010",
  publisher =    "Verlag proWiWi e.V.",
  address =      "Ilmenau, Germany",
  pages =        "48",
  month =        apr,
  year =         "2010",
  ISBN =         "3-940882-23-2",
  ISBN-13 =      "978-3-940882-23-3",
  ISSN =         "1866-2145 (print), 2192-4643 (electronic)",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 17:35:58 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@InCollection{Brahler:2011:BGS,
  author =       "Gernot Br{\"a}hler and Markus Bensmann and Hans-Ralph
                 Jakobi",
  editor =       "????",
  booktitle =    "Ilmenauer Schriften zur Betriebswirtschaftslehre",
  title =        "{Das Benfordsche Gesetz und seine Anwendbarkeit bei
                 der digitalen Pr{\"u}fung von Fahrtenb{\"u}chern}.
                 ({German}) [{The} {Benford} law and its applicability
                 in the digital examination of logbooks]",
  volume =       "3/2011",
  publisher =    "Verlag proWiWi e.V.",
  address =      "Ilmenau, Germany",
  pages =        "??--??",
  month =        mar,
  year =         "2011",
  ISBN =         "3-940882-28-3",
  ISBN-13 =      "978-3-940882-28-8",
  ISSN =         "1866-2145 (print), 2192-4643 (electronic)",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 18:21:29 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.econstor.eu/dspace/bitstream/10419/55703/1/662518055.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Brakman:1999:RZT,
  author =       "Steven Brakman and Harry Garretsen and Charles {Van
                 Marrewijk} and Marianne {Van Den Berg}",
  title =        "The Return of {Zipf}: Towards a Further Understanding
                 of the Rank--Size Distribution",
  journal =      j-J-REG-SCI,
  volume =       "39",
  number =       "1",
  pages =        "183--213",
  year =         "1999",
  DOI =          "http://dx.doi.org/10.1111/1467-9787.00129",
  ISSN =         "0022-4146 (print), 1467-9787 (electronic)",
  ISSN-L =       "0022-4146",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Regional Science",
}

@Article{Brambilla:1976:DDA,
  author =       "Francisco Brambilla",
  title =        "La distribuzione delle aziende secondo le dimensioni.
                 {Verifica} empirica della legge logonormale e di quella
                 di {Zipf} e nuovi modelli interpretativi. ({Italian})
                 [{The} distribution of firms by size. {Empirical} test
                 of the log-normal law and {Zipf}'s law and new models
                 of interpretation]",
  journal =      "Giornale degli Economisti e Annali de Economia (Nuova
                 Serie)",
  volume =       "35",
  number =       "3--4",
  pages =        "131--153, 235",
  month =        mar # "\slash " # apr,
  year =         "1976",
  CODEN =        "????",
  ISSN =         "0017-0097",
  ISSN-L =       "0017-0097",
  MRclass =      "90A15",
  MRnumber =     "0452510 (56 \#10789)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/23242834",
  acknowledgement = ack-nhfb,
  ajournal =     "Giorn. Econom. Ann. Econom. (N.S.)",
  fjournal =     "Giornale degli Economisti e Annali de Economia",
  language =     "Italian",
}

@Article{Bravo-Marquez:2010:HLM,
  author =       "Felipe Bravo-Marquez and Gaston L'Huillier and
                 Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez",
  title =        "Hypergeometric Language Model and {Zipf}-Like Scoring
                 Function for {Web} Document Similarity Retrieval",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6393",
  pages =        "303--308",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-16321-0_32",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:49:42 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32",
  acknowledgement = ack-nhfb,
  book-DOI =     "http://dx.doi.org/10.1007/978-3-642-16321-0",
  book-URL =     "http://www.springerlink.com/content/978-3-642-16321-0",
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Breunig:2011:SEI,
  author =       "Christian Breunig and Achim Goerres",
  title =        "Searching for electoral irregularities in an
                 established democracy: Applying {Benford's Law} tests
                 to {Bundestag} elections in {Unified Germany}",
  journal =      j-ELECT-STUDIES,
  volume =       "30",
  number =       "3",
  pages =        "534--545",
  month =        sep,
  year =         "2011",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/j.electstud.2011.03.005",
  ISSN =         "0261-3794 (print), 1873-6890 (electronic)",
  ISSN-L =       "0261-3794",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0261379411000370",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Benford's Law",
}

@Article{Brookes:1977:TBL,
  author =       "Bertram C. Brookes",
  title =        "Theory of the {Bradford Law}",
  journal =      j-J-DOC,
  volume =       "33",
  number =       "3",
  pages =        "180--209",
  month =        "????",
  year =         "1977",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/eb026641",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:16:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Brookes:1978:FRD,
  author =       "Bertram C. Brookes and Jos{\'e} M. Griffiths",
  title =        "Frequency-rank distributions",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "1",
  pages =        "5--13",
  month =        jan,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/asi.4630290104",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 10:40:13 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1980:FISa,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part I}.
                 {Philosophical} aspects",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "3--4",
  pages =        "125--133",
  month =        jun,
  year =         "1980",
  CODEN =        "JISCDI",
  DOI =          "http://dx.doi.org/10.1177/016555158000200302",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/2/3-4/125.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1980:FISb,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part II}.
                 {Quantitative} aspects: classes of things and the
                 challenge of human individuality",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "5",
  pages =        "209--221",
  month =        oct,
  year =         "1980",
  CODEN =        "JISCDI",
  DOI =          "http://dx.doi.org/10.1177/016555158000200502",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 11:01:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/2/5/209.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1980:FISc,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part III}.
                 {Quantitative} aspects: Objective maps and subjective
                 landscapes",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "6",
  pages =        "269--275",
  month =        dec,
  year =         "1980",
  CODEN =        "JISCDI",
  DOI =          "http://dx.doi.org/10.1177/016555158000200602",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/2/6/269.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1981:FIS,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part IV}.
                 {Information} science: the changing paradigm",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "3",
  number =       "1",
  pages =        "3--12",
  month =        feb,
  year =         "1981",
  CODEN =        "JISCDI",
  DOI =          "http://dx.doi.org/10.1177/016555158100300102",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/3/1/3",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1984:RTE,
  author =       "Bertram C. Brookes",
  title =        "Ranking techniques and the empirical log law",
  journal =      j-INFO-PROC-MAN,
  volume =       "20",
  number =       "1--2",
  pages =        "37--46",
  month =        "????",
  year =         "1984",
  CODEN =        "IPMADK",
  DOI =          "http://dx.doi.org/10.1016/0306-4573(84)90038-4",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Mon Feb 25 10:38:32 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0306457384900384",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brown:1970:MOU,
  author =       "J. L. {Brown, Jr.} and R. L. Duncan",
  title =        "Modulo One Uniform Distribution of the Sequence of
                 Logarithms of Certain Recursive Sequences",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "5",
  pages =        "482--486",
  month =        dec,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:31 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  note =         "See remark \cite{Kuipers:1973:RPD}.",
  URL =          "http://www.fq.math.ca/Scanned/8-5/brown.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Brown:2005:BLS,
  author =       "Richard J. C. Brown",
  title =        "{Benford}'s law and the screening of analytical data:
                 the case of pollutant concentrations in ambient air",
  journal =      j-ANALYST,
  volume =       "130",
  number =       "9",
  pages =        "1280--1285",
  month =        "????",
  year =         "2005",
  CODEN =        "ANALAO",
  DOI =          "http://dx.doi.org/10.1039/B504462F",
  ISSN =         "0003-2654 (print), 1364-5528 (electronic)",
  ISSN-L =       "0003-2654",
  bibdate =      "Sat Feb 16 17:27:51 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pubmed/16096674",
  acknowledgement = ack-nhfb,
  fjournal =     "The Analyst",
}

@Article{Brown:2007:UZL,
  author =       "R. J. C. Brown",
  title =        "The use of {Zipf}'s law in the screening of analytical
                 data: a step beyond {Benford}",
  journal =      j-ANALYST,
  volume =       "132",
  number =       "4",
  pages =        "344",
  year =         "2007",
  CODEN =        "ANALAO",
  DOI =          "http://dx.doi.org/10.1039/b618255k",
  ISSN =         "0003-2654 (print), 1364-5528 (electronic)",
  ISSN-L =       "0003-2654",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007Ana...132..344B",
  abstract =     "This study shows for the first time the effectiveness
                 of Zipf's law in screening analytical data sets for
                 outliers, data formatting and data transcription
                 errors, particularly when the data sets are small. In
                 the case of pollutant concentrations in ambient air,
                 the multivariate nature of the measurement, and the
                 relationship between the measured values of these
                 multivariant quantities are the characteristics that
                 allow a Zipf's law approach to data screening to be
                 successful. Furthermore, it has been shown that Zipf's
                 law has advantages over other novel data screening
                 techniques, such as Benford's law, in terms of
                 sensitivity and scope",
  acknowledgement = ack-nhfb,
  fjournal =     "The Analyst",
}

@Article{Browne:1998:FBL,
  author =       "Malcolm W. Browne",
  title =        "Following {Benford's Law}, or Looking Out for {No.
                 1}",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "F4--F4",
  day =          "4",
  month =        aug,
  year =         "1998",
  CODEN =        "NYTIAO",
  ISSN =         "0362-4331 (print), 1542-667X, 1553-8095",
  ISSN-L =       "0362-4331",
  bibdate =      "Sat Feb 16 14:29:48 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Science section.",
  URL =          "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
}

@Article{Buck:1993:IBF,
  author =       "B. Buck and A. C. Merchant and S. M. Perez",
  title =        "An illustration of {Benford}'s first digit law using
                 alpha decay half lives",
  journal =      j-EUR-J-PHYS,
  volume =       "14",
  number =       "2",
  pages =        "59--63",
  month =        "????",
  year =         "1993",
  CODEN =        "EJPHD4",
  ISSN =         "0143-0807 (print), 1361-6404 (electronic)",
  ISSN-L =       "0143-0807",
  bibdate =      "Mon Nov 14 17:32:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/1993EJPh...14...59B",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Physics",
}

@TechReport{Bul:2011:BGG,
  author =       "K. Bul",
  title =        "{Das Benford'sche Gesetz}. ({German}) [{Benford's
                 Law}]",
  type =         "Working paper",
  institution =  "Max-von-Laue-gymnasium",
  address =      "Koblenz, Germany",
  year =         "2011",
  bibdate =      "Fri Mar 22 08:44:32 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  language =     "German",
}

@Article{Bumby:1969:FAM,
  author =       "R. Bumby and E. Ellentuck",
  title =        "Finitely additive measures and the first digit
                 problem",
  journal =      j-FUNDAM-MATH,
  volume =       "65",
  number =       "??",
  pages =        "33--42",
  month =        "????",
  year =         "1969",
  CODEN =        "????",
  ISSN =         "0016-2736",
  ISSN-L =       "0016-2736",
  bibdate =      "Sat Nov 12 16:19:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fundamenta mathematicae",
}

@Article{Bunt:1984:MPL,
  author =       "Richard B. Bunt and Jennifer M. Murphy and Shikharesh
                 Majumdar",
  title =        "A measure of program locality and its application",
  journal =      j-SIGMETRICS,
  volume =       "12",
  number =       "3",
  pages =        "28--40",
  month =        aug,
  year =         "1984",
  CODEN =        "????",
  DOI =          "http://doi.acm.org/10.1145/1031382.809311",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Thu Jun 26 11:00:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Although the phenomenon of locality has long been
                 recognized as the single most important characteristic
                 of program behaviour, relatively little work has been
                 done in attempting to measure it. Recent work has led
                 to the development of an intrinsic measure of program
                 locality based on the Bradford--Zipf distribution.
                 Potential applications for such a measure are many, and
                 include the evaluation of program restructuring methods
                 (manual and automatic), the prediction of system
                 performance, the validation of program behaviour
                 models, and the enhanced understanding of the phenomena
                 that characterize program behaviour. A consideration of
                 each of these areas is given in connection with the
                 proposed measure, both to increase confidence in the
                 validity of the measure and to illustrate a methodology
                 for dealing with such problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
}

@Article{Burgos:1996:ZSB,
  author =       "Javier D. Burgos and Pedro Moreno-Tovar",
  title =        "{Zipf}-scaling behavior in the immune system",
  journal =      j-BIOSYSTEMS,
  volume =       "39",
  number =       "3",
  pages =        "227--232",
  day =          "15",
  month =        nov,
  year =         "1996",
  CODEN =        "BSYMBO",
  DOI =          "http://dx.doi.org/10.1016/0303-2647(96)01618-8",
  ISSN =         "0303-2647 (print), 1872-8324 (electronic)",
  ISSN-L =       "0303-2647",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0303264796016188",
  acknowledgement = ack-nhfb,
  fjournal =     "Biosystems (A6E)",
  keywords =     "Zipf's Law",
}

@Article{Burke:1991:BLP,
  author =       "John Burke and Eric Kincanon",
  title =        "{Benford}'s law and physical constants: The
                 distribution of initial digits",
  journal =      j-AMER-J-PHYSICS,
  volume =       "59",
  number =       "10",
  pages =        "952--952",
  month =        oct,
  year =         "1991",
  CODEN =        "AJPIAS",
  DOI =          "http://dx.doi.org/10.1119/1.16838",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Mon Nov 14 17:31:11 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B;
                 http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
}

@InProceedings{Burns:2009:SSR,
  author =       "B. D. Burns",
  editor =       "N. Taatgen and H. van Rijn",
  booktitle =    "{Proceedings of the Thirty-First Annual Conference of
                 the Cognitive Science Society, Cognitive Science
                 Society, Austin, TX}",
  title =        "Sensitivity to Statistical Regularities: People
                 (Largely) Follow {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "2872--2877",
  year =         "2009",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Nov 18 11:57:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Busta:1992:TRN,
  author =       "B. Busta and R. Sundheim",
  title =        "Tax return numbers tend to obey {Benford}'s law",
  type =         "Working Paper",
  number =       "W93-106-94",
  institution =  "Center for Business Research, St. Cloud State
                 University",
  address =      "St. Cloud, MN, USA",
  year =         "1992",
  bibdate =      "Sat Feb 16 17:29:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Busta:1998:UBL,
  author =       "Bruce Busta and Randy Weinberg",
  title =        "Using {Benford's Law} and Neural Networks as a Review
                 Procedure",
  journal =      "Managerial Auditing Journal",
  volume =       "13",
  number =       "6",
  pages =        "356--366",
  month =        "????",
  year =         "1998",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1108/02686909810222375",
  ISSN =         "0268-6902 (print), 1758-7735 (electronic)",
  ISSN-L =       "0268-6902",
  bibdate =      "Tue Nov 22 18:50:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Campanario:2011:BLC,
  author =       "Juan Campanario and Mar{\'\i}a Coslado",
  title =        "{Benford}'s law and citations, articles and impact
                 factors of scientific journals",
  journal =      j-SCIENTOMETRICS,
  volume =       "88",
  number =       "2",
  pages =        "421--432",
  month =        aug,
  year =         "2011",
  CODEN =        "SCNTDX",
  DOI =          "http://dx.doi.org/10.1007/s11192-011-0387-9",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Fri Nov 25 10:43:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
}

@Article{Campanino:1996:IIM,
  author =       "Massimo Campanino and Stefano Isola",
  title =        "Infinite invariant measures for non-uniformly
                 expanding transformations of $ [0, 1] $: Weak law of
                 large numbers with anomalous scaling",
  journal =      j-FORUM-MATH,
  volume =       "8",
  number =       "1",
  pages =        "71--92",
  year =         "1996",
  CODEN =        "FOMAEF",
  DOI =          "http://dx.doi.org/10.1515/form.1996.8.71",
  ISSN =         "0933-7741 (print), 1435-5337 (electronic)",
  ISSN-L =       "0933-7741",
  bibdate =      "Sat Nov 12 10:33:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0837.60022",
  abstract =     "We consider a class of maps of $ [0, 1] $ with an
                 indifferent fixed point at 0 and expanding everywhere
                 else. Using the invariant ergodic probability measure
                 of a suitable, everywhere expanding, induced
                 transformation we are able to study the infinite
                 invariant measure of the original map in some detail.
                 Given a continuous function with compact support in
                 $]0, 1]$, we prove that its time averages satisfy a
                 `weak law of large numbers' with anomalous scaling $ n
                 / \log n $ and give an upper bound for the decay of
                 correlations.",
  acknowledgement = ack-nhfb,
  ajournal =     "Forum Math.",
  classmath =    "60F05 (Weak limit theorems) 28D05 (Measure-preserving
                 transformations) 37A99 (Ergodic theory)",
  fjournal =     "Forum Mathematicum",
  keywords =     "decay of correlations; invariant ergodic probability
                 measure; weak law of large numbers",
}

@Article{Campi:2005:ZLM,
  author =       "X. Campi and H. Krivine",
  title =        "{Zipf}'s law in multifragmentation",
  journal =      j-PHYS-REV-C,
  volume =       "72",
  number =       "??",
  pages =        "057602",
  day =          "30",
  month =        nov,
  year =         "2005",
  CODEN =        "PRVCAN",
  DOI =          "http://dx.doi.org/10.1103/PhysRevC.72.057602",
  ISSN =         "0556-2813 (print), 1089-490X, 1538-4497",
  ISSN-L =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevC.72.057602",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  journal-URL =  "http://prc.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Canessa:2003:TAFa,
  author =       "Enrique Canessa",
  title =        "Theory of Analogous Force on Number Sets",
  journal =      "ArXiv e-prints",
  year =         "2003",
  bibdate =      "Mon Nov 21 06:56:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/cond-mat/0307703",
  abstract =     "A general statistical thermodynamic theory that
                 considers given sequences of $x$-integers to play the
                 role of particles of known type in an isolated elastic
                 system is proposed. By also considering some explicit
                 discrete probability distributions $ p_x $ for natural
                 numbers, we claim that they lead to a better
                 understanding of probabilistic laws associated with
                 number theory. Sequences of numbers are treated as the
                 size measure of finite sets. By considering $ p_x $ to
                 describe complex phenomena, the theory leads to derive
                 a distinct analogous force $ f_x $ on number sets
                 proportional to $ (\frac {\partial p_x}{\partial x})_T
                 $ at an analogous system temperature $T$. In
                 particular, this yields to an understanding of the
                 uneven distribution of integers of random sets in terms
                 of analogous scale invariance and a screened inverse
                 square force acting on the significant digits. The
                 theory also allows to establish recursion relations to
                 predict sequences of Fibonacci numbers and to give an
                 answer to the interesting theoretical question of the
                 appearance of the Benford's law in Fibonacci numbers. A
                 possible relevance to prime numbers is also analyzed.",
  acknowledgement = ack-nhfb,
  remark =       "To appear in Phys. A.",
}

@Article{Canessa:2003:TAFb,
  author =       "Enrique Canessa",
  title =        "Theory of analogous force on number sets",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "1--2",
  pages =        "44--52",
  month =        oct,
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(03)00526-0",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437103005260",
  abstract =     "A general statistical thermodynamic theory that
                 considers given sequences of $x$-integers to play the
                 role of particles of known type in an isolated elastic
                 system is proposed. By also considering some explicit
                 discrete probability distributions $ p_x $ for natural
                 numbers, we claim that they lead to a better
                 understanding of probabilistic laws associated with
                 number theory. Sequences of numbers are treated as the
                 size measure of finite sets. By considering $ p_x $ to
                 describe complex phenomena, the theory leads to derive
                 a distinct analogous force $ f_x $ on number sets
                 proportional to $ (\partial p_x / \partial x)T $ at an
                 analogous system temperature $T$. In particular, this
                 leads to an understanding of the uneven distribution of
                 integers of random sets in terms of analogous scale
                 invariance and a screened inverse square force acting
                 on the significant digits. The theory also allows to
                 establish recursion relations to predict sequences of
                 Fibonacci numbers and to give an answer to the
                 interesting theoretical question of the appearance of
                 the Benford's law in Fibonacci numbers. A possible
                 relevance to prime numbers is also analyzed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law; Fibonacci numbers; prime numbers",
}

@Article{Cantu:2011:FDA,
  author =       "F. Cantu and S. M. Saiegh",
  title =        "Fraudulent Democracy? {An} Analysis of {Argentina}'s
                 Infamous Decade Using Supervised Machine Learning",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "409--433",
  month =        "Autumn",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1093/pan/mpr033",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Mon Feb 18 18:24:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pan.oxfordjournals.org/content/19/4/409.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  keywords =     "Benford's Law",
}

@Article{Carslow:1988:AIN,
  author =       "C. Carslow",
  title =        "Anomalies in Income Numbers. {Evidence} of Goal
                 Oriented Behavior",
  journal =      j-ACCOUNT-REV,
  volume =       "63",
  number =       "2",
  pages =        "321--327",
  month =        apr,
  year =         "1988",
  CODEN =        "ACRVAS",
  ISSN =         "0001-4826 (print), 1558-7967 (electronic)",
  ISSN-L =       "0001-4826",
  bibdate =      "Sat Dec 10 11:19:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/248109",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  keywords =     "Benford's Law",
  remark =       "This paper references neither Newcomb nor Benford, but
                 it uses their digit-frequency formula from
                 \cite{Feller:1966:IPT} to compare with data on revenues
                 of New Zealand companies.",
}

@Article{Cartlidge:2010:NNO,
  author =       "Edwin Cartlidge",
  title =        "In nature, number one dominates",
  journal =      "Institute of Physics, Environmental Research Letters",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        oct,
  year =         "2010",
  DOI =          "????",
  bibdate =      "Mon Feb 18 17:38:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://environmentalresearchweb.org/cws/article/news/44124",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Castillo:1997:FGP,
  author =       "Enrique Castillo and Ali S. Hadi",
  title =        "Fitting the Generalized {Pareto} Distribution to
                 Data",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "92",
  number =       "440",
  pages =        "1609--1620",
  month =        dec,
  year =         "1997",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Mon Oct 30 06:57:36 MST 2000",
  bibsource =    "http://www.amstat.org/publications/jasa/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  URL =          "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM;
                 http://www.jstor.org/stable/2965432",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Chacko:2007:EPB,
  author =       "Manoj Chacko and P. Yageen Thomas",
  title =        "Estimation of a Parameter of Bivariate {Pareto}
                 Distribution by Ranked Set Sampling",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "6",
  pages =        "703--714",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Chakravorty:2008:TAE,
  author =       "Douglas N. Hales and V. Sridharan and Abirami
                 Radhakrishnan and Satya S. Chakravorty and Samia M.
                 Siha",
  title =        "Testing the accuracy of employee-reported data: An
                 inexpensive alternative approach to traditional
                 methods",
  journal =      j-EUR-J-OPER-RES,
  volume =       "189",
  number =       "3",
  pages =        "583--593",
  day =          "16",
  month =        sep,
  year =         "2008",
  CODEN =        "EJORDT",
  DOI =          "http://dx.doi.org/10.1016/j.ejor.2006.09.092",
  ISSN =         "0377-2217 (print), 1872-6860 (electronic)",
  ISSN-L =       "0377-2217",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Operational Research",
  keywords =     "Benford's Law",
  xxauthor =     "S. Chakravorty and Samia M. Siha",
}

@Article{Chakravorty:2009:TBL,
  author =       "S. Chakravorty and V. Sridharan",
  title =        "Testing {Benford's Law} for improving supply chain
                 decision-making: a field experiment",
  journal =      j-DRUG-DISCOVERY-TODAY,
  volume =       "122",
  number =       "2",
  pages =        "606--618",
  month =        dec,
  year =         "2009",
  CODEN =        "DDTOFS",
  DOI =          "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
  ISSN =         "1359-6446 (print), 1878-5832 (electronic)",
  ISSN-L =       "1359-6446",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
  acknowledgement = ack-nhfb,
  fjournal =     "Drug Discovery Today",
  keywords =     "Benford's Law",
}

@Article{Challet:2004:BPD,
  author =       "Damien Challet and Andrea Lombardoni",
  title =        "Bug propagation and debugging in asymmetric software
                 structures",
  journal =      j-PHYS-REV-E,
  volume =       "70",
  number =       "4",
  pages =        "046109",
  month =        oct,
  year =         "2004",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.70.046109",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 08:15:07 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.70.046109;
                 http://pre.aps.org/abstract/PRE/v70/i4/e046109",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "4",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Linux; Unix; Zipf's Law",
  pagecount =    "5",
}

@Article{Chang:2011:CGR,
  author =       "Harry M. Chang",
  title =        "Constructing $n$-gram rules for natural language
                 models through exploring the limitation of the
                 {Zipf--Mandelbrot} law",
  journal =      j-COMPUTING,
  volume =       "91",
  number =       "3",
  pages =        "241--264",
  month =        mar,
  year =         "2011",
  CODEN =        "CMPTA2",
  DOI =          "http://dx.doi.org/10.1007/s00607-010-0116-x",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68T50",
  MRnumber =     "2776088",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing. Archives for Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}

@PhdThesis{Chen:1978:ZL,
  author =       "Wen-Chen Chen",
  title =        "On {Zipf}'s law",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  pages =        "114",
  year =         "1978",
  MRclass =      "Thesis",
  MRnumber =     "2627928",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871",
  acknowledgement = ack-nhfb,
  remark =       "Available from ProQuest LLC, Ann Arbor, MI, USA.
                 Author given name appears as Wen-Cheng in MathSciNet
                 database.",
}

@Article{Chen:1980:WFZ,
  author =       "Wen Chen Chen",
  title =        "On the weak form of {Zipf}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "17",
  number =       "3",
  pages =        "611--622",
  year =         "1980",
  CODEN =        "JPRBAM",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "62E10 (62F10)",
  MRnumber =     "580021 (81m:62021)",
  MRreviewer =   "Patrick L. Brockett",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3212955",
  ZMnumber =     "Zbl 0435.60017",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
}

@Article{Chen:1986:RBL,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "A relationship between {Lotka's Law}, {Bradford's
                 Law}, and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "5",
  pages =        "307--314",
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO;2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Chen:1987:AZL,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "Analysis of {Zipf}'s law: An index approach",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "171--182",
  day =          "1",
  month =        apr,
  year =         "1987",
  CODEN =        "IPMADK",
  DOI =          "http://dx.doi.org/10.1016/0306-4573(87)90002-1",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0306457387900021",
  ZMnumber =     "0614.62150",
  abstract =     "A rigorous analysis of Zipf's law is made using an
                 index for the sequence of observed values of the
                 variables in a Zipf-type relationship. Three important
                 properties relating rank, count, and frequency are
                 identified. Using this approach, the shape of Zipf-type
                 curves can be described in terms of three distinct
                 regions and two parameters of the Mandelbrot--Zipf law.
                 This result has considerable practical significance,
                 since it provides rigorous foundations for the
                 application of Zipf's law.",
  acknowledgement = ack-nhfb,
  classmath =    "62P99 (Appl. of statistics)",
  fjournal =     "Information Processing and Management",
  keywords =     "index approach; Mandelbrot-Zipf law; Zipf's law",
}

@Article{Chen:1989:ZLT,
  author =       "Ye-Sho Chen",
  title =        "{Zipf}'s laws in text modeling",
  journal =      "International Journal of General Systems. Methodology,
                 Applications, Education",
  volume =       "15",
  number =       "3",
  pages =        "233--252",
  year =         "1989",
  CODEN =        "IJGSAX",
  DOI =          "http://dx.doi.org/10.1080/03081078908935048",
  ISSN =         "0308-1079, 1026-7492, 1563-5104",
  ISSN-L =       "0308-1079",
  MRclass =      "92A90",
  MRnumber =     "1015844",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Internat. J. Gen. Systems",
  fjournal =     "International Journal of General Systems. Methodology,
                 Applications, Education",
}

@Article{Chen:1991:ZLN,
  author =       "Ye-Sho Chen",
  title =        "{Zipf}'s law in natural languages, programming
                 languages, and command languages: the {Simon--Yule}
                 approach",
  journal =      j-INT-J-SYST-SCI,
  volume =       "22",
  number =       "11",
  pages =        "2299--2312",
  year =         "1991",
  CODEN =        "IJSYA9",
  DOI =          "http://dx.doi.org/10.1080/00207729108910791",
  ISSN =         "0020-7721",
  ISSN-L =       "0020-7721",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0793.68020",
  abstract =     "Zipf's law and issues in natural languages,
                 programming languages and command languages related to
                 it, are reviewed. We point out the need for a unified
                 theory to resolve the issues. Based on Herbert Simon's
                 creative process for scientific discovery, we evaluate
                 four leading theories of language generation. As a
                 result, the Simon--Yule model of text generation is
                 selected as a promising theory. The implications of the
                 theory related to the issues in natural languages,
                 programming languages and command languages are
                 discussed.",
  acknowledgement = ack-nhfb,
  classmath =    "68N15 (Programming languages) 68T50 (Natural language
                 processing)",
  fjournal =     "International Journal of Systems Science",
  keywords =     "command languages; natural languages; programming
                 languages; Simon-Yule model; text generation; Zipf's
                 law",
}

@Article{Chen:1997:NHS,
  author =       "Weishing Chen and Tai-Hsi Wu",
  title =        "A non-homogeneous software reliability model based on
                 {Zipf}'s law",
  journal =      "International Journal of Quality \& Reliability
                 Management",
  volume =       "14",
  number =       "4",
  pages =        "409--431",
  month =        "????",
  year =         "1997",
  DOI =          "http://dx.doi.org/10.1108/02656719710170666",
  ISSN =         "0265-671X (print), 1758-6682 (electronic)",
  ISSN-L =       "0265-671X",
  bibdate =      "Fri Nov 25 07:08:17 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chen:2004:MFM,
  author =       "Yanguang Chen and Yixing Zhou",
  title =        "Multi-fractal measures of city-size distributions
                 based on the three-parameter {Zipf} model",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "22",
  number =       "4",
  pages =        "793--805",
  day =          "1",
  month =        nov,
  year =         "2004",
  CODEN =        "CSFOEH",
  DOI =          "http://dx.doi.org/10.1016/j.chaos.2004.02.059",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0960077904001031",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:MRB,
  author =       "Yanguang Chen",
  title =        "The mathematical relationship between {Zipf}'s law and
                 the hierarchical scaling law",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "11",
  pages =        "3285--3299",
  day =          "1",
  month =        jun,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2011.12.031",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437111009678",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:ZLF,
  author =       "Yanguang Chen",
  title =        "{Zipf}'s law, $ 1 / f $ noise, and fractal hierarchy",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "45",
  number =       "1",
  pages =        "63--73",
  day =          "15",
  month =        jan,
  year =         "2012",
  CODEN =        "CSFOEH",
  DOI =          "http://dx.doi.org/10.1016/j.chaos.2011.10.001",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0960077911001901",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:ZLH,
  author =       "Yanguang Chen",
  title =        "{Zipf}'s law, hierarchical structure, and
                 cards-shuffling model for urban development",
  journal =      j-DISCRETE-DYN-NAT-SOC,
  pages =        "480196",
  year =         "2012",
  CODEN =        "DDNSFA",
  DOI =          "http://dx.doi.org/10.1155/2012/480196",
  ISSN =         "1026-0226 (print), 1607-887X (electronic)",
  ISSN-L =       "1026-0226",
  MRclass =      "91D10",
  MRnumber =     "2914043",
  MRreviewer =   "Sandra L. Arlinghaus",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Discrete Dyn. Nat. Soc.",
  fjournal =     "Discrete Dynamics in Nature and Society. An
                 International Multidisciplinary Research and Review
                 Journal",
  pagecount =    "21",
}

@Article{Chida:2011:LSI,
  author =       "Satoshi Chida and Naoto Miyoshi",
  title =        "Limiting size index distributions for ball-bin models
                 with {Zipf}-type frequencies",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "63",
  number =       "4",
  pages =        "745--768",
  year =         "2011",
  CODEN =        "AISXAD",
  DOI =          "http://dx.doi.org/10.1007/s10463-010-0276-7",
  ISSN =         "0020-3157 (print), 1572-9052 (electronic)",
  ISSN-L =       "0020-3157",
  MRclass =      "60C05 (60F15 60J27)",
  MRnumber =     "2805906 (2012f:60035)",
  MRreviewer =   "Elvira Di Nardo",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
}

@Article{Cho:2007:BBL,
  author =       "Wendy K. Tam Cho and Brian J. Gaines",
  title =        "Breaking the ({Benford}) law: statistical fraud
                 detection in campaign finance",
  journal =      j-AMER-STAT,
  volume =       "61",
  number =       "3",
  pages =        "218--223",
  month =        aug,
  year =         "2007",
  CODEN =        "ASTAAJ",
  DOI =          "http://dx.doi.org/10.1198/000313007X223496",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2393725",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496;
                 http://www.tandfonline.com/doi/abs/10.1198/000313007X223496",
  abstract =     "Benford's law is seeing increasing use as a diagnostic
                 tool for isolating pockets of large datasets with
                 irregularities that deserve closer inspection. Popular
                 and academic accounts of campaign finance are rife with
                 tales of corruption, but the complete dataset of
                 transactions for federal campaigns is enormous.
                 Performing a systematic sweep is extremely arduous;
                 hence, these data are a natural candidate for initial
                 screening by comparison to Benford's distributions.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Chou:2009:BLN,
  author =       "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and
                 Zuozheng Wang and Huan Zheng",
  title =        "{Benford's Law} and Number Selection in Fixed-Odds
                 Numbers Game",
  journal =      j-J-GAMBL-STUD,
  volume =       "25",
  number =       "4",
  pages =        "503--521",
  month =        dec,
  year =         "2009",
  CODEN =        "JGSTEM",
  DOI =          "http://dx.doi.org/10.1007/s10899-009-9145-9",
  ISSN =         "1050-5350 (print), 1573-3602 (electronic)",
  ISSN-L =       "1050-5350",
  bibdate =      "Sat Feb 16 15:35:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s10899-009-9145-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Gambling Studies",
}

@Article{Chuang:2009:FPS,
  author =       "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen",
  title =        "Feature-preserved sampling over streaming data",
  journal =      j-TKDD,
  volume =       "2",
  number =       "4",
  pages =        "15:1--15:??",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://doi.acm.org/10.1145/1460797.1460798",
  ISSN =         "1556-4681 (print), 1556-472X (electronic)",
  ISSN-L =       "1556-4681",
  bibdate =      "Fri Apr 24 17:59:51 MDT 2009",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tkdd/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this article, we explore a novel sampling model,
                 called {\em feature preserved sampling\/} ({\em FPS\/})
                 that sequentially generates a high-quality sample over
                 sliding windows. The sampling quality we consider
                 refers to the degree of consistency between the sample
                 proportion and the population proportion of each
                 attribute value in a window. Due to the time-variant
                 nature of real-world datasets, users are more likely to
                 be interested in the most recent data. However,
                 previous works have not been able to generate a
                 high-quality sample over sliding windows that precisely
                 preserves up-to-date population characteristics.
                 Motivated by this shortcoming, we have developed the
                 {\em FPS\/} algorithm, which has several advantages:
                 (1) it sequentially generates a sample from a
                 time-variant data source over sliding windows; (2) the
                 execution time of {\em FPS\/} is linear with respect to
                 the database size; (3) the {\em relative\/}
                 proportional differences between the sample proportions
                 and population proportions of most distinct attribute
                 values are guaranteed to be below a specified error
                 threshold, $ \epsilon $, while the {\em relative\/}
                 proportion differences of the remaining attribute
                 values are as close to $ \epsilon $ as possible, which
                 ensures that the generated sample is of high quality;
                 (4) the sample rate is close to the user specified rate
                 so that a high quality sampling result can be obtained
                 without increasing the sample size; (5) by a thorough
                 analytical and empirical study, we prove that {\em
                 FPS\/} has acceptable space overheads, especially when
                 the attribute values have Zipfian distributions, and
                 {\em FPS\/} can also excellently preserve the
                 population proportion of multivariate features in the
                 sample; and (6) {\em FPS\/} can be applied to infinite
                 streams and finite datasets equally, and the generated
                 samples can be used for various applications. Our
                 experiments on both real and synthetic data validate
                 that {\em FPS\/} can effectively obtain a high quality
                 sample of the desired size. In addition, while using
                 the sample generated by {\em FPS\/} in various mining
                 applications, a significant improvement in efficiency
                 can be achieved without compromising the model's
                 precision.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Knowledge Discovery from Data
                 (TKDD)",
  keywords =     "sampling; Streaming mining",
}

@Article{Cigler:1961:NET,
  author =       "J. Cigler and G. Helmberg",
  title =        "{Neuere Entwicklungen der Theorie der
                 Gleichverteilung}. ({German}) [{Recent} developments in
                 the theory of uniform distribution]",
  journal =      j-DEUTSCH-MATH-V,
  volume =       "64",
  number =       "??",
  pages =        "1--50",
  month =        "????",
  year =         "1961",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Nov 12 16:33:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Jber. Deutsch. Math.--Verein",
  language =     "German",
}

@Article{Cigler:1964:MSU,
  author =       "J. Cigler",
  title =        "Methods of summability and uniform distribution $
                 \bmod 1 $",
  journal =      j-COMPOS-MATH,
  volume =       "16",
  number =       "??",
  pages =        "44--51",
  year =         "1964",
  CODEN =        "CMPMAF",
  ISSN =         "0010-437X (print), 1570-5846 (electronic)",
  ISSN-L =       "0010-437X",
  bibdate =      "Mon Nov 14 10:15:31 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Compositio Mathematica",
}

@TechReport{Ciofalo:2005:EBF,
  author =       "Michele Ciofalo",
  title =        "Entropy, {Benford}'s first digit law, and the
                 distribution of everything",
  type =         "Report",
  institution =  "Dipartimento di Ingegneria Nucleare, Universit{\`a}
                 degli Studi di Palermo",
  address =      "Palermo, Italy",
  pages =        "34",
  year =         "2005",
  bibdate =      "Sun Feb 17 08:23:55 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Clark:1977:ESL,
  author =       "Douglas W. Clark and C. Cordell Green",
  title =        "An Empirical Study of List Structure in {Lisp}",
  journal =      j-CACM,
  volume =       "20",
  number =       "2",
  pages =        "78--87",
  month =        feb,
  year =         "1977",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:31:28 MST 2001",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Static measurements of the list structure of five
                 large Lisp programs are reported and analyzed. These
                 measurements reveal substantial regularity, or
                 predictability, among pointers to atoms and especially
                 among pointers to lists. Pointers to atoms are found to
                 obey, roughly, Zipf's law, which governs word
                 frequencies in natural languages; pointers to lists
                 usually point to a location physically nearby in
                 memory. The use of such regularities in the
                 space-efficient representation of list structure is
                 discussed.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques); C6140D (High level
                 languages)",
  classification = "723",
  comment =      "Great paper; evidence pro CDR-coding, con fancy CONS",
  corpsource =   "Carnegie-Mellon Univ., Pittsburgh, PA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  journalabr =   "Commun ACM",
  keywords =     "computer programming languages; data processing ---
                 Data Structures; empirical study; LISP; list structure;
                 measurements; regularity",
  oldlabel =     "ClarkG77",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77",
}

@Article{Clauset:2007:FST,
  author =       "Aaron Clauset and Maxwell Young and Kristian Skrede
                 Gleditsch",
  title =        "On the Frequency of Severe Terrorist Events",
  journal =      j-J-CONFL-RESOLUT,
  volume =       "51",
  number =       "1",
  pages =        "58--87",
  month =        feb,
  year =         "2007",
  CODEN =        "JCFRAL",
  DOI =          "http://dx.doi.org/10.1177/0022002706296157",
  ISSN =         "0022-0027 (print), 1552-8766 (electronic)",
  ISSN-L =       "0022-0027",
  bibdate =      "Thu Nov 24 14:07:17 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jcr.sagepub.com;
                 http://jcr.sagepub.com/content/51/1/58.abstract;
                 http://www.jstor.org/journals/00220027.html",
  abstract =     "In the spirit of Lewis Richardson's original study of
                 the statistics of deadly conflicts, we study the
                 frequency and severity of terrorist attacks worldwide
                 since 1968. We show that these events are uniformly
                 characterized by the phenomenon of ``scale
                 invariance,'' that is, the frequency scales as an
                 inverse power of the severity, $ P(x) \approx x{-
                 \alpha } $. We find that this property is a robust
                 feature of terrorism, persisting when we control for
                 economic development of the target country, the type of
                 weapon used, and even for short time scales. Further,
                 we show that the center of the distribution oscillates
                 slightly with a period of roughly 13 years, that there
                 exist significant temporal correlations in the
                 frequency of severe events, and that current models of
                 event incidence cannot account for these variations or
                 the scale invariance property of global terrorism.
                 Finally, we describe a simple toy model for the
                 generation of these statistics and briefly discuss its
                 implications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Conflict Resolution",
}

@Article{Clauset:2007:PLD,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-law distributions in empirical data",
  journal =      "ArXiv Physics e-prints",
  day =          "7",
  month =        jun,
  year =         "2007",
  bibdate =      "Thu Feb 28 08:52:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "arXiv:0706.1062.",
  URL =          "http://arxiv.org/abs/0706.1062v1",
  acknowledgement = ack-nhfb,
  pagecount =    "27",
}

@Article{Clauset:2007:PLDa,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-law distributions in empirical data",
  journal =      "ArXiv Physics e-prints",
  day =          "2",
  month =        feb,
  year =         "2009",
  DOI =          "http://dx.doi.org/10.1137/070710111",
  bibdate =      "Thu Feb 28 08:52:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "arXiv:0706.1062.",
  URL =          "http://arxiv.org/abs/0706.1062v1",
  acknowledgement = ack-nhfb,
  pagecount =    "43",
}

@Article{Clauset:2009:PLDb,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-Law Distributions in Empirical Data",
  journal =      j-SIAM-REVIEW,
  volume =       "51",
  number =       "4",
  pages =        "661--703",
  month =        "????",
  year =         "2009",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/070710111",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Mon May 17 17:56:49 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Cleary:2005:ADA,
  author =       "Richard Cleary and Jay C. Thibodeau",
  title =        "Applying Digital Analysis Using {Benford's Law} to
                 Detect Fraud: The Dangers of Type {I} Errors",
  journal =      j-AUDITING,
  volume =       "24",
  number =       "1",
  pages =        "77--81",
  month =        may,
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.2308/aud.2005.24.1.77",
  ISSN =         "0278-0380 (print), 1558-7991 (electronic)",
  ISSN-L =       "0278-0380",
  bibdate =      "Tue Nov 15 09:17:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaapubs.org/loi/ajpt;
                 http://link.aip.org/link/AJPTXX/v24/i1/p77/s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@Article{Clippe:2012:BLT,
  author =       "Paulette Clippe and Marcel Ausloos",
  title =        "{Benford}'s law and {Theil} transform of financial
                 data",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "24",
  pages =        "6556--6567",
  day =          "15",
  month =        dec,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2012.07.063",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437112007546",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
}

@Article{Coderre:1999:FDU,
  author =       "David Coderre",
  title =        "Fraud Detection Using Digital Analysis",
  journal =      j-EDPACS,
  volume =       "27",
  number =       "3",
  pages =        "1--8",
  month =        "????",
  year =         "1999",
  CODEN =        "EDPCDF",
  DOI =          "http://dx.doi.org/10.1201/1079/43249.27.3.19990901/30268.1",
  ISSN =         "0736-6981 (print), 1936-1009 (electronic)",
  ISSN-L =       "0736-6981",
  bibdate =      "Sat Jan 07 09:20:49 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1",
  acknowledgement = ack-nhfb,
  fjournal =     "EDPACS",
  keywords =     "Benford's Law",
  onlinedate =   "21 Dec 2006",
}

@Article{Cohen:1976:EFD,
  author =       "Daniel I. A. Cohen",
  title =        "An explanation of the first digit phenomenon",
  journal =      j-J-COMB-THEORY-A,
  volume =       "20",
  number =       "3",
  pages =        "367--370",
  month =        may,
  year =         "1976",
  CODEN =        "JCBTA7",
  ISSN =         "0097-3165",
  ISSN-L =       "0097-3165",
  bibdate =      "Thu Feb 15 16:29:51 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory (Series A)",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Cohen:1984:PNF,
  author =       "D. I. A. Cohen and T. M. Katz",
  title =        "Prime numbers and the first digit phenomenon",
  journal =      j-J-NUMBER-THEORY,
  volume =       "18",
  number =       "3",
  pages =        "261--268",
  month =        jun,
  year =         "1984",
  CODEN =        "JNUTA9",
  DOI =          "http://dx.doi.org/10.1016/0022-314X(84)90061-1",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Fri Nov 25 13:58:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
}

@Article{Cohen:2005:PCL,
  author =       "Edith Cohen and Carsten Lund",
  title =        "Packet classification in large {ISPs}: design and
                 evaluation of decision tree classifiers",
  journal =      j-SIGMETRICS,
  volume =       "33",
  number =       "1",
  pages =        "73--84",
  month =        jun,
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://doi.acm.org/10.1145/1064212.1064222",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Fri Jun 27 09:21:27 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Packet classification, although extensively studied,
                 is an evolving problem. Growing and changing needs
                 necessitate the use of larger filters with more complex
                 rules. The increased complexity and size pose
                 implementation challenges on current hardware solutions
                 and drive the development of software classifiers, in
                 particular, decision-tree based classifiers. Important
                 performance measures for these classifiers are time and
                 memory due to required high throughput and use of
                 limited fast memory. We analyze Tier 1 ISP data that
                 includes filters and corresponding traffic from over a
                 hundred edge routers and thousands of interfaces. We
                 provide a comprehensive view on packet classification
                 in an operational network and glean insights that help
                 us design more effective classification algorithms. We
                 propose and evaluate decision tree classifiers with
                 {\em common branches}. These classifiers have linear
                 worst-case memory bounds and require much less memory
                 than standard decision tree classifiers, but
                 nonetheless, we show that on our data have similar
                 average and worst-case time performance. We argue that
                 common-branches exploit structure that is present in
                 real-life data sets. We observe a strong Zipf-like
                 pattern in the usage of rules in a classifier, where a
                 very small number of rules resolves the bulk of traffic
                 and most rules are essentially never used. Inspired by
                 this observation, we propose {\em traffic-aware\/}
                 classifiers that obtain superior average-case and
                 bounded worst-case performance. Good average-case can
                 boost performance of software classifiers that can be
                 used in small to medium sized routers and are also
                 important for traffic analysis and traffic
                 engineering.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "access control lists; decision trees; packet
                 filtering; routing",
}

@Article{Coile:1977:LFD,
  author =       "Russell C. Coile",
  title =        "{Lotka}'s Frequency Distribution of Scientific
                 Productivity",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "6",
  pages =        "366--370",
  month =        nov,
  year =         "1977",
  CODEN =        "AISJB6",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:08:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  keywords =     "Lotka's Law",
}

@Article{Condon:1928:SV,
  author =       "E. U. Condon",
  title =        "Statistics of vocabulary",
  journal =      j-SCIENCE,
  volume =       "67",
  number =       "1733",
  pages =        "300--??",
  day =          "16",
  month =        mar,
  year =         "1928",
  CODEN =        "SCIEAS",
  DOI =          "http://dx.doi.org/10.1126/science.67.1733.300",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Fri Nov 25 09:04:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
}

@Article{Cong:2004:WTP,
  author =       "Lin Cong and Zhipeng Li",
  title =        "On {Wilson}'s theorem and {Polignac} conjecture",
  journal =      "ArXiv e-prints",
  day =          "2",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Feb 18 07:03:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math.NT/0408018",
  abstract =     "We introduce Wilson's theorem and Clement's result and
                 present a necessary and sufficient condition for $p$
                 and $ p + 2 k $ to be primes where $k$ is a positive
                 integer. By using Simiov's Theorem, we derive an
                 improved version of Clement's result and
                 characterizations of Polignac twin primes which
                 parallel previous characterizations.",
  acknowledgement = ack-nhfb,
}

@Misc{Conway:2010:CFM,
  author =       "D. Conway",
  title =        "{Benford's Law} Tests for {Wikileaks} Data",
  howpublished = "Zero Intelligence Agents website.",
  day =          "1",
  month =        aug,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:39:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.drewconway.com/zia/?p=2234",
  acknowledgement = ack-nhfb,
}

@InCollection{Corazza:2010:CFM,
  author =       "Marco Corazza and Andrea Ellero and Alberto Zorzi",
  booktitle =    "Mathematical and statistical methods for actuarial
                 sciences and finance",
  title =        "Checking financial markets via {Benford}'s law: the
                 {S\&P 500} case",
  publisher =    "Springer Italia",
  address =      "Milan, Italy",
  pages =        "93--102",
  year =         "2010",
  DOI =          "http://dx.doi.org/10.1007/978-88-470-1481-7_10",
  MRclass =      "62P05",
  MRnumber =     "2676191",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Corominas-Murtra:2010:UZL,
  author =       "Bernat Corominas-Murtra and Ricard V. Sol{\'e}",
  title =        "Universality of {Zipf}'s law",
  journal =      j-PHYS-REV-E,
  volume =       "82",
  number =       "1",
  pages =        "011102",
  day =          "1",
  month =        jul,
  year =         "2010",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.82.011102",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  MRclass =      "82B03 (62B10)",
  MRnumber =     "2736361 (2011j:82002)",
  MRreviewer =   "N. N. Ganikhodjaev",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.82.011102",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "9",
}

@Article{Corominas-Murtra:2011:EZL,
  author =       "Bernat Corominas-Murtra and Jordi Fortuny and Ricard
                 V. Sol{\'e}",
  title =        "Emergence of {Zipf}'s law in the evolution of
                 communication",
  journal =      j-PHYS-REV-E,
  volume =       "83",
  number =       "1",
  pages =        "036115",
  day =          "28",
  month =        mar,
  year =         "2011",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.83.036115",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.83.036115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "9",
}

@Article{Costas:2008:NCC,
  author =       "Eduardo Costas and Victoria L{\'o}pez-Rodas and F.
                 Javier Toro and Antonio Flores-Moya",
  title =        "The number of cells in colonies of the cyanobacterium
                 {{\em Microcystis aeruginosa\/}} satisfies {Benford}'s
                 law",
  journal =      j-AQUAT-BOT,
  volume =       "89",
  number =       "3",
  pages =        "341--343",
  month =        oct,
  year =         "2008",
  CODEN =        "AQBODS",
  DOI =          "http://dx.doi.org/10.1016/j.aquabot.2008.03.011",
  ISSN =         "0304-3770 (print), 1879-1522 (electronic)",
  ISSN-L =       "0304-3770",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304377008000533",
  acknowledgement = ack-nhfb,
  fjournal =     "Aquatic Botany",
  keywords =     "Benford's Law",
}

@Article{Courtland:2010:CML,
  author =       "Rachel Courtland",
  title =        "Curious mathematical law is rife in nature",
  journal =      j-NEW-SCIENTIST,
  volume =       "208",
  number =       "2782",
  pages =        "10--10",
  day =          "16",
  month =        oct,
  year =         "2010",
  CODEN =        "NWSCAL",
  DOI =          "http://dx.doi.org/10.1016/S0262-4079(10)62497-9",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262407910624979",
  acknowledgement = ack-nhfb,
  fjournal =     "The New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law; earthquake detection",
  xxISSN =       "0262-4079, 0028-6664",
}

@Article{Cristelli:2012:TMT,
  author =       "Matthieu Cristelli and Michael Batty and Luciano
                 Pietronero",
  title =        "There is More than a Power Law in {Zipf}",
  journal =      j-SCI-REP,
  volume =       "2",
  number =       "??",
  pages =        "1--7",
  month =        nov,
  year =         "2012",
  CODEN =        "SRCEC3",
  DOI =          "http://dx.doi.org/10.1038/srep00812",
  ISSN =         "2045-2322",
  ISSN-L =       "2045-2322",
  bibdate =      "Tue Feb 26 07:32:11 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/srep/2012/121108/srep00812/full/srep00812.html",
  accepted =     "28 August 2012",
  acknowledgement = ack-nhfb,
  articleno =    "812",
  fjournal =     "Scientific Reports",
  onlinedate =   "08 November 2012",
  received =     "15 August 2012",
}

@Article{Czirok:1995:CBS,
  author =       "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo
                 Havlin and H. Eugene Stanley",
  title =        "Correlations in binary sequences and a generalized
                 {Zipf} analysis",
  journal =      j-PHYS-REV-E,
  volume =       "52",
  number =       "??",
  pages =        "446--??",
  day =          "1",
  month =        jul,
  year =         "1995",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.52.446",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.52.446",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Czirok:1996:POP,
  author =       "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and
                 Tam{\'a}s Vicsek",
  title =        "Possible origin of power-law behavior in $n$-tuple
                 {Zipf} analysis",
  journal =      j-PHYS-REV-E,
  volume =       "53",
  number =       "??",
  pages =        "6371--??",
  day =          "1",
  month =        jun,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.53.6371",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.53.6371",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Dahui:2005:TRZ,
  author =       "Wang Dahui and Li Menghui and Di Zengru",
  title =        "True reason for {Zipf}'s law in language",
  journal =      j-PHYSICA-A,
  volume =       "358",
  number =       "2--4",
  pages =        "545--550",
  day =          "15",
  month =        dec,
  year =         "2005",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2005.04.021",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437105004085",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@InProceedings{Dallacasa:2006:TBS,
  author =       "F. Dallacasa and Valerio Dallacasa",
  editor =       "????",
  booktitle =    "{5th International Conference: APLIMAT 2006, Slovak
                 University of Technology, Bratislava}",
  title =        "Temporal behaviour of stock data from {Benford}'s
                 law",
  publisher =    "????",
  address =      "????",
  pages =        "425--432",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:32:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  price =        "US\$",
  URL =          "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Davis:1976:SRI,
  author =       "Basil Davis",
  title =        "Some Remarks on Initial Digits",
  journal =      j-FIB-QUART,
  volume =       "14",
  number =       "1",
  pages =        "13--14",
  month =        feb,
  year =         "1976",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:05 MDT 2011",
  bibsource =    "http://www.fq.math.ca/14-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/14-1/davis.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Deakin:1993:ADB,
  author =       "Michael A. B. Deakin",
  title =        "Another derivation of {Benford}'s law",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "20",
  number =       "5",
  pages =        "162--163",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "0311-0729",
  ISSN-L =       "0311-0729",
  MRclass =      "11K36",
  MRnumber =     "1268513 (95j:11072)",
  MRreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Mathematical Society Gazette",
}

@Article{Debreceny:2010:DMJ,
  author =       "S. Debreceny and Glen L. Gray",
  title =        "Data mining journal entries for fraud detection: An
                 exploratory study",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "157--181",
  month =        sep,
  year =         "2010",
  CODEN =        "IJAIA7",
  DOI =          "http://dx.doi.org/10.1016/j.accinf.2010.08.001",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See discussion
                 \cite{Grabski:2010:DDM,Kriel:2010:DDM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089510000540;
                 http://www.sciencedirect.com/science/journal/14670895",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
}

@Article{DeCeuster:1998:HPB,
  author =       "M. J. K. DeCeuster and G. Dhaene and T. Schatteman",
  title =        "On the hypothesis of psychological barriers in stock
                 markets and {Benford}'s law",
  journal =      j-J-EMPIR-FINANCE,
  volume =       "5",
  number =       "3",
  pages =        "263--279",
  month =        sep,
  year =         "1998",
  CODEN =        "JEFIEC",
  DOI =          "http://dx.doi.org/10.1016/S0927-5398(97)00024-8",
  ISSN =         "0927-5398 (print), 1879-1727 (electronic)",
  ISSN-L =       "0927-5398",
  bibdate =      "Sun Nov 13 11:33:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Empirical Finance",
}

@Article{Decker:2007:GPC,
  author =       "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E.
                 Moses",
  title =        "Global Patterns of City Size Distributions and Their
                 Fundamental Drivers",
  journal =      j-PLOS-ONE,
  volume =       "2",
  number =       "9",
  pages =        "e934",
  month =        sep,
  year =         "2007",
  CODEN =        "POLNCL",
  DOI =          "http://dx.doi.org/10.1371/journal.pone.0000934",
  ISSN =         "1932-6203",
  bibdate =      "Wed Feb 27 06:29:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0000934",
  abstract =     "Urban areas and their voracious appetites are
                 increasingly dominating the flows of energy and
                 materials around the globe. Understanding the size
                 distribution and dynamics of urban areas is vital if we
                 are to manage their growth and mitigate their negative
                 impacts on global ecosystems. For over 50 years, city
                 size distributions have been assumed to universally
                 follow a power function, and many theories have been
                 put forth to explain what has become known as Zipf's
                 law (the instance where the exponent of the power
                 function equals unity). Most previous studies, however,
                 only include the largest cities that comprise the tail
                 of the distribution. Here we show that national,
                 regional and continental city size distributions,
                 whether based on census data or inferred from cluster
                 areas of remotely-sensed nighttime lights, are in fact
                 lognormally distributed through the majority of cities
                 and only approach power functions for the largest
                 cities in the distribution tails. To explore generating
                 processes, we use a simple model incorporating only two
                 basic human dynamics, migration and reproduction, that
                 nonetheless generates distributions very similar to
                 those found empirically. Our results suggest that
                 macroscopic patterns of human settlements may be far
                 more constrained by fundamental ecological principles
                 than more fine-scale socioeconomic factors.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  keywords =     "Zipf's Law",
  pagecount =    "6",
}

@TechReport{Deckert:2010:IBL,
  author =       "Joseph Deckert and Mikhail Myagkov and Peter C.
                 Ordeshook",
  title =        "The Irrelevance of {Benford's Law} for Detecting Fraud
                 in Elections",
  type =         "{CALTECH} working paper",
  number =       "9",
  institution =  "California Institute of Technology",
  address =      "Pasadena, CA, USA",
  pages =        "27",
  day =          "9",
  month =        mar,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:40:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://vote.caltech.edu/drupal/node/327",
  acknowledgement = ack-nhfb,
  remark =       "From the abstract: ``..., we argue here that Benford's
                 Law is essentially useless as a forensic indicator of
                 fraud.''",
}

@Article{Deckert:2011:BLD,
  author =       "Joseph Deckert and Mikhail Myagkov and Peter C.
                 Ordeshook",
  title =        "{Benford's Law} and the Detection of Election Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "245--268",
  month =        "Summer",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1093/pan/mpr014",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Mon Feb 18 18:26:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mebane:2011:CBL} for a rebuttal.",
  URL =          "http://pan.oxfordjournals.org/content/19/3/245.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  remark =       "The authors argue that application of Benford's Law
                 tests to election results to detect fraud is
                 inconclusive and ``essentially equivalent to a toss of
                 a coin''.",
}

@InProceedings{DelAcebo:2005:BLN,
  author =       "Esteve {Del Acebo} and Mateu Sbert",
  title =        "{Benford's Law} for Natural and Synthetic Images",
  crossref =     "Neumann:2005:CAE",
  pages =        "169--176",
  year =         "2005",
  DOI =          "http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
  bibdate =      "Tue Nov 15 08:46:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Deligny:2010:RRL,
  author =       "H. Deligny and P. Jolissaint",
  title =        "Relations de r{\'e}currence lin{\'e}aires,
                 primitivit{\'e} et loi de {Benford}. ({French})
                 [{Linear} recurrence relations, primitivity, and
                 {Benford's Law}]",
  journal =      "ArXiv e-prints",
  day =          "23",
  month =        jul,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 18:14:51 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D;
                 http://arxiv.org/abs/1007.5349",
  abstract =     "We prove that many sequences of positive numbers $
                 (a_n) $ defined by finite linear difference equations $
                 a_{n + k} = c_{k - 1} a_{n + k - 1} + \ldots {} + c_0
                 a_n $ with suitable nonnegative reals coefficients $
                 c_i $ satisfy Benford's Law on the first digit in many
                 bases $ b > 2 $. Our techniques rely on
                 Perron--Frobenius theory via the companion matrix of
                 the characteristic polynomial of the defining
                 equation.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1007.5349",
  keywords =     "Mathematics - Dynamical Systems, Mathematics - Rings
                 and Algebras, 11A99",
  language =     "French",
  primaryclass = "math.DS",
}

@Article{Deligny:2013:RRL,
  author =       "Hugues Deligny and Paul Jolissaint",
  title =        "Relations de r{\'e}currence lin{\'e}aires,
                 primitivit{\'e} et loi de {Benford}. ({French})
                 [{Linear} recurrence relations, primitivity, and
                 {Benford}'s law]",
  journal =      j-ELEM-MATH,
  volume =       "68",
  number =       "1",
  pages =        "9--21",
  year =         "2013",
  DOI =          "http://dx.doi.org/10.4171/EM/213",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRnumber =     "3016461",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Denisov:1997:FBS,
  author =       "S. Denisov",
  title =        "Fractal binary sequences: {Tsallis} thermodynamics and
                 the {Zipf} law",
  journal =      j-PHYS-LET-A,
  volume =       "235",
  number =       "5",
  pages =        "447--451",
  day =          "17",
  month =        nov,
  year =         "1997",
  CODEN =        "PYLAAG",
  DOI =          "http://dx.doi.org/10.1016/S0375-9601(97)00688-9",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0375960197006889",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  keywords =     "Zipf's Law",
}

@Article{Depken:2008:BZB,
  author =       "Craig A. {Depken II}",
  title =        "{Benford}, {Zipf} and the blogosphere",
  journal =      j-APPL-ECON-LETT,
  volume =       "15",
  number =       "9",
  pages =        "689--692",
  month =        "????",
  year =         "2008",
  DOI =          "http://dx.doi.org/10.1080/13504850600735270",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Sat Jan 07 09:18:33 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  onlinedate =   "04 Jul 2008",
}

@Article{Devooght:1957:LZM,
  author =       "J. Devooght",
  title =        "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the
                 {Zipf--Mandelbrot} law]",
  journal =      "Acad. Roy. Belg. Bull. Cl. Sci. (5)",
  volume =       "43",
  pages =        "244--251",
  year =         "1957",
  CODEN =        "????",
  ISSN =         "0001-4141",
  ISSN-L =       "0001-4141",
  MRclass =      "94.0X",
  MRnumber =     "0088412 (19,516a)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe
                 des Sciences. Koninklijke Belgische Academie.
                 Mededelingen van de Klasse der Wetenschappen. 5e
                 S{\'e}rie",
  language =     "French",
}

@TechReport{Diaconis:1973:LMI,
  author =       "Persi Diaconis",
  title =        "Limits of measures of the integers with applications
                 to random number generators and the distribution of
                 leading digits",
  type =         "Memorandum",
  number =       "NS-211",
  institution =  "Department of Statistics, Harvard University",
  address =      "Cambridge, MA, USA",
  day =          "22",
  month =        mar,
  year =         "1973",
  bibdate =      "Sat Nov 12 16:23:20 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Diaconis:1974:WSA,
  author =       "Persi Diaconis",
  title =        "Weak and Strong Averages in probability and the theory
                 numbers",
  type =         "{Ph.D.} thesis",
  school =       "Department of Statistics, Harvard University",
  address =      "Cambridge, MA, USA",
  pages =        "xvii + 117",
  year =         "1974",
  bibdate =      "Mon Nov 14 10:26:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Diaconis:1977:DLD,
  author =       "Persi Diaconis",
  title =        "The distribution of leading digits and uniform
                 distribution $ \bmod 1 $",
  journal =      j-ANN-PROBAB,
  volume =       "5",
  number =       "1",
  pages =        "72--81",
  month =        feb,
  year =         "1977",
  CODEN =        "APBYAE",
  DOI =          "http://dx.doi.org/10.1214/aop/1176995891",
  ISSN =         "0091-1798",
  ISSN-L =       "0091-1798",
  bibdate =      "Sun Apr 20 10:44:17 MDT 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.aop/1176995891",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aop",
  keywords =     "Benford's Law",
}

@Article{Diaconis:1979:RP,
  author =       "Persi Diaconis and David Freedman",
  title =        "On Rounding Percentages",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "74",
  number =       "366",
  pages =        "359--364",
  month =        jun,
  year =         "1979",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Nov 23 11:24:59 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "The authors extend prior work on correctness of sums
                 of rounded percentages \cite{Mosteller:1967:DSR}, and
                 criticize biased rounding practices in
                 \cite{Benford:1938:LAN}.",
  URL =          "http://www.jstor.org/stable/2284288",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Benford's Law",
  remark =       "When percentage-column entries are rounded, their sum
                 may differ from 100\%. The authors use a prior proof
                 \cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
                 values, the probability of a correct sum is $ \sqrt {6
                 / (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
                 rounding may produce large changes in computed
                 chi-squared values, and they conclude their article
                 with this recommendation: ``it is important to
                 calculate with many-digit accuracy when computing $
                 \chi^2 $ for large sample sizes.''",
}

@TechReport{Diekmann:2002:DFM,
  author =       "Andreas Diekmann",
  title =        "{Diagnose von Fehlerquellen und methodische
                 Qualit{\"a}t in der sozialwissenschaftlichen
                 Forschung}. ({German}) [{Diagnosis} of errors and
                 methodological quality in social science research]",
  type =         "Report",
  number =       "ITA-02-04",
  institution =  "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung",
  address =      "Vienna, Austria",
  pages =        "????",
  year =         "2002",
  bibdate =      "Thu Nov 17 19:11:00 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Diekmann:2004:DEE,
  author =       "Andreas Diekmann",
  title =        "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit
                 der Benford Verteilung}. ({German}) [{Data}
                 falsification. {Results} from experiments with the
                 {Benford} distribution]",
  type =         "Report",
  institution =  "ETH Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  year =         "2004",
  bibdate =      "Fri Nov 18 12:09:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Diekmann:2004:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  type =         "Report",
  institution =  "ETH Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "26",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Dec 10 11:12:29 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by ``Benford's law''. Recently, a test
                 against this distribution was used to identify
                 fraudulent accounting data. This test is based on the
                 supposition that real data follow the Benford
                 distribution while fabricated data do not. Is it
                 possible to apply Benford tests to detect fabricated or
                 falsified scientific data as well as fraudulent
                 financial data? We approached this question in two
                 ways. First, we examined the use of the Benford
                 distribution as a standard by checking digit
                 frequencies in published statistical estimates. Second,
                 we conducted experiments in which subjects were asked
                 to fabricate statistical estimates (regression
                 coefficients). These experimental data were scrutinized
                 for possible deviations from the Benford distribution.
                 There were two main findings. First, the digits of the
                 published regression coefficients were approximately
                 Benford distributed. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. At least in the case of regression
                 coefficients, there were indications that checks for
                 digit-preference anomalies should focus less on the
                 first and more on the second and higher-digits",
  acknowledgement = ack-nhfb,
}

@Article{Diekmann:2007:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "3--4",
  pages =        "321--329",
  year =         "2007",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/02664760601004940",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRnumber =     "2380543",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by `Benford's law'. Recently, a test against
                 this distribution was used to identify fraudulent
                 accounting data. This test is based on the supposition
                 that first, second, third, and other digits in real
                 data follow the Benford distribution while the digits
                 in fabricated data do not. Is it possible to apply
                 Benford tests to detect fabricated or falsified
                 scientific data as well as fraudulent financial data?
                 We approached this question in two ways. First, we
                 examined the use of the Benford distribution as a
                 standard by checking the frequencies of the nine
                 possible first and ten possible second digits in
                 published statistical estimates. Second, we conducted
                 experiments in which subjects were asked to fabricate
                 statistical estimates (regression coefficients). The
                 digits in these experimental data were scrutinized for
                 possible deviations from the Benford distribution.
                 There were two main findings. First, both digits of the
                 published regression coefficients were approximately
                 Benford distributed or at least followed a pattern of
                 monotonic decline. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. Surprisingly, first digits of faked
                 data also exhibited a pattern of monotonic decline,
                 while second, third, and fourth digits were distributed
                 less in accordance with Benford's law. At least in the
                 case of regression coefficients, there were indications
                 that checks for digit-preference anomalies should focus
                 less on the first (i.e., leftmost) and more on later
                 digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; data fabrication; digital analysis;
                 distribution of digits from regression coefficients;
                 first digit law; Zipf's Law",
}

@Article{Diekmann:2010:BLF,
  author =       "Andreas Diekmann and Ben Jann",
  title =        "{Benford's Law} and Fraud Detection: Facts and
                 Legends",
  journal =      j-GER-ECON-REV,
  volume =       "11",
  number =       "3",
  pages =        "397--401",
  month =        aug,
  year =         "2010",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1111/j.1468-0475.2010.00510.x",
  ISSN =         "1465-6485 (print), 1468-0475 (electronic)",
  ISSN-L =       "1465-6485",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  keywords =     "Benford's law; false negative; false positive; fraud
                 detection; regression coefficients",
  onlinedate =   "6 Apr 2010",
}

@Article{Diekmann:2012:MUB,
  author =       "Andreas Diekmann",
  title =        "Making Use of ``{Benford's Law}'' for the Randomized
                 Response Technique",
  journal =      j-SOC-METH-RES,
  volume =       "41",
  number =       "2",
  pages =        "325--334",
  month =        may,
  year =         "2012",
  DOI =          "http://dx.doi.org/10.1177/0049124112452525",
  ISSN =         "0049-1241 (print), 1552-8294 (electronic)",
  ISSN-L =       "0049-1241",
  bibdate =      "Mon Feb 18 19:03:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://smr.sagepub.com/content/41/2/325;
                 http://www.socio.ethz.ch/news/Diekmann_Benford_RRT_SMR_2012.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Sociological Methods and Research",
}

@Article{diGiovanni:2013:FET,
  author =       "Julian di Giovanni and Andrei A. Levchenko",
  title =        "Firm entry, trade, and welfare in {Zipf}'s world",
  journal =      j-J-INT-ECON,
  volume =       "89",
  number =       "2",
  pages =        "283--296",
  day =          "15",
  month =        mar,
  year =         "2013",
  CODEN =        "JIECBE",
  DOI =          "http://dx.doi.org/10.1016/j.jinteco.2012.08.002",
  ISSN =         "0022-1996 (print), 1873-0353 (electronic)",
  ISSN-L =       "0022-1996",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022199612001365",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of International Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09247963",
  keywords =     "Zipf's Law",
}

@Article{Docampo:2009:BLA,
  author =       "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and
                 Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio
                 Flores-Moya",
  title =        "{Benford}'s law applied to aerobiological data and its
                 potential as a quality control tool",
  journal =      j-AEROBIOLOGIA,
  volume =       "25",
  number =       "4",
  pages =        "275--283",
  month =        dec,
  year =         "2009",
  CODEN =        "AROBFT",
  DOI =          "http://dx.doi.org/10.1007/s10453-009-9132-8",
  ISSN =         "0393-5965 (print), 1573-3025 (electronic)",
  ISSN-L =       "0393-5965",
  bibdate =      "Fri Nov 25 10:47:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132",
  acknowledgement = ack-nhfb,
  fjournal =     "Aerobiologia",
}

@Article{Dolgikh:2001:PCS,
  author =       "Dmitry G. Dolgikh and Andrei M. Sukhov",
  title =        "Parameters of cache systems based on a {Zipf}-like
                 distribution",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "37",
  number =       "6",
  pages =        "711--716",
  day =          "15",
  month =        dec,
  year =         "2001",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/S1389-1286(01)00243-2",
  ISSN =         "1389-1286 (print), 1872-7069 (electronic)",
  ISSN-L =       "1389-1286",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.elsevier.com/locate/issn/13891286;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S1389128601002432",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Networks (Amsterdam, Netherlands: 1999)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/13891286",
  keywords =     "Zipf's Law",
}

@Article{Dorfleitner:2009:PBE,
  author =       "Gregor Dorfleitner and Christian Klein",
  title =        "Psychological barriers in {European} stock markets:
                 Where are they?",
  journal =      j-GLOB-FINANCE-J,
  volume =       "19",
  number =       "3",
  pages =        "268--285",
  month =        oct,
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/j.gfj.2008.09.001",
  ISSN =         "1044-0283 (print), 1873-5665 (electronic)",
  ISSN-L =       "1044-0283",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1044028308000549",
  acknowledgement = ack-nhfb,
  fjournal =     "Global Finance Journal",
  keywords =     "Benford's Law",
}

@Article{Dorogovtsev:2006:FON,
  author =       "S. N. Dorogovtsev and J. F. F. Mendes and J. G.
                 Oliveira",
  title =        "Frequency of occurrence of numbers in the {World Wide
                 Web}",
  journal =      j-PHYSICA-A,
  volume =       "360",
  number =       "2",
  pages =        "548--556",
  month =        feb,
  year =         "2006",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2005.06.064",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://arxiv.org/abs/physics/0504185;
                 http://www.sciencedirect.com/science/article/pii/S0378437105006874",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law",
}

@Article{Doyle:2011:ITA,
  author =       "Laurance R. Doyle and Brenda McCowan and Simon
                 Johnston and Sean F. Hanser",
  title =        "Information theory, animal communication, and the
                 search for extraterrestrial intelligence",
  journal =      j-ACTA-ASTRONAUT,
  volume =       "68",
  number =       "3--4",
  pages =        "406--417",
  month =        feb # "\slash " # mar,
  year =         "2011",
  CODEN =        "AASTCF",
  DOI =          "http://dx.doi.org/10.1016/j.actaastro.2009.11.018",
  ISSN =         "0094-5765 (print), 1879-2030 (electronic)",
  ISSN-L =       "0094-5765",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0094576509005682",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Astronautica",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Drake:2000:CAA,
  author =       "P. D. Drake and M. J. Nigrini",
  title =        "Computer assisted analytical procedures using
                 {Benford}'s law",
  journal =      j-J-ACCOUNT-EDUC,
  volume =       "18",
  number =       "2",
  pages =        "127--146",
  month =        "Spring",
  year =         "2000",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/S0748-5751(00)00008-7",
  ISSN =         "0748-5751 (print), 1873-1996 (electronic)",
  ISSN-L =       "0748-5751",
  bibdate =      "Tue Nov 22 10:36:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0748575100000087;
                 http://www.sciencedirect.com/science/journal/07485751",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accounting Education",
}

@Article{Dubinsky:2001:MFF,
  author =       "Bruce G. Dubinsky",
  title =        "Math formula fights fraud",
  journal =      "Legal Times of {Washington}",
  volume =       "XXIV",
  number =       "9",
  pages =        "??--??",
  day =          "26",
  month =        feb,
  year =         "2001",
  ISSN =         "0732-7536",
  ISSN-L =       "0732-7536",
  bibdate =      "Sat Feb 16 17:35:39 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  xxjournal =    "Legal Times",
}

@Article{Dumbgen:2007:EBA,
  author =       "L. D{\"u}mbgen and C. Leuenberger",
  title =        "Explicit bounds for the approximation error in
                 {Benford}'s law",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0705.4488",
  keywords =     "Mathematics - Probability, 60E15, 60F99",
  primaryclass = "math.PR",
}

@Article{Dumbgen:2008:EBA,
  author =       "Lutz D{\"u}mbgen and Christoph Leuenberger",
  title =        "Explicit bounds for the approximation error in
                 {Benford}'s law",
  journal =      j-ELECTRON-COMMUN-PROBAB,
  volume =       "13",
  pages =        "99--112",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "1083-589X",
  ISSN-L =       "1083-589X",
  MRclass =      "60E15 (60F99)",
  MRnumber =     "2386066 (2009b:60056)",
  MRreviewer =   "Pieter C. Allaart",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://arxiv.org/abs/0705.4488;
                 http://weber.math.washington.edu/~ejpecp/ECP/index.php",
  abstract =     "Benford's law states that for many random variables $
                 X > 0 $ its leading digit $ D = D(X) $ satisfies
                 approximately the equation $ P(D = d) = \log_{10}(1 + 1
                 / d) $ for $ d = 1, 2, \ldots {}, 9 $. This phenomenon
                 follows from another, maybe more intuitive fact,
                 applied to $ Y := \log_{10}(X) $: For many real random
                 variables $Y$, the remainder $ U := Y - \floor (Y) $ is
                 approximately uniformly distributed on $ [0, 1) $. The
                 present paper provides new explicit bounds for the
                 latter approximation in terms of the total variation of
                 the density of $Y$ or some derivative of it. These
                 bounds are an interesting alternative to traditional
                 Fourier methods which yield mostly qualitative results.
                 As a by-product we obtain explicit bounds for the
                 approximation error in Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Communications in Probability",
}

@Article{Duncan:1967:AUD,
  author =       "R. L. Duncan",
  title =        "An Application of Uniform Distributions to the
                 {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "2",
  pages =        "137--140",
  month =        apr,
  year =         "1967",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:52 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/5-2/duncan.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Duncan:1969:NID,
  author =       "R. L. Duncan",
  title =        "Note on the Initial Digit Problem",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "5",
  pages =        "474--475",
  month =        dec,
  year =         "1969",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:21 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/7-5/duncan.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Dunn:1980:SFW,
  author =       "Stanley Dunn",
  title =        "Surveyor's Forum: {Working} on Interpretations",
  journal =      j-COMP-SURV,
  volume =       "12",
  number =       "2",
  pages =        "255--255",
  month =        jun,
  year =         "1980",
  CODEN =        "CMSVAN",
  DOI =          "http://doi.acm.org/10.1145/356810.356817",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:27:10 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Duran:1974:ACS,
  author =       "J. Peter Duran",
  title =        "Almost convergence, summability and ergodicity",
  journal =      j-CAN-J-MATH,
  volume =       "26",
  number =       "??",
  pages =        "372--387",
  month =        "????",
  year =         "1974",
  CODEN =        "CJMAAB",
  DOI =          "http://dx.doi.org/10.4153/CJM-1974-039-6",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:38:45 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v26/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  remark =       "In relation to Benford's Law, see theorem 6.2.",
}

@Article{Duranton:2006:SFZ,
  author =       "Gilles Duranton",
  title =        "Some foundations for {Zipf}'s law: Product
                 proliferation and local spillovers",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "36",
  number =       "4",
  pages =        "542--563",
  day =          "1",
  month =        jul,
  year =         "2006",
  CODEN =        "RSUEDM",
  DOI =          "http://dx.doi.org/10.1016/j.regsciurbeco.2006.03.008",
  ISSN =         "0166-0462 (print), 1879-2308 (electronic)",
  ISSN-L =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0166046206000354",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01660462",
  keywords =     "Zipf's Law",
}

@Book{Durrett:1991:PTE,
  author =       "Richard Durrett",
  title =        "Probability: theory and examples",
  publisher =    "Wadsworth and Brooks\slash Cole Advanced Books and
                 Software",
  address =      "Pacific Grove, CA, USA",
  pages =        "ix + 453",
  year =         "1991",
  ISBN =         "0-534-13206-5",
  ISBN-13 =      "978-0-534-13206-4",
  LCCN =         "QA273 .D865 1991",
  bibdate =      "Mon Nov 21 10:06:18 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$49.95",
  series =       "The Wadsworth and Brooks\slash Cole statistics\slash
                 probability series",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is treated on pp. 300ff. Hill \cite[page
                 893]{Hill:1995:BII} reports that Durrett has a proof
                 that the $k$-th digit of powers of integers follows
                 Benford's Law.",
  subject =      "Probabilities",
}

@Book{Durrett:2005:PTE,
  author =       "Richard Durrett",
  title =        "Probability: theory and examples",
  publisher =    "Thomson Brooks\slash Cole",
  address =      "Belmont, CA, USA",
  edition =      "Third",
  pages =        "xi + 497",
  year =         "2005",
  ISBN =         "0-534-42441-4",
  ISBN-13 =      "978-0-534-42441-1",
  LCCN =         "QA273 .D865 2005",
  bibdate =      "Mon Nov 21 10:00:11 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Duxbury advanced series",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is treated on pp. 337ff. Hill \cite[page
                 893]{Hill:1995:BII} reports that the 1991 edition has a
                 proof that the $k$-th digit of powers of integers
                 follows Benford's Law.",
  subject =      "Probabilities",
}

@Article{Durtschi:2004:EUB,
  author =       "C. Durtschi and W. Hillison and C. Pacini",
  title =        "The Effective Use of {Benford's Law} to Assist in
                 Detecting Fraud in Accounting Data",
  journal =      j-J-FORENSIC-ACCOUNT,
  volume =       "5",
  number =       "1",
  pages =        "17--34",
  month =        "????",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "1524-5586",
  bibdate =      "Sun Nov 13 11:35:18 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@Article{Edwards:2011:LFP,
  author =       "Roderick Edwards and Laura Collins",
  title =        "Lexical Frequency Profiles and {Zipf's Law}",
  journal =      "Language Learning",
  volume =       "61",
  number =       "1",
  pages =        "1--30",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1111/j.1467-9922.2010.00616.x",
  ISSN =         "0023-8333 (print), 1467-9922 (electronic)",
  ISSN-L =       "0023-8333",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "L2 vocabulary learning; L2 vocabulary size; modeling
                 vocabulary learning; Zipf's law",
}

@Article{Egghe:1985:CLL,
  author =       "L. Egghe",
  title =        "Consequences of {Lotka's Law} for the {Law of
                 Bradford}",
  journal =      j-J-DOC,
  volume =       "41",
  number =       "3",
  pages =        "173--189",
  month =        "????",
  year =         "1985",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/eb026780",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:23:22 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  keywords =     "Bradford's Law",
}

@Article{Egghe:1999:LZM,
  author =       "L. Egghe",
  title =        "On the law of {Zipf--Mandelbrot} for multi-word
                 phrases",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "50",
  number =       "3",
  pages =        "233--241",
  month =        "????",
  year =         "1999",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO;2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Sep 10 06:09:31 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  onlinedate =   "17 Feb 1999",
}

@Book{Egghe:2005:PLI,
  author =       "Leo Egghe",
  title =        "Power laws in the information production process:
                 {Lotkaian} informetrics",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xvii + 427",
  year =         "2005",
  ISBN =         "0-12-088753-3, 0-08-048011-X (e-book)",
  ISBN-13 =      "978-0-12-088753-8, 978-0-08-048011-4 (e-book)",
  LCCN =         "Z669.8 .E44 2005",
  bibdate =      "Mon Feb 25 10:42:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See pages 204--205 for Benford's Law discussion.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject-dates = "Lotka, Alfred James, (1880--1949)",
  tableofcontents = "Basic theory of Lotkaian informetrics \\
                 Three-dimensional Lotkaian informetrics \\
                 Lotkaian concentration theory \\
                 Lotkaian fractal complexity theory \\
                 Lotkaian informetrics of systems in which items can
                 have multiple sources \\
                 Further applications in Lotkaian informetrics \\
                 Lotkaian informetrics: an introduction",
}

@Article{Egghe:2006:DHL,
  author =       "L. Egghe",
  title =        "The dependence of the height of a {Lorenz} curve of a
                 {Zipf} function on the size of the system",
  journal =      j-MATH-COMP-MODELLING,
  volume =       "43",
  number =       "7--8",
  pages =        "870--879",
  day =          "15",
  month =        apr,
  year =         "2006",
  CODEN =        "MCMOEG",
  DOI =          "http://dx.doi.org/10.1016/j.mcm.2005.09.033",
  ISSN =         "0895-7177 (print), 1872-9479 (electronic)",
  ISSN-L =       "0895-7177",
  MRclass =      "94A15 (91B82)",
  MRnumber =     "2218323 (2006k:94033)",
  MRreviewer =   "Ulrich Tamm",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S089571770500508X",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computer Modelling",
  keywords =     "Zipf's Law",
}

@Article{Egghe:2007:UHL,
  author =       "Leo Egghe",
  title =        "Untangling {Herdan's Law} and {Heaps' Law}:
                 Mathematical and informetric arguments",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "58",
  number =       "5",
  pages =        "702--709",
  year =         "2007",
  CODEN =        "JASIEF",
  DOI =          "http://dx.doi.org/10.1002/asi.20524",
  ISSN =         "1532-2890",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 25 08:31:49 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  keywords =     "Heaps' law in information retrieval; Herdan's law in
                 linguistics",
}

@Article{Egghe:2010:NSP,
  author =       "Leo Egghe",
  title =        "A new short proof of {Naranan}'s theorem, explaining
                 {Lotka's Law} and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "61",
  number =       "12",
  pages =        "2581--2583",
  year =         "2010",
  CODEN =        "JASIEF",
  DOI =          "http://dx.doi.org/10.1002/asi.21431",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}

@Article{Egghe:2011:BLS,
  author =       "Leo Egghe",
  title =        "{Benford}'s law is a simple consequence of {Zipf}'s
                 law",
  journal =      "ISSI Newsletter",
  volume =       "7",
  number =       "3",
  pages =        "55--56",
  month =        sep,
  year =         "2011",
  DOI =          "????",
  bibdate =      "Mon Feb 18 18:27:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.issi-society.info/archives/newsletter27.pdf",
  abstract =     "We show that benford's law (describing the logarithmic
                 distribution of the numbers 1, 2, \ldots{}, 9 as first
                 digits of data in decimal form) can be deduced from the
                 classical law of zipf. this explains Bensford's law as
                 a scientometric or informetric law.",
  acknowledgement = ack-nhfb,
}

@Article{Egghe:2012:AGL,
  author =       "Leo Egghe and Raf Guns",
  title =        "Applications of the generalized law of {Benford} to
                 informetric data",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "63",
  number =       "8",
  pages =        "1662--1665",
  month =        aug,
  year =         "2012",
  CODEN =        "JASIEF",
  DOI =          "http://dx.doi.org/10.1002/asi.22690",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 18 19:05:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/asi.22690/abstract",
  abstract =     "In a previous work (Egghe, 2011), the first author
                 showed that Benford's law (describing the logarithmic
                 distribution of the numbers 1, 2, \ldots{}, 9 as first
                 digits of data in decimal form) is related to the
                 classical law of Zipf with exponent 1. The work of
                 Campanario and Coslado (2011), however, shows that
                 Benford's law does not always fit practical data in a
                 statistical sense. In this article, we use a
                 generalization of Benford's law related to the general
                 law of Zipf with exponent $ \beta > 0 $. Using data
                 from Campanario and Coslado, we apply nonlinear least
                 squares to determine the optimal $ \beta $ and show
                 that this generalized law of Benford fits the data
                 better than the classical law of Benford.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}

@TechReport{Eliahou:2011:MDP,
  author =       "Shalom Eliahou and Bruno Mass{\'e} and Dominique
                 Schneider",
  title =        "On the mantissa distribution of powers of natural and
                 prime numbers",
  type =         "Preprint",
  institution =  "Universit{\'e} du Littoral C{\^o}te d'Opale",
  address =      "Nord-Pas-de-Calais, France",
  pages =        "14",
  day =          "15",
  month =        nov,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:27:51 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://fr.wikipedia.org/wiki/Universit%C3%A9_du_Littoral_C%C3%B4te_d%27Opale;
                 http://www-lmpa.univ-littoral.fr/publications/articles/lmpa447.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Eliahou:2012:MDP,
  author =       "Shalom Eliahou and Bruno Mass{\'e} and Dominique
                 Schneider",
  title =        "On the mantissa distribution of powers of natural and
                 prime numbers",
  journal =      "Acta Mathematica Hungarica",
  volume =       "??",
  number =       "??",
  pages =        "1--5",
  month =        jun,
  year =         "2012",
  DOI =          "http://dx.doi.org/10.1007/s10474-012-0244-1",
  ISSN =         "0001-5954, 0236-5294, 1588-2632",
  ISSN-L =       "0001-5954",
  bibdate =      "Mon Feb 18 19:06:54 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007%2Fs10474-012-0244-1",
  acknowledgement = ack-nhfb,
}

@Article{Eliazar:2011:LLZ,
  author =       "Iddo Eliazar",
  title =        "Limit laws for {Zipf}'s law",
  journal =      j-J-PHYS-A,
  volume =       "44",
  number =       "2",
  pages =        "022001",
  year =         "2011",
  CODEN =        "JPHAC5",
  DOI =          "http://dx.doi.org/10.1088/1751-8113/44/2/022001",
  ISSN =         "1751-8113",
  ISSN-L =       "0305-4470",
  MRclass =      "62G30 (91D20)",
  MRnumber =     "2749082 (2011i:62083)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "Zbl 1204.62196",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Physics. A. Mathematical and Theoretical",
  journal-URL =  "http://iopscience.iop.org/0305-4470",
  pagecount =    "6",
}

@Article{Eliazar:2012:PLC,
  author =       "Iddo I. Eliazar and Morrel H. Cohen",
  title =        "Power-law connections: From {Zipf} to {Heaps} and
                 beyond",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "56--74",
  day =          "1",
  month =        may,
  year =         "2012",
  CODEN =        "IPMADK",
  DOI =          "http://dx.doi.org/10.1016/j.aop.2013.01.013",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0003491613000171",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  keywords =     "Zipf's Law",
}

@Article{elSehity:2005:PDA,
  author =       "Tarek el Sehity and Erik Hoelzl and Erich Kirchler",
  title =        "Price developments after a nominal shock: {Benford's
                 Law} and psychological pricing after the euro
                 introduction",
  journal =      j-INT-J-RES-MARK,
  volume =       "22",
  number =       "4",
  pages =        "471--480",
  month =        dec,
  year =         "2005",
  CODEN =        "IJRME6",
  DOI =          "http://dx.doi.org/10.1016/j.ijresmar.2005.09.002",
  ISSN =         "0167-8116 (print), 1873-8001 (electronic)",
  ISSN-L =       "0167-8116",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167811605000522",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Research in Marketing",
  keywords =     "Benford's Law",
}

@Article{Elshoff:1978:SSC,
  author =       "James L. Elshoff",
  title =        "A study of the structural composition of {PL/I}
                 programs",
  journal =      j-SIGPLAN,
  volume =       "13",
  number =       "6",
  pages =        "29--37",
  month =        jun,
  year =         "1978",
  CODEN =        "SINODQ",
  DOI =          "http://doi.acm.org/10.1145/987515.987518",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Wed Jun 18 16:08:52 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Some research on a theory of the structural
                 composition of an algorithm has recently been reported.
                 The theory embodies models of operator and operand
                 distributions that have been proposed by Bayer, Zipf,
                 and Zweben. This paper reports a study in which the
                 three models of operator distributions are compared
                 with the measured distributions found in 34 PL/I
                 programs. Two of three models, one by Zipf and one by
                 Zweben, are shown to correlate highly with the measured
                 distributions. Two variations of the Zipf model are
                 then formulated and tested with good results. Also, the
                 relationship between the method of counting operators
                 and the models is investigated.",
  acknowledgement = ack-nhfb,
  classification = "C4240 (Programming and algorithm theory); C6140D
                 (High level languages)",
  corpsource =   "Computer Sci. Dept., General Motors Res. Labs.,
                 Warren, MI, USA",
  fjournal =     "ACM SIG{\-}PLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "counting operators; operator distributions; PL/1; PL/1
                 programs; programming theory; structural composition",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Engel:2003:BLE,
  author =       "Hans-Andreas Engel and Christoph Leuenberger",
  title =        "{Benford}'s law for exponential random variables",
  journal =      j-STAT-PROB-LETT,
  volume =       "63",
  number =       "4",
  pages =        "361--365",
  day =          "15",
  month =        jul,
  year =         "2003",
  CODEN =        "SPLTDC",
  DOI =          "http://dx.doi.org/10.1016/S0167-7152(03)00101-9",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60E99 (60C05)",
  MRnumber =     "1996184 (2004d:60050)",
  MRreviewer =   "Ulrich M. Hirth",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Book{Estoup:1916:GSM,
  author =       "J. B. Estoup",
  title =        "Gammes St{\'e}nographiques: m{\'e}thode \& exercices
                 pour l'acquisition de la vitesse ({French})
                 [Stenographic ranges: method and exercises for
                 achieving speed]",
  publisher =    "Institut St{\'e}nographique de France",
  address =      "Paris, France",
  edition =      "Fourth",
  pages =        "151",
  year =         "1916",
  LCCN =         "????",
  bibdate =      "Thu Nov 24 14:24:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This on shorthand writing is the earliest known
                 publication of the power-law distribution of word
                 frequencies, generally credited to
                 \cite{Zipf:1932:SSP}.",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  language =     "French",
}

@Article{Faber:1985:AML,
  author =       "Vance Faber and Andrew B. {White, Jr.} and G. Milton
                 Wing",
  title =        "Analysis of a model that leads to the {Pareto} law of
                 wealth distribution",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "112",
  number =       "2",
  pages =        "579--594",
  year =         "1985",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1016/0022-247X(85)90264-1",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "90A14",
  MRnumber =     "813621 (87b:90027)",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
}

@Article{Fairthorne:1969:PDE,
  author =       "Robert A. Fairthorne",
  title =        "Progress in Documentation: Empirical Hyperbolic
                 Distributions ({Bradford--Zipf--Mandelbrot}) for
                 Bibliometric Description and Prediction",
  journal =      j-J-DOC,
  volume =       "25",
  number =       "4",
  pages =        "313--343",
  month =        dec,
  year =         "1969",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/eb026481",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 06:27:27 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprinted in \cite{Fairthorne:2005:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Article{Fairthorne:2005:PDE,
  author =       "Robert A. Fairthorne",
  title =        "Progress in Documentation: Empirical Hyperbolic
                 Distributions ({Bradford--Zipf--Mandelbrot}) for
                 Bibliometric Description and Prediction",
  journal =      j-J-DOC,
  volume =       "61",
  number =       "2",
  pages =        "171--193",
  month =        "????",
  year =         "2005",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/00220410510585179",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 06:27:27 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprint of \cite{Fairthorne:1969:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Article{Family:1989:KDG,
  author =       "Fereydoon Family and Paul Meakin",
  title =        "Kinetics of droplet growth processes: Simulations,
                 theory, and experiments",
  journal =      j-PHYS-REV-A,
  volume =       "40",
  number =       "7",
  pages =        "3836--3854",
  month =        oct,
  year =         "1989",
  CODEN =        "PLRAAN",
  DOI =          "http://dx.doi.org/10.1103/PhysRevA.40.3836",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  ISSN-L =       "1050-2947",
  bibdate =      "Thu Feb 28 10:49:20 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevA.40.3836",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  journal-URL =  "http://pra.aps.org/browse",
}

@Misc{Farbaniec:2011:AFD,
  author =       "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
                 Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
  title =        "Application of the first digit law in credibility
                 evaluation of the financial accounting data based on
                 particular cases",
  howpublished = "Lecture slides for 10th International Congress on
                 Internal Control, Internal Audit, Fraud and
                 Anti-Corruption Issues, Krak{\'o}w, September 14--16,
                 2011.",
  pages =        "27",
  year =         "2011",
  bibdate =      "Thu Dec 01 21:27:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://benford.pl/documents/benford_pikw.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farbaniec:2011:UBL,
  author =       "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
                 Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
  editor =       "????",
  booktitle =    "10th International Congress on Internal Control,
                 Internal Audit, Fraud and Anti-Corruption Issues,
                 Krak{\'o}w, September 14--16, 2011",
  title =        "Using {Benford}'s law to detect irregularities in the
                 collection of data",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2011",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Dec 01 21:32:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Farkas:2010:SUN,
  author =       "Janos Farkas and Gy{\"o}rgy Gyurky",
  title =        "The significance of using the {Newcomb--Benford} law
                 as a test of nuclear half-life calculations",
  journal =      "Acta Physica Polonica, B",
  volume =       "41",
  pages =        "1213--1221",
  year =         "2010",
  CODEN =        "APOBBB",
  ISSN =         "0587-4254 (print), 1509-5770 (electronic)",
  ISSN-L =       "0587-4254",
  bibdate =      "Mon Nov 14 16:21:42 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F;
                 http://arxiv.org/abs/1006.3615",
  abstract =     "Half-life number sequences collected from nuclear data
                 charts are found to obey the Newcomb--Benford law.
                 Based on this fact, it has been suggested recently,
                 that this law should be used to test the quality of
                 nuclear decay models. In this paper we briefly recall
                 how, when and why the Newcomb--Benford law can be
                 observed in a set of numbers with a given probability
                 distribution. We investigate the special case of
                 nuclear half-lives, and show that the law provides no
                 additional clue in understanding decay half-lives.
                 Thus, it can play no significant role in testing
                 nuclear decay theories.",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Phys. Pol. B",
  ajournal-2 =   "Acta Phys. Polon. B",
  archiveprefix = "arXiv",
  eprint =       "1006.3615",
  primaryclass = "math-ph",
}

@Article{Fedorowicz:1982:TFZ,
  author =       "Jane Fedorowicz",
  title =        "The Theoretical Foundation of {Zipf's Law} and Its
                 Application to the Bibliographic Database Environment",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "33",
  number =       "5",
  pages =        "285--293",
  year =         "1982",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/asi.4630330507",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Fedorowicz:1984:DEU,
  author =       "Jane Fedorowicz",
  title =        "Database evaluation using multiple regression
                 techniques",
  journal =      j-SIGMOD,
  volume =       "14",
  number =       "2",
  pages =        "70--76",
  year =         "1984",
  CODEN =        "SRECD8",
  ISBN =         "0-89791-128-8",
  ISBN-13 =      "978-0-89791-128-3",
  ISSN =         "0163-5808 (print), 1943-5835 (electronic)",
  ISSN-L =       "0163-5808",
  bibdate =      "Mon Dec 9 07:58:51 MST 1996",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A model of the inverted file of an automated
                 bibliographic system is constructed using the Zipf
                 distribution of word frequency. By ascertaining the
                 parameters of the Zipfian model of the inverted file
                 system, one can estimate the minimum data storage
                 requirements of the database. In addition, given a few
                 additional system parameters, access time for a
                 specified query can be estimated. The estimation
                 procedures are accomplished using logarithmic
                 transformations and multiple regression techniques.
                 This paper introduces the Zipfian models, their
                 regression formulation, and their results and
                 interpretation for application to database
                 evaluation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Northwestern Univ, Kellogg Graduate Sch of Management,
                 Evanston, IL, USA",
  affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of
                 Management, Evanston, IL, USA",
  classification = "723; 901; 922",
  conference =   "SIGMOD '84, Proceedings of Annual Meeting (ACM Special
                 Interest Group on Management of Data).",
  fjournal =     "SIGMOD Record (ACM Special Interest Group on
                 Management of Data)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J689",
  keywords =     "access time model; bibliographic techniques; database
                 systems; evaluation; information storage systems;
                 mathematical models; multiple regression techniques;
                 Zipfian model",
  meetingaddress = "Boston, MA, USA",
  sponsor =      "ACM, Special Interest Group on Management of Data, New
                 York, NY, USA",
}

@Article{Fedorowicz:1987:DPE,
  author =       "Jane Fedorowicz",
  title =        "Database Performance Evaluation in an Indexed File
                 Environment",
  journal =      j-TODS,
  volume =       "12",
  number =       "1",
  pages =        "85--110",
  month =        mar,
  year =         "1987",
  CODEN =        "ATDSD3",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  bibdate =      "Sat Apr 14 10:34:48 MDT 2001",
  bibsource =    "Compendex database; Database/Graefe.bib;
                 Database/Wiederhold.bib; http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf;
                 http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/;
                 http://www.acm.org/pubs/toc/Abstracts/tods/13675.html",
  abstract =     "The use of database systems for managerial decision
                 making often incorporates information-retrieval
                 capabilities with numeric report generation. Of great
                 concern to the user of such a system is the response
                 time associated with issuing a query to the database.
                 This study presents a procedure for estimating response
                 time for one of the most frequently encountered
                 physical storage mechanisms, the indexed file. The
                 model provides a fairly high degree of accuracy, but is
                 simple enough so that the cost of applying the model is
                 not exorbitant. The model incorporates the knowledge
                 that the distribution of access key occurrences is
                 known to follow Zipf's law. It first estimates the
                 access time required to complete the query, which
                 includes the time needed for all input and output
                 transactions, and CPU time used in performing the
                 search. The effects of multiple users on an
                 individual's response time are then assessed using a
                 simple regression estimation technique. The two-step
                 procedure allows for the separation of access time from
                 multiuser influences.",
  acknowledgement = ack-nhfb,
  affiliation =  "Boston Univ, Boston, MA, USA",
  affiliationaddress = "Boston Univ, Boston, MA, USA",
  annote =       "a procedure for estimating response time; distribution
                 of access key occurrences follow Zipf's law. Early
                 version with Kellogg, J. L. Model provides a fairly
                 high degree of accuracy but is simple. The effects of
                 multiple users are assessed using simple regression
                 estimation.",
  classification = "723; 912; 922",
  fjournal =     "ACM Transactions on Database Systems",
  generalterms = "Design; Performance",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
  keywords =     "data processing --- File organization; database
                 performance; database systems; indexed file
                 environment; MANAGEMENT --- Information Systems;
                 multiple users, design; Performance; performance;
                 response time; statistical methods --- regression
                 analysis; Zipf's law",
  subject =      "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems
                 Management, File organization. {\bf H.2.2}: Information
                 Systems, DATABASE MANAGEMENT, Physical Design, Access
                 methods. {\bf H.3.2}: Information Systems, INFORMATION
                 STORAGE AND RETRIEVAL, Information Storage, File
                 organization. {\bf H.3.3}: Information Systems,
                 INFORMATION STORAGE AND RETRIEVAL, Information Search
                 and Retrieval, Retrieval models.",
}

@Article{Feldstein:1976:CED,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Convergence Estimates for the Distribution of Trailing
                 Digits",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "287--297",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "http://doi.acm.org/10.1145/321941.321948",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "An analysis is made of the distribution of trailing
                 digits (tail end digits) of positive real
                 floating-point numbers represented in arbitrary base $
                 \beta $ and randomly chosen from a logarithmic
                 distribution. The analysis shows that the $n$ th digit
                 for $ n \geq 2 $ is actually approximately uniformly
                 distributed. The approximation depends upon both $n$
                 and the base beta. It becomes better as $n$ increases,
                 and it is exact in the limit as $ n \rightarrow \infty
                 $. A table of this distribution is presented for
                 various $ \beta $ and $n$, along with a table of the
                 maximum digit by digit deviation $ \Delta $ of the
                 logarithmic distribution from the uniform distribution.
                 Various asymptotic results for $ \Delta $ are
                 included.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "Benford's Law; computer arithmetic; computer
                 programming; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, underflow, and severe loss of significance
                 in floating-point addition and subtraction",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "6",
  number =       "2",
  pages =        "241--251",
  month =        apr,
  year =         "1986",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G05",
  MRnumber =     "89h:65065",
  bibdate =      "Sat Dec 23 14:52:49 2000",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this paper it is shown that, under the assumption
                 of the logarithmic distribution of numbers,
                 floating-point addition and subtraction can result in
                 overflow or underflow with alarming frequency --- a
                 frequency that increases rapidly with machine speed
                 unless the range of the exponent is also increased. If
                 numbers are assumed to be distributed in accordance
                 with Sweeney's (1965) experiments, then severe loss of
                 significance occurs with large probability in floating
                 point subtraction. These results have implications for
                 computer design and lead to the suggestion of a long
                 word format which will reduce the risks to acceptable
                 levels.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@Book{Feller:1950:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "????",
  year =         "1950",
  LCCN =         "QA273 .F37",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley series in probability and mathematical
                 statistics. Probability and mathematical statistics",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
}

@Book{Feller:1957:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "461 (vol. 1), 626 (vol. 2)",
  year =         "1957",
  LCCN =         "QA273 .F3712",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://catdir.loc.gov/catdir/toc/onix01/57010805.html",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
}

@Book{Feller:1966:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xviii + 626",
  year =         "1966",
  ISSN =         "0271-6232",
  LCCN =         "QA273 .F3727 1966",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley series in probability and mathematical
                 statistics. Probability and mathematical statistics",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
  remark =       "Benford's Law is discussed on p. 62.",
}

@Book{Feller:1968:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory and its
                 Applications",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Third",
  pages =        "xviii + 509",
  year =         "1968",
  ISBN =         "0-471-25708-7",
  ISBN-13 =      "978-0-471-25708-0",
  LCCN =         "QA273 .F3713",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a
                 discussion of flaws in the derivation of Benford's Law
                 in this book.",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
  remark =       "Pages 63--64 (of xxiv + 669) in 1971 printing have
                 only brief mention of two papers
                 \cite{Benford:1938:LAN,Pinkham:1961:DFS}.",
}

@Article{FerreriCancho:2002:ZLR,
  author =       "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
  title =        "{Zipf}'s law and random texts",
  journal =      j-ADV-COMPLEX-SYST,
  volume =       "5",
  number =       "1",
  pages =        "1--6",
  year =         "2002",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1142/S0219525902000468",
  ISSN =         "0219-5259",
  bibdate =      "Sat Nov 12 11:00:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1090.91595",
  abstract =     "Random-text models have been proposed as an
                 explanation for the power law relationship between word
                 frequency and rank, the so-called Zipf's law. They are
                 generally regarded as null hypotheses rather than
                 models in the strict sense. In this context, recent
                 theories of language emergence and evolution assume
                 this law as a priori information with no need of
                 explanation. Here, random texts and real texts are
                 compared through (a) the so-called lexical spectrum and
                 (b) the distribution of words having the same length.
                 It is shown that real texts fill the lexical spectrum
                 much more efficiently and regardless of the word
                 length, suggesting that the meaningfulness of Zipf's
                 law is high.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics)",
  fjournal =     "Advances in Complex Systems",
  journal-URL =  "http://www.worldscinet.com/acs/acs.shtml",
  keywords =     "Human language; monkey languages; random texts;
                 scaling; Zipf's law",
}

@Article{FerreriCancho:2003:LEO,
  author =       "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
  title =        "Least effort and the origins of scaling in human
                 language",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "100",
  number =       "3",
  pages =        "788--791",
  day =          "4",
  month =        feb,
  year =         "2003",
  CODEN =        "PNASA6",
  DOI =          "http://dx.doi.org/10.1073/pnas.0335980100",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  bibdate =      "Tue Nov 15 09:44:47 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/search",
  keywords =     "Zipf's Law",
  onlinedate =   "January 22, 2003",
}

@Article{FerreriCancho:2005:CZL,
  author =       "Ramon {Ferrer i Cancho} and Oliver Riordan and
                 B{\'e}la Bollob{\'a}s",
  title =        "The consequences of {Zipf}'s law for syntax and
                 symbolic reference",
  journal =      j-PROC-R-SOC-LOND-SER-B-BIO-SCI,
  volume =       "272",
  number =       "1562",
  pages =        "561--565",
  day =          "7",
  month =        mar,
  year =         "2005",
  CODEN =        "PRLBA4",
  DOI =          "http://dx.doi.org/10.1098/rspb.2004.2957",
  ISSN =         "0962-8452 (print), 1471-2954 (electronic)",
  ISSN-L =       "0962-8452",
  bibdate =      "Tue Nov 15 11:27:26 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rspb.royalsocietypublishing.org/content/272/1562/561.full",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series B.
                 Biological sciences",
}

@Article{Fewster:2009:SEB,
  author =       "Rachel M. Fewster",
  title =        "A Simple Explanation of {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "63",
  number =       "1",
  pages =        "26--32",
  month =        feb,
  year =         "2009",
  CODEN =        "ASTAAJ",
  DOI =          "http://dx.doi.org/10.1198/tast.2009.0005",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2655700",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Filipponi:1995:SPA,
  author =       "Piero Filipponi and Renato Menicocci",
  title =        "Some Probabilistic Aspects of the Terminal Digits of
                 {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "33",
  number =       "4",
  pages =        "325--331",
  month =        aug,
  year =         "1995",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:02:19 MDT 2011",
  bibsource =    "http://www.fq.math.ca/33-4.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Fischer:2010:HCS,
  author =       "Martin H. Fischer and Richard A. Mills and Samuel
                 Shaki",
  title =        "How to cook a {SNARC}: Number placement in text
                 rapidly changes spatial-numerical associations",
  journal =      j-BRAIN-COGN,
  volume =       "72",
  number =       "3",
  pages =        "333--336",
  month =        apr,
  year =         "2010",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/j.bandc.2009.10.010",
  ISSN =         "0278-2626 (print), 1090-2147 (electronic)",
  ISSN-L =       "0278-2626",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0278262609002024",
  acknowledgement = ack-nhfb,
  fjournal =     "Brain and Cognition",
  keywords =     "Benford's Law; Spatial Numerical Association of
                 Response Codes (SNARC)",
}

@Article{Flehinger:1966:PRI,
  author =       "B. J. (Betty J.) Flehinger",
  title =        "On the probability that a random integer has initial
                 digit {$A$}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "73",
  number =       "10",
  pages =        "1056--1061",
  month =        dec,
  year =         "1966",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2314636",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Sat Nov 12 15:33:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2314636",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Book{Fleiss:1981:SMR,
  author =       "Joseph L. Fleiss",
  title =        "Statistical Methods for Rates and Proportions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xviii + 321",
  year =         "1981",
  ISBN =         "0-471-06428-9",
  ISBN-13 =      "978-0-471-06428-2",
  LCCN =         "QA279 .F58 1981",
  bibdate =      "Fri Mar 22 08:46:57 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in probability and mathematical
                 statistics",
  URL =          "http://www.loc.gov/catdir/description/wiley032/80026382.html;
                 http://www.loc.gov/catdir/enhancements/fy0607/80026382-b.html;
                 http://www.loc.gov/catdir/toc/onix02/80026382.html",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Analysis of variance; Sampling (Statistics);
                 Biometry",
}

@Book{Fleiss:2003:SMR,
  author =       "Joseph L. Fleiss and Bruce A. Levin and Myunghee Cho
                 Paik",
  title =        "Statistical Methods for Rates and Proportions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Third",
  pages =        "xxvii + 760",
  year =         "2003",
  ISBN =         "0-471-52629-0 (hardcover)",
  ISBN-13 =      "978-0-471-52629-2 (hardcover)",
  LCCN =         "QA279 .F58 2003",
  bibdate =      "Fri Mar 22 08:46:57 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in probability and statistics",
  URL =          "http://www.loc.gov/catdir/bios/wiley042/2002191005.html;
                 http://www.loc.gov/catdir/description/wiley034/2002191005.html;
                 http://www.loc.gov/catdir/toc/wiley031/2002191005.html",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Analysis of variance; Sampling (Statistics);
                 Biometry",
  tableofcontents = "Preface \\
                 Preface to the Second Edition \\
                 Preface to the First Edition \\
                 1. An Introduction to Applied Probability \\
                 2. Statistical Inference for a Single Proportion \\
                 3. Assessing Significance in a Fourfold Table \\
                 4. Determining Sample Sizes Needed to Detect a
                 Difference Between Two Proportions \\
                 5. How to Randomize \\
                 \\
                 6. Comparative Studies: Cross-Sectional, Naturalistic,
                 or Multinomial Sampling \\
                 \\
                 7. Comparative Studies: Prospective and Retrospective
                 Sampling \\
                 8. Randomized Controlled Trials \\
                 9. The Comparison of Proportions from Several
                 Independent Samples \\
                 10. Combining Evidence from Fourfold Tables \\
                 11. Logistic Regression \\
                 12. Poisson Regression \\
                 13. Analysis of Data from Matched Samples \\
                 14. Regression Models for Matched Samples \\
                 15. Analysis of Correlated Binary Data \\
                 16. Missing Data \\
                 17. Misclassification Errors: Effects, Control, and
                 Adjustment \\
                 18. The Measurement of Interrater Agreement \\
                 19. The Standardization of Rates \\
                 Appendix A. Numerical Tables \\
                 Appendix B. The Basic Theory of Maximum Likelihood",
}

@Article{Fontanari:2004:SNM,
  author =       "J. F. Fontanari and L. I. Perlovsky",
  title =        "Solvable null model for the distribution of word
                 frequencies",
  journal =      j-PHYS-REV-E,
  volume =       "70",
  number =       "??",
  pages =        "042901",
  day =          "25",
  month =        oct,
  year =         "2004",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.70.042901",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.70.042901",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Formann:2010:NBL,
  author =       "A. K. Formann and R. J. Morris",
  title =        "The {Newcomb--Benford Law} in Its Relation to Some
                 Common Distributions",
  journal =      j-PLOS-ONE,
  volume =       "51",
  month =        may,
  year =         "2010",
  CODEN =        "POLNCL",
  DOI =          "http://dx.doi.org/10.1371/journal.pone.0010541",
  ISSN =         "1932-6203",
  ISSN-L =       "1932-6203",
  bibdate =      "Mon Nov 14 18:19:09 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010PLoSO...510541F",
  acknowledgement = ack-nhfb,
  ages =         "10541",
  fjournal =     "PLoS One",
}

@Article{Franel:1917:PTL,
  author =       "J. Franel",
  title =        "{{\`A}} propos des tables de logarithmes. ({French})
                 [{On} tables of logarithms]",
  journal =      "Festschrift Naturforschenden der Gesellschaft in
                 Z{\"u}rich Vierteljahrsschrift",
  volume =       "62",
  number =       "??",
  pages =        "286--295",
  month =        "????",
  year =         "1917",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 10:09:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Friar:2012:GSB,
  author =       "James L. Friar and Terrance Goldman and Juan
                 P{\'e}rez-Mercader",
  title =        "Genome Sizes and the {Benford} Distribution",
  journal =      j-PLOS-ONE,
  volume =       "7",
  number =       "5",
  pages =        "e36624",
  month =        "????",
  year =         "2012",
  CODEN =        "POLNCL",
  DOI =          "http://dx.doi.org/10.1371/journal.pone.0036624",
  ISSN =         "1932-6203",
  ISSN-L =       "1932-6203",
  bibdate =      "Mon Feb 18 19:08:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  accepted =     "11 April 2012",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  onlinedate =   "18 May 2012",
  received =     "7 April 2011",
}

@Article{Friedberg:1984:DFD,
  author =       "Steven H. Friedberg",
  title =        "The distribution of first digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "15",
  number =       "2",
  pages =        "120--125",
  month =        mar,
  year =         "1984",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Sat Feb 16 17:38:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2686516",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
}

@InProceedings{Fu:2007:GBL,
  author =       "D. Fu and Y. Q. Shi and W. Su",
  editor =       "Edward J. {Delp III} and Ping Wah Wong",
  booktitle =    "{Society of Photo-Optical Instrumentation Engineers
                 (SPIE)} Conference Series",
  title =        "A generalized {Benford}'s law for {JPEG} coefficients
                 and its applications in image forensics",
  volume =       "6505",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  month =        feb,
  year =         "2007",
  DOI =          "http://dx.doi.org/10.1117/12.704723",
  ISSN =         "0277-786X (print), 1996-756X (electronic)",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Society of Photo-Optical Instrumentation Engineers
                 (SPIE) Conference Series",
  URL =          "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F",
  acknowledgement = ack-nhfb,
}

@Article{Fuchs:1984:PDP,
  author =       "A. Fuchs and G. Letta",
  title =        "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}.
                 ({French}) [{On} the problem of the first decimal
                 digit]",
  journal =      "{Bollettino della Unione Matem{\`a}tica Italiana.
                 Serie VI. B}",
  volume =       "3",
  pages =        "451--461",
  year =         "1984",
  ISSN =         "0392-4041",
  ISSN-L =       "0392-4041",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0557.60011",
  ajournal =     "Boll. Unione Mat. Ital., VI. Ser., B",
  keywords =     "analytical density; asymptotic density; first-digit
                 problem",
  language =     "French",
  ZMclass =      "60B99 (Probability theory on general structures)",
  ZMreviewer =   "R. Scozzafava",
}

@Article{Fuchs:1994:PDP,
  author =       "Aim{\'e} Fuchs and Giorgio Letta",
  title =        "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
                 les nombres premiers. ({French}) [The problem for the
                 first decimal digit of prime numbers",
  journal =      "Rendiconti della Accademia Nazionale delle Scienze
                 detta dei XL. Serie V. Memorie di Matem{\`a}tica",
  volume =       "18",
  number =       "1",
  pages =        "81--87",
  month =        "????",
  year =         "1994",
  bibdate =      "Sat Feb 16 17:40:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
  ZMnumber =     "0838.11004",
  acknowledgement = ack-nhfb,
  ajournal =     "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.",
  keywords =     "asymptotic densities; logarithmic density; primes;
                 relative densities",
  language =     "French",
  xxjournal =    "Rend. Acad. Naz. Sci. Detta",
  xxvolume =     "XL",
  ZMclass =      "11B05 (Topology etc. of sets of numbers); 11K16
                 (Normal numbers, etc.)",
  ZMreviewer =   "I. Z. Ruzsa (Budapest)",
}

@Article{Fuchs:1996:PDP,
  author =       "Aim{\'e} Fuchs and Giorgio Letta",
  title =        "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
                 les nombres premiers. ({French}) [The problem for the
                 first decimal digit of prime numbers",
  journal =      j-ELECT-J-COMB,
  volume =       "3",
  number =       "2",
  pages =        "R25:1--R25:7",
  month =        "????",
  year =         "1996",
  ISSN =         "1077-8926 (print), 1097-1440 (electronic)",
  ISSN-L =       "1077-8926",
  bibdate =      "Sat Feb 16 17:40:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The Foata Festschrift volume.",
  URL =          "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
  ZMnumber =     "0853.11006",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Combinatorics",
  language =     "French",
  xxpages =      "601--607",
}

@Article{Fujiwara:2004:DPZ,
  author =       "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki
                 Aoyama and Mauro Gallegati and Wataru Souma",
  title =        "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An}
                 analysis with {European} firms",
  journal =      j-PHYSICA-A,
  volume =       "335",
  number =       "1--2",
  pages =        "197--216",
  day =          "1",
  month =        apr,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2003.12.015",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437103011294",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:GPZ,
  author =       "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di
                 Guilmi} and Wataru Souma and Mauro Gallegati",
  title =        "{Gibrat} and {Pareto--Zipf} revisited with {European}
                 firms",
  journal =      j-PHYSICA-A,
  volume =       "344",
  number =       "1--2",
  pages =        "112--116",
  day =          "1",
  month =        dec,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2004.06.098",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437104009173",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:ZLF,
  author =       "Yoshi Fujiwara",
  title =        "{Zipf} law in firms bankruptcy",
  journal =      j-PHYSICA-A,
  volume =       "337",
  number =       "1--2",
  pages =        "219--230",
  day =          "1",
  month =        jun,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2004.01.037",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B38",
  MRnumber =     "2092316",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437104001165",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Book{Furlan:1946:HSU,
  author =       "Luigi Vladimir Furlan",
  title =        "{Das Harmoniegesetz der Statistik: Eine Untersuchung
                 {\"u}ber die metrische Interdependenz der sozialen
                 Erscheinungen}. ({German}) [{The} {Law of Harmony} in
                 statistics: an investigation of the metrical
                 interdependence of social phenomena]",
  volume =       "2",
  publisher =    "Verlag f{\"u}r Recht und Gesellschaft A.-G.",
  address =      "Basel, Switzerland",
  pages =        "xii + 504",
  year =         "1946",
  LCCN =         "HA29 .F85",
  bibdate =      "Mon Nov 14 09:40:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "{Beihefte zum Assekuranzjahrbuch}",
  acknowledgement = ack-nhfb,
  author-dates = "1886--",
  keywords =     "Benford--Furlan Law",
  language =     "German",
}

@Article{Furry:1945:DND,
  author =       "W. H. Furry and Henry Hurwitz",
  title =        "Distribution of Numbers and Distribution of
                 Significant Figures",
  journal =      j-NATURE,
  volume =       "155",
  number =       "3924",
  pages =        "52--53",
  day =          "13",
  month =        jan,
  year =         "1945",
  CODEN =        "NATUAS",
  DOI =          "http://dx.doi.org/10.1038/155052a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:51:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Furusawa:2003:ZLG,
  author =       "Chikara Furusawa and Kunihiko Kaneko",
  title =        "{Zipf's Law} in Gene Expression",
  journal =      j-PHYS-REV-LET,
  volume =       "90",
  number =       "??",
  pages =        "088102",
  day =          "26",
  month =        feb,
  year =         "2003",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.90.088102",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Gabaix:1999:ZLC,
  author =       "Xavier Gabaix",
  title =        "{Zipf}'s law for cities: An explanation",
  journal =      j-Q-J-ECON,
  volume =       "114",
  number =       "3",
  pages =        "739--767",
  year =         "1999",
  CODEN =        "QJECAT",
  DOI =          "http://dx.doi.org/10.1162/003355399556133",
  ISSN =         "0033-5533 (print), 1531-4650 (electronic)",
  ISSN-L =       "0033-5533",
  bibdate =      "Sat Nov 12 10:57:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0952.91059",
  abstract =     "Zipf's law is a very tight constraint on the class of
                 admissible models of local growth. It says that for
                 most countries the size distribution of cities
                 strikingly fits a power law: the number of cities with
                 populations greater than $S$ is proportional to $ 1 / S
                 $. Suppose that, at least in the upper tail, all cities
                 follow some proportional growth process (this appears
                 to be verified empirically). This automatically leads
                 their distribution to converge to Zipf's law.",
  acknowledgement = ack-nhfb,
  ajournal =     "Q. J. Econ.",
  classmath =    "91B62 (Dynamic economic models etc.) 91B72 (Spatial
                 models)",
  fjournal =     "The Quarterly Journal of Economics",
  keywords =     "local growth; Zipf's law",
}

@Article{Gabaix:2003:TPL,
  author =       "Xavier Gabaix and Parameswaran Gopikrishnan and
                 Vasiliki Plerou and H. Eugene Stanley",
  title =        "A theory of power-law distributions in financial
                 market fluctuations",
  journal =      j-NATURE,
  volume =       "423",
  number =       "6937",
  pages =        "267--270",
  day =          "15",
  month =        may,
  year =         "2003",
  CODEN =        "NATUAS",
  DOI =          "http://dx.doi.org/10.1038/nature01624",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Feb 27 06:45:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Zipf's Law",
}

@Article{Gaite:2006:CSZ,
  author =       "Jos{\'e} Gaite",
  title =        "Cut-out sets and the {Zipf} law for fractal voids",
  journal =      j-PHYSICA-D,
  volume =       "223",
  number =       "2",
  pages =        "248--255",
  day =          "15",
  month =        nov,
  year =         "2006",
  CODEN =        "PDNPDT",
  DOI =          "http://dx.doi.org/10.1016/j.physd.2006.09.021",
  ISSN =         "0167-2789 (print), 1872-8022 (electronic)",
  ISSN-L =       "0167-2789",
  MRclass =      "28A80",
  MRnumber =     "2307212",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167278906003848",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica. D, Nonlinear phenomena",
  keywords =     "Zipf's Law",
}

@Article{Gambini:2012:PDD,
  author =       "Alessandro Gambini and Giovanni Mingari Scarpello and
                 Daniele Ritelli",
  title =        "Probability of digits by dividing random numbers: a $
                 \psi $ and $ \zeta $ functions approach",
  journal =      j-EXPO-MATH,
  volume =       "30",
  number =       "3",
  pages =        "223--238",
  month =        "????",
  year =         "2012",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/j.exmath.2012.03.001",
  ISSN =         "0723-0869 (print), 1878-0792 (electronic)",
  ISSN-L =       "0723-0869",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0723086912000230",
  acknowledgement = ack-nhfb,
  ajournal =     "Expo. Math.",
  fjournal =     "Expositiones Mathematicae",
  hoc-program-1 = "func p(r) return(1/20 + (1/2)*(psi((r + 11)/10) -
                 psi(r/10 + 1)))",
  hoc-program-2 = "for (r = 0; r < 10; ++r) printf({"}%2d: %.5f {"}, r,
                 p(r)); println {""}",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07230869",
  keywords =     "Euler $\psi$ function; Hurwitz $\zeta$ function",
  remark =       "This paper proves formulas for the probability of
                 first-digit occurrences in the ratios of random
                 integers, and compares the predictions with the
                 somewhat different ones from Benford's Law. Their work
                 simplifies a result of Ces{\`a}ro (1885), and predicts
                 that the probability of the first quotient digit being
                 $r$ is given by $ p(r) = 1 / 20 + (1 / 2)*(\psi ((r +
                 11) / 10) - \psi (r / 10 + 1))) $. That predicts these
                 pairs of $ (r, p(r)) $: $ (0, 0.12673) $, $ (1,
                 0.11736) $, $ (2, 0.10992) $, $ (3, 0.10390) $, $ (4,
                 0.09894) $, $ (5, 0.09478) $, $ (6, 0.09125) $, $ (7,
                 0.08822) $, $ (8, 0.08560) $, $ (9, 0.08330) $. Those
                 values may be compared with the Benford's Law
                 prediction for the second digit (possibly zero) of $
                 (0, 0.120) $, $ (1, 0.114) $, $ (2, 0.109) $, $ (3,
                 0.104) $, $ (4, 0.100) $, $ (5, 0.097) $, $ (6, 0.093)
                 $, $ (7, 0.090) $, $ (8, 0.088) $, and $ (9, 0.085)
                 $.",
}

@Article{Gan:2006:ZLS,
  author =       "Li Gan and Dong Li and Shunfeng Song",
  title =        "Is the {Zipf} law spurious in explaining city-size
                 distributions?",
  journal =      j-ECONOM-LETT,
  volume =       "92",
  number =       "2",
  pages =        "256--262",
  day =          "1",
  month =        aug,
  year =         "2006",
  CODEN =        "ECLEDS",
  DOI =          "http://dx.doi.org/10.1016/j.econlet.2006.03.004",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176506000772",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@InCollection{Gangopadhyay:2013:EZL,
  author =       "Kausik Gangopadhyay and Banasri Basu",
  title =        "Evolution of {Zipf}'s law for {Indian} urban
                 agglomerations via-{\`a}-vis {Chinese} urban
                 agglomerations",
  crossref =     "Abergel:2013:ESR",
  pages =        "119--129",
  year =         "2013",
  DOI =          "http://dx.doi.org/10.1007/978-88-470-2553-0_8",
  MRclass =      "91B80",
  MRnumber =     "2963609",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "New Econ. Windows",
  acknowledgement = ack-nhfb,
}

@Article{Garcia:2011:FPA,
  author =       "Juan Manuel Garcia Garcia",
  title =        "A fixed-point algorithm to estimate the {Yule-Simon}
                 distribution parameter",
  journal =      j-APPL-MATH-COMP,
  volume =       "217",
  number =       "21",
  pages =        "8560--8566",
  day =          "1",
  month =        jul,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "http://dx.doi.org/10.1016/j.amc.2011.03.092",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 12:05:30 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311004607",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Gauvrit:2008:PLB,
  author =       "Nicolas Gauvrit and Jean-Paul Delahaye",
  title =        "Pourquoi la loi de {Benford} n'est pas
                 myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is
                 not mysterious]",
  journal =      "Math{\'e}matiques et Sciences Humaines = Mathematics
                 and Social Sciences",
  volume =       "46",
  number =       "182",
  pages =        "7--15",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "0987-6936 (print), 1950-6821 (electronic)",
  ISSN-L =       "0987-6936",
  MRclass =      "62A01 (91E10)",
  MRnumber =     "2433183 (2009f:62008)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Sci. Hum. Math. Soc. Sci.",
  fjournal =     "Math{\'e}matiques et Sciences Humaines= Mathematics
                 and Social Sciences",
  language =     "French",
}

@Article{Gauvrit:2009:LBG,
  author =       "Nicolas Gauvrit and Jean-Paul Delahaye",
  title =        "Loi de {Benford} g{\'e}n{\'e}rale. ({French})
                 [{General} {Benford}'s law]",
  journal =      "Math. Sci. Hum. Math. Soc. Sci.",
  volume =       "??",
  number =       "186",
  pages =        "5--15",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0987-6936 (print), 1950-6821 (electronic)",
  ISSN-L =       "0987-6936",
  MRclass =      "62E10 (11A63 37A45)",
  MRnumber =     "2562062 (2010i:62029)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://msh.revues.org/document11034.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Math{\'e}matiques et Sciences Humaines. Mathematics
                 and Social Sciences",
  language =     "French",
}

@Article{Gauvrit:2009:SRI,
  author =       "N. Gauvrit and J.-P. Delahaye",
  title =        "Scatter and regularity imply {Benford}'s law \ldots{}
                 and more",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G;
                 http://arxiv.org/abs/0910.1359",
  abstract =     "A random variable (r.v.) $X$ is said to follow
                 Benford's law if $ \log (X) $ is uniform $ \bmod 1 $.
                 Many experimental data sets prove to follow an
                 approximate version of it, and so do many mathematical
                 series and continuous random variables. This phenomenon
                 received some interest, and several explanations have
                 been put forward. Most of them focus on specific data,
                 depending on strong assumptions, often linked with the
                 log function. Some authors hinted --- implicitly ---
                 that the two most important characteristics of a random
                 variable when it comes to Benford are regularity and
                 scatter. In a first part, we prove two theorems, making
                 up a formal version of this intuition: scattered and
                 regular r.v.'s do approximately follow Benford's law.
                 The proofs only need simple mathematical tools, making
                 the analysis easy. Previous explanations thus become
                 corollaries of a more general and simpler one. These
                 results suggest that Benford's law does not depend on
                 properties linked with the log function. We thus
                 propose and test a general version of the Benford's
                 law. The success of these tests may be viewed as an a
                 posteriori validation of the analysis formulated in the
                 first part.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0910.1359",
  keywords =     "Mathematics - Probability, Statistics - Methodology,
                 G.3",
  primaryclass = "math.PR",
}

@InCollection{Gauvrit:2011:SRI,
  author =       "N. Gauvrit and J-P. Delahaye",
  title =        "Scatter and Regularity Implies {Benford's Law}\ldots{}
                 and More",
  crossref =     "Zenil:2011:RTC",
  pages =        "53--69",
  year =         "2011",
  bibdate =      "Mon Feb 18 18:29:00 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Geiringer:1948:RVF,
  author =       "Hilda Geiringer",
  title =        "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz
                 der Statistik: Eine Untersuchung {\"u}ber die metrische
                 Interdependenz der sozialen Erscheinungen}. ({German})
                 [{The} {Law of Harmony} in statistics: an investigation
                 of the metrical interdependence of social phenomena]",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "43",
  number =       "242",
  pages =        "325--328",
  month =        jun,
  year =         "1948",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Mon Nov 14 09:42:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See \cite{Furlan:1946:HSU}.",
  URL =          "http://www.jstor.org/stable/2280379",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Gelbukh:2001:ZHL,
  author =       "Alexander Gelbukh and Grigori Sidorov",
  title =        "{Zipf} and {Heaps Laws}' Coefficients Depend on
                 Language",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2004",
  pages =        "332--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
}

@InCollection{Gell-Mann:1997:ETZ,
  author =       "Murray Gell-Mann",
  title =        "Empirical Theory --- {Zipf}'s Law",
  crossref =     "Gell-Mann:1997:QJA",
  pages =        "92--97",
  year =         "1997",
  bibdate =      "Mon Sep 01 10:20:00 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Genolini:2010:EIP,
  author =       "Christophe Genolini and Tarak Driss",
  title =        "Eveiller l'int{\'e}r{\^e}t pour la statistique par
                 l'exemple. ({French}) [{Raising} interest in statistics
                 by example]",
  journal =      "Statistique et Enseignement",
  volume =       "1",
  number =       "2",
  pages =        "49--57",
  month =        "????",
  year =         "2010",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "2108-6745",
  ISSN-L =       "2108-6745",
  bibdate =      "Mon Feb 18 17:43:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.statistique-et-enseignement.fr/",
  keywords =     "Benford's Law",
  language =     "French",
}

@TechReport{Gent:2001:BL,
  author =       "Ian Gent and Toby Walsh",
  title =        "{Benford's Law}",
  type =         "Report",
  institution =  "School of Computer Science, University of St. Andrews,
                 and Department of Computer Science, University of
                 York",
  address =      "St. Andrews, Scotland and York, England",
  pages =        "7",
  day =          "2",
  month =        feb,
  year =         "2001",
  bibdate =      "Fri Nov 18 08:37:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf",
  abstract =     "Benford's Law predicts the frequency of the leading
                 digit in numbers met in a wide range of naturally
                 occurring phenomena. In data following Benford's Law,
                 numbers start with a small leading digit more often
                 those with a large leading digit. Here we demonstrate
                 that Benford's Law also describes a wide range of
                 computational phenomena. In particular, we show that a
                 number of different statistics associated with
                 computation like space and runtime often follow
                 Benford's Law. We also show that search cost on input
                 data that follows Benford's Law is often very different
                 to that on more uniform data. These results could be
                 used to improve algorithm performance (for example, for
                 load balancing or disk de-fragmentation), as well as to
                 help model algorithm performance. Benford's Law can
                 also be used to generate data for benchmarking
                 algorithms that may be more realistic than purely
                 random data.",
  acknowledgement = ack-nhfb,
  remark =       "PDF file no longer at the St. Andrews URL on 18
                 November 2011, but recovered from
                 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.",
}

@Article{Geyer:2004:DFD,
  author =       "Christina Lynn Geyer and Patricia Pepple Williamson",
  title =        "Detecting fraud in data sets using {Benford's Law}",
  journal =      j-COMM-STAT,
  volume =       "B33",
  number =       "1",
  pages =        "229--246",
  month =        "????",
  year =         "2004",
  CODEN =        "CSSCDB",
  DOI =          "http://dx.doi.org/10.1081/SAC-120028442",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  MRclass =      "62-07",
  MRnumber =     "2044866",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Statist. Simulation Comput.",
  fjournal =     "Communications in Statistics. Simulation and
                 Computation",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Geyer:2012:ABL,
  author =       "A. Geyer and J. Mart{\'\i}",
  title =        "Applying {Benford}'s law to volcanology",
  journal =      "Geology",
  volume =       "40",
  number =       "4",
  pages =        "327--330",
  month =        apr,
  year =         "2012",
  DOI =          "http://dx.doi.org/10.1130/G32787.1",
  bibdate =      "Mon Feb 18 19:11:36 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://geology.gsapubs.org/content/40/4/327",
  acknowledgement = ack-nhfb,
}

@Book{Gibrat:1931:IE,
  author =       "Robert Gibrat",
  title =        "Les In{\'e}galit{\'e}s {\'e}conomiques",
  publisher =    "Librairie du Recueil Sirey",
  address =      "Paris, France",
  pages =        "286",
  year =         "1931",
  LCCN =         "HB251.GIB",
  bibdate =      "Mon Feb 18 14:43:11 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 library.ox.ac.uk:210/ADVANCE",
  note =         "Applications: aux in{\'e}galit{\'e}s des richesses,
                 {\`a} la concentration des entreprises, aux populations
                 des villes, aux statistiques des familles, etc. d'une
                 loi nouvelle. La loi de l'effet proportionnel.",
  URL =          "http://en.wikipedia.org/wiki/Gibrat%27s_law",
  acknowledgement = ack-nhfb,
  author-dates = "1904--1980",
  remark-1 =     "According to at least one library catalog (SWB), this
                 book may be the author's doctoral dissertation from
                 l'Universit{\'e} de Paris in 1931.",
  remark-2 =     "This book is cited as the origin of Gibrat's Law, or
                 Gibrat's rule of proportionate growth, that ``the size
                 of a firm and its growth rate are independent''.",
}

@TechReport{Giles:2005:BLN,
  author =       "David E. Giles",
  title =        "{Benford's Law} and Naturally Occurring Prices in
                 Certain {ebaY} Auctions",
  type =         "Econometrics Working Paper",
  number =       "EWP0505",
  institution =  "Department of Economics, University of Victoria",
  address =      "Victoria, BC, Canada",
  month =        may,
  year =         "2005",
  ISSN =         "1485-6441",
  bibdate =      "Thu Feb 15 16:24:39 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://web.uvic.ca/econ/ewp0505.pdf",
  abstract =     "We show that certain the winning bids for certain ebaY
                 auctions obey Benford's Law. One implication of this is
                 that it is unlikely that these bids are subject to
                 collusion among bidders, or ``shilling'' on the part of
                 sellers. Parenthetically, we also show that numbers
                 from the naturally occurring Fibonacci and Lucas
                 sequences also obey Benford's Law.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Giles:2007:BLN,
  author =       "D. E. Giles",
  title =        "{Benford's Law} and naturally occurring prices in
                 certain {eBay} auctions",
  journal =      j-APPL-ECON-LETT,
  volume =       "14",
  number =       "3",
  pages =        "157--161",
  year =         "2007",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/13504850500425667",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Wed Nov 16 09:49:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/toc/rael20/current",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  keywords =     "Benford's Law; Fibonacci sequences; Lucas sequences",
}

@Article{Gini:1957:SFD,
  author =       "Corrado Gini",
  title =        "Sulla frequenza delle cifre iniziali dei numeri
                 osservati. ({Italian}) [{On} the frequency of initial
                 digits of observed numbers]",
  journal =      "{Bulletin de l'Institut International de
                 Statistique}",
  volume =       "35",
  number =       "2",
  pages =        "57--76",
  year =         "1957",
  CODEN =        "BISQA3",
  ISSN =         "????",
  MRclass =      "62.00",
  MRnumber =     "0117807 (22 \#8581)",
  bibdate =      "Sun Sep 18 11:54:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "29th session, 2nd delivery, Rio de Janerio.",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Internat. Stat.",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
  xxvolume =     "34 (wrong!)",
}

@Article{Gisin:2009:EEV,
  author =       "Vladimir Gisin and Andrey Markov and Igor Vinukov",
  title =        "Estimation of extreme values of returns using the
                 {Zipf--Mandelbrot} flow",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "50",
  number =       "2",
  pages =        "245--250",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1311-8080",
  ISSN-L =       "1314-3395",
  MRclass =      "60G70 (91B28 91B84)",
  MRnumber =     "2488836",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
}

@Article{Giuliano:2010:UPI,
  author =       "Rita Giuliano and {\'E}lise Janvresse",
  title =        "A unifying probabilistic interpretation of {Benford}'s
                 law",
  journal =      "Uniform Distribution Theory",
  volume =       "5",
  number =       "2",
  pages =        "169--182",
  year =         "2010",
  CODEN =        "????",
  ISSN =         "1336-913X",
  ISSN-L =       "1336-913X",
  MRclass =      "60J10 (11K99 60A99)",
  MRnumber =     "2781415",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Unif. Distrib. Theory",
  fjournal =     "Uniform Distribution Theory",
}

@Article{Giuliano:2011:WCS,
  author =       "Rita Giuliano",
  title =        "Weak convergence of sequences from fractional parts of
                 random variables and applications",
  journal =      j-THEORY-PROBAB-MATH-STAT,
  volume =       "83",
  number =       "??",
  pages =        "49--58",
  month =        "????",
  year =         "2011",
  CODEN =        "TPMSCO",
  DOI =          "????",
  ISSN =         "0094-9000 (print), 1547-7363 (electronic)",
  ISSN-L =       "0094-9000",
  MRclass =      "60F05, 60G52, 60G70, 11K06 (62G07, 42A10, 42A61)",
  MRnumber =     "http://www.ams.org/mathscinet-getitem?mr=2768848",
  bibdate =      "Mon Feb 18 17:47:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and Mathematical Statistics",
  journal-URL =  "http://www.ams.org/publications/journals/journalsframework/tpms",
  keywords =     "Benford's Law",
}

@TechReport{Gonzales-Garcia:2009:BLM,
  author =       "J. Gonzales-Garcia and G. Pastor",
  title =        "{Benford's Law} and Macroeconomic Data Quality",
  type =         "Working Paper",
  institution =  "International Monetary Fund",
  address =      "????",
  year =         "2009",
  bibdate =      "Tue Nov 22 18:53:16 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437",
  acknowledgement = ack-nhfb,
}

@Article{Good:1965:LE,
  author =       "I. J. Good",
  title =        "Letter to the Editor",
  journal =      j-AMER-STAT,
  volume =       "19",
  number =       "3",
  pages =        "43--43",
  month =        jun,
  year =         "1965",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 09:56:33 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2681423",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law",
  remark =       "Refers to \cite{Pinkham:1961:DFS}, and cites a review
                 of that article published by Good in Mathematical
                 Reviews (1962), page 214, which I have not yet been
                 able to locate.",
}

@InCollection{Gorroochurn:2012:BPB,
  author =       "Prakash Gorroochurn",
  title =        "{Benford} and the Peculiar Behavior of the First
                 Significant Digit (1938)",
  crossref =     "Gorroochurn:2012:CPP",
  chapter =      "27",
  pages =        "233--239",
  year =         "2012",
  DOI =          "http://dx.doi.org/10.1002/9781118314340.ch27",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "(Benford) distribution; a distribution of
                 distributions; and Benford's law; Benford and the
                 peculiar behavior of the first significant digit
                 (1938); First 100 Fibonacci Numbers; first-digit law or
                 Benford's law; scale invariance; the leading digit and
                 its behavior",
}

@Article{Goto:1992:SEB,
  author =       "Kazuo Got{\^o}",
  title =        "Some examples of {Benford} sequences",
  journal =      "Math. J. Okayama Univ.",
  volume =       "34",
  pages =        "225--232 (1994)",
  year =         "1992",
  CODEN =        "MJOKAP",
  ISSN =         "0030-1566",
  ISSN-L =       "0030-1566",
  MRclass =      "11K36",
  MRnumber =     "1272624 (95c:11097)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Journal of Okayama University",
}

@Article{Gottwald:2002:NBL,
  author =       "Georg A. Gottwald and Matthew Nicol",
  title =        "On the nature of {Benford's Law}",
  journal =      j-PHYSICA-A,
  volume =       "303",
  number =       "3--4",
  pages =        "387--396",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(01)00497-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "60C05 (28D05 60E05 82B05)",
  MRnumber =     "1917635 (2003d:60015)",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://adsabs.harvard.edu/abs/2002PhyA..303..387G;
                 http://www.sciencedirect.com/science/article/pii/S0378437101004976",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Goudsmit:1944:SFN,
  author =       "S. A. Goudsmit and W. H. Furry",
  title =        "Significant Figures of Numbers in Statistical Tables",
  journal =      j-NATURE,
  volume =       "154",
  number =       "3921",
  pages =        "800--801",
  day =          "23",
  month =        dec,
  year =         "1944",
  CODEN =        "NATUAS",
  DOI =          "http://dx.doi.org/10.1038/154800a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:57:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See later work \cite{Logan:1978:FDP}, and severe
                 criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.",
  URL =          "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
  abstract =     "A rough qualitative explanation of this fact can
                 easily be given. If we consider tables in which the
                 entries become rarer the larger they are, we can draw
                 the obvious conclusion that in any interval, say,
                 between 10 and 99, or 10,000 and 99,999, there are more
                 entries on the small side than on the large side.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@Article{Goudsmit:1977:PEP,
  author =       "Samuel Goudsmit",
  title =        "Pitfalls in Elementary Probability",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "121",
  number =       "2",
  pages =        "188--189",
  day =          "29",
  month =        apr,
  year =         "1977",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X",
  bibdate =      "Fri Mar 22 08:50:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Based on a lecture presented November 11, 1976.",
  URL =          "http://www.jstor.org/stable/986527",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  keywords =     "Benford's Law; biased coin flips; biased dice throws;
                 roulette wheels",
}

@Article{Grabski:2010:DDM,
  author =       "Severin Grabski",
  title =        "Discussion of {``Data mining journal entries for fraud
                 detection: An exploratory study''}",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "182--185",
  month =        sep,
  year =         "2010",
  CODEN =        "IJAIA7",
  DOI =          "http://dx.doi.org/10.1016/j.accinf.2010.07.008",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089510000394",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
}

@Article{Green:1986:BRP,
  author =       "M. W. Green",
  title =        "Book Reviews: {{\em Pareto Distributions}}, by {B. C.
                 Arnold}",
  journal =      j-APPL-STAT,
  volume =       "35",
  number =       "2",
  pages =        "215--215",
  year =         "1986",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:24:36 MDT 2001",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@InProceedings{Grekos:2003:RSC,
  author =       "G. Grekos and R. Giuliano-Antonini",
  editor =       "????",
  booktitle =    "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July
                 6--12, 2003}",
  title =        "Regular sets and conditional density: an extension of
                 {Benford}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:43:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Grendar:2007:ENP,
  author =       "Marian Grendar and George Judge and Laura Schechter",
  title =        "An empirical non-parametric likelihood family of
                 data-based {Benford}-like distributions",
  journal =      j-PHYSICA-A,
  volume =       "380",
  number =       "??",
  pages =        "429--438",
  day =          "1",
  month =        jul,
  year =         "2007",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2007.02.062",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://adsabs.harvard.edu/abs/2007PhyA..380..429G;
                 http://www.sciencedirect.com/science/article/pii/S0378437107001963",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
  keywords =     "Benford's Law",
}

@InProceedings{Guettler:2012:BGQ,
  author =       "S. Guettler and F. Thiemann and R. A. E. Mueller",
  editor =       "M. Clasen and G. Fr{\"o}hlich and H. Bernhardt and K.
                 Hildebrand and B. Theuvsen",
  booktitle =    "{Informationstechnologie f{\"u}r eine nachhaltige
                 Landbewirtschaftung. Fokus Forstwirtschaft. Referate
                 der 32. GIL-Jahrestagung, 29. Februar--1. M{\"a}rz
                 2012, Freising}. ({German}) [Information technology for
                 sustainable land management. Focus on forestry. Papers
                 of the 32nd GIL Annual Conference 29, February--1 March
                 2012, Freising]",
  title =        "{Benfords Gesetz: Ein Qualit{\"a}tstest f{\"u}r
                 statistische Reihen angewendet auf Handelsdaten f{\"u}r
                 Agrarprodukte}. ({German}) [{Benford's Law}: a quality
                 test applied for statistical series on trade data for
                 agricultural products]",
  volume =       "194",
  publisher =    "Gesellschaft f{\"u}r Informatik.",
  address =      "Bonn, Germany",
  pages =        "111--114",
  year =         "2012",
  ISBN =         "3-88579-288-5",
  ISBN-13 =      "978-3-88579-288-8",
  ISSN =         "1617-5468",
  LCCN =         "????",
  bibdate =      "Tue Feb 19 05:44:08 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Informatics",
  URL =          "http://www.gil-net.de/Publikationen/24_111.pdf",
  acknowledgement = ack-nhfb,
  bookpages =    "334 (est.)",
  language =     "German",
}

@Article{Gunnel:2009:DBL,
  author =       "S. G{\"u}nnel and K.-H. T{\"o}dter",
  title =        "Does {Benford's Law} Hold in Economic Research and
                 Forecasting?",
  journal =      j-EMPIRICA,
  volume =       "36",
  number =       "3",
  pages =        "273--292",
  month =        aug,
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1007/s10663-008-9084-1",
  ISSN =         "0340-8744 (print), 1573-6911 (electronic)",
  ISSN-L =       "0340-8744",
  bibdate =      "Thu Nov 17 19:16:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.springerlink.com/content/100261/",
  abstract =     "First and higher order digits in data sets of natural
                 and socio-economic processes often follow a
                 distribution called Benford's law. This phenomenon has
                 been used in business and scientific applications,
                 especially in fraud detection for financial data. In
                 this paper, we analyse whether Benford's law holds in
                 economic research and forecasting. First, we examine
                 the distribution of regression coefficients and
                 standard errors in research papers, published in
                 Empirica and Applied Economics Letters. Second, we
                 analyse forecasts of GDP growth and CPI inflation in
                 Germany, published in Consensus Forecasts. There are
                 two main findings: The relative frequencies of the
                 first and second digits in economic research are
                 broadly consistent with Benford's law. In sharp
                 contrast, the second digits of Consensus Forecasts
                 exhibit a massive excess of zeros and fives, raising
                 doubts on their information content.",
  acknowledgement = ack-nhfb,
  fjournal =     "Empirica",
}

@Article{Gunther:1992:PCZ,
  author =       "R. G{\"u}nther and B. Schapiro and P. Wagner",
  title =        "Physical complexity and {Zipf}'s law",
  journal =      j-INT-J-THEOR-PHYS,
  volume =       "31",
  number =       "3",
  pages =        "525--543",
  year =         "1992",
  CODEN =        "IJTPBM",
  DOI =          "http://dx.doi.org/10.1007/BF00740003",
  ISSN =         "0020-7748 (print), 1572-9575 (electronic)",
  ISSN-L =       "0020-7748",
  MRclass =      "58F40",
  MRnumber =     "1154668 (92k:58252)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Theoretical Physics",
  journal-URL =  "http://link.springer.com/journal/10773",
}

@Article{Gunther:1996:ZLE,
  author =       "R. G{\"u}nther and L. Levitin and B. Schapiro and P.
                 Wagner",
  title =        "{Zipf}'s law and the effect of ranking on probability
                 distributions",
  journal =      j-INT-J-THEOR-PHYS,
  volume =       "35",
  number =       "2",
  pages =        "395--417",
  year =         "1996",
  CODEN =        "IJTPBM",
  DOI =          "http://dx.doi.org/10.1007/BF02083823",
  ISSN =         "0020-7748 (print), 1572-9575 (electronic)",
  ISSN-L =       "0020-7748",
  bibdate =      "Sat Nov 12 10:53:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0843.60002",
  abstract =     "Ranking procedures are widely used in the description
                 of many different types of complex systems. Zipf's law
                 is one of the most remarkable frequency-rank
                 relationships and has been observed independently in
                 physics, linguistics, biology, demography, etc. We show
                 that ranking plays a crucial role in making it possible
                 to detect empirical relationships in systems that exist
                 in one realization only, even when the statistical
                 ensemble to which the systems belong has a very broad
                 probability distribution. Analytical results and
                 numerical simulations are presented which clarify the
                 relations between the probability distributions and the
                 behavior of expected values for unranked and ranked
                 random variables. This analysis is performed, in
                 particular, for the evolutionary model presented in our
                 previous papers which leads to Zipf's law and reveals
                 the underlying mechanism of this phenomenon in terms of
                 a system with interdependent and interacting components
                 as opposed to the ``ideal gas'' models suggested by
                 previous researchers. The ranking procedure applied to
                 this model leads to a new, unexpected phenomenon: a
                 characteristic ``staircase'' behavior of the mean
                 values of the ranked variables (ranked occupation
                 numbers). This result is due to the broadness of the
                 probability distributions for the occupation numbers
                 and does not follow from the ``ideal gas'' model. Thus,
                 it provides an opportunity, by comparison with
                 empirical data, to obtain evidence as to which model
                 relates to reality.",
  acknowledgement = ack-nhfb,
  classmath =    "60A99 (Foundations of probability theory)",
  fjournal =     "International Journal of Theoretical Physics",
  journal-URL =  "http://link.springer.com/journal/10773",
  keywords =     "numerical simulations; ranking procedures; Zipf's
                 law",
}

@Article{Guo:2007:DIM,
  author =       "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao
                 and Xiaodong Zhang",
  title =        "Does {Internet} media traffic really follow
                 {Zipf}-like distribution?",
  journal =      j-SIGMETRICS,
  volume =       "35",
  number =       "1",
  pages =        "359--360",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  DOI =          "http://doi.acm.org/10.1145/1254882.1254929",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Fri Jun 27 09:42:48 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "It is commonly agreed that Web traffic follows the
                 Zipf-like distribution, which is an analytical
                 foundation for improving Web access performance by
                 client-server based proxy caching systems on the
                 Internet. However, some recent studies have observed
                 non-Zipf-like distributions of Internet media traffic
                 in different content delivery systems. Due to the
                 variety of media delivery systems and the diversity of
                 media content, existing studies on media traffic are
                 largely workload specific, and the observed access
                 patterns are often different from or even conflict with
                 each other. For Web media systems, study [3] reports
                 that the access pattern of streaming media is Zipf-like
                 in a university campus network, while study [2] finds
                 that it is not Zipf-like in an enterprise media
                 server.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "media; stretched exponential; Zipf-like",
}

@Article{Gupta:2007:IMS,
  author =       "Arjun K. Gupta and Saralees Nadarajah",
  title =        "Information matrices for some bivariate {Pareto}
                 distributions",
  journal =      j-APPL-MATH-COMP,
  volume =       "184",
  number =       "2",
  pages =        "1069--1079",
  day =          "15",
  month =        jan,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:01 MDT 2008",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@InProceedings{Haferkorn:2013:HVA,
  author =       "Martin Haferkorn",
  editor =       "Fethi Rabhi and Peter Gomber",
  booktitle =    "{Enterprise applications and services in the finance
                 industry: 6th International Workshop, FinanceCom 2012,
                 Barcelona, Spain, June 10, 2012. Revised papers}",
  title =        "Humans vs. Algorithms --- Who Follows
                 {Newcomb--Benford's Law} Better with Their Order
                 Volume?",
  chapter =      "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "61--70",
  year =         "2013",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-36219-4_4",
  ISBN =         "3-642-36219-2",
  ISBN-13 =      "978-3-642-36219-4",
  LCCN =         "HG173 .I58 2012",
  bibdate =      "Wed Feb 13 19:15:28 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4_4",
  acknowledgement = ack-nhfb,
  book-URL =     "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4",
  remark =       "This may be the first publication to reference this
                 bibliography. It examines trading patterns of several
                 days on the German Stock Exchange (Deutsche B{\"o}rse),
                 with a total volume of almost 10 million trades, split
                 almost equally between human and algorithmic traders.
                 It finds that the algorithmic trades follow Benford's
                 Law closely, but the human trades do not. It points out
                 that algorithmic trading could be manipulated to make
                 it look more like human trades, so as not to alert
                 competitors to its actions.",
  subject =      "Financial services industry; Information technology;
                 Congresses; Data processing",
}

@Unpublished{Hafner:1969:CSR,
  author =       "Everett M. Hafner",
  title =        "Circular slide roulette",
  year =         "1969",
  bibdate =      "Mon Nov 14 10:00:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unpublished but dated 1969. Presented in 1975 in an
                 address at Hampshire College, Amherst, MA, USA",
  acknowledgement = ack-nhfb,
}

@Article{Haight:1969:TPD,
  author =       "F. A. Haight",
  title =        "Two probability distributions connected with {Zipf}'s
                 rank-size conjecture",
  journal =      j-ZASTOS-MAT,
  volume =       "10",
  pages =        "225--228",
  year =         "1969",
  CODEN =        "ZAMTAK",
  ISSN =         "0044-1899",
  ISSN-L =       "0044-1899",
  MRclass =      "62.31",
  MRnumber =     "0246425 (39 \#7729)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Polska Akademia Nauk. Instytut Matematyczny.
                 Zastosowania Matematyki",
}

@Article{Hales:2009:TBL,
  author =       "Douglas N. Hales and Satya S. Chakravorty and V.
                 Sridharan",
  title =        "Testing {Benford's Law} for improving supply chain
                 decision-making: a field experiment",
  journal =      j-INT-J-PROD-ECON,
  volume =       "122",
  number =       "2",
  pages =        "606--618",
  month =        dec,
  year =         "2009",
  CODEN =        "JPCEYE",
  DOI =          "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
  ISSN =         "0925-5273 (print), 1873-7579 (electronic)",
  ISSN-L =       "0925-5273",
  bibdate =      "Wed Nov 23 18:41:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. j. prod. econ.",
  fjournal =     "International Journal of Production Economics",
}

@Book{Hamming:1962:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "411",
  year =         "1962",
  LCCN =         "QA297 .H28",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis; Electronic digital computers",
}

@Article{Hamming:1965:NLB,
  author =       "R. W. Hamming and W. L. Mammel",
  title =        "A Note on the Location of the Binary Point in a
                 Computing Machine",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "260--261",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "http://dx.doi.org/10.1109/PGEC.1965.264258",
  ISSN =         "0367-7508",
  ISSN-L =       "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "http://www.computer.org/tc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "The authors consider the low-level multiplication
                 circuit efficiency of placing the binary point before
                 or after the first bit. If the leading bit is equally
                 likely to be a 0 or a 1, then their analysis shows that
                 it is better to place the point before the leading bit.
                 However, they report that a more likely distribution is
                 logarithmic (as predicted by Benford's Law, although
                 the Newcomb / Benford work is neither mentioned nor
                 cited), in which case there is no advantage for either
                 choice of placement of the binary point. They conclude
                 that it would be humane to place it after the leading
                 digit, by analogy with how people learn decimal
                 arithmetic.",
}

@Article{Hamming:1970:DN,
  author =       "R. W. Hamming",
  title =        "On the Distribution of Numbers",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "8",
  pages =        "1609--1625",
  month =        oct,
  year =         "1970",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  ISSN-L =       "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
  abstract =     "This paper examines the distribution of the mantissas
                 of floating-point numbers and shows how the arithmetic
                 operations of a computer transform various
                 distributions toward the limiting distribution $$ r(x)
                 = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
                 $b$ is the base of the number system). The paper also
                 gives a number of applications to hardware, software,
                 and general computing which show that this distribution
                 is not merely an amusing curiosity. A brief examination
                 of the distribution of exponents is include.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Hand:2007:DDD,
  author =       "David Hand",
  title =        "Deception and Dishonesty with Data: Fraud in Science",
  journal =      j-SIGNIF,
  volume =       "4",
  number =       "1",
  pages =        "22--25",
  month =        mar,
  year =         "2007",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1111/j.1740-9713.2007.00215.x",
  ISSN =         "1740-9705 (print), 1740-9713 (electronic)",
  ISSN-L =       "1740-9705",
  bibdate =      "Thu Nov 17 19:17:58 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Significance ({Oxford, England})",
}

@Article{Handurukande:2006:PSB,
  author =       "S. B. Handurukande and A.-M. Kermarrec and F. {Le
                 Fessant} and L. Massouli{\'e} and S. Patarin",
  title =        "Peer sharing behaviour in the {eDonkey} network, and
                 implications for the design of server-less file sharing
                 systems",
  journal =      j-OPER-SYS-REV,
  volume =       "40",
  number =       "4",
  pages =        "359--371",
  month =        oct,
  year =         "2006",
  CODEN =        "OSRED8",
  DOI =          "http://doi.acm.org/10.1145/1218063.1217970",
  ISSN =         "0163-5980 (print), 1943-586X (electronic)",
  ISSN-L =       "0163-5980",
  bibdate =      "Fri Jun 20 17:14:10 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this paper we present an empirical study of a
                 workload gathered by crawling the eDonkey network --- a
                 dominant peer-to-peer file sharing system --- for over
                 50 days. We first confirm the presence of some known
                 features, in particular the prevalence of free-riding
                 and the Zipf-like distribution of file popularity. We
                 also analyze the evolution of document popularity. We
                 then provide an in-depth analysis of several clustering
                 properties of such workloads. We measure the
                 geographical clustering of peers offering a given file.
                 We find that most files are offered mostly by peers of
                 a single country, although popular files don't have
                 such a clear home country. We then analyze the overlap
                 between contents offered by different peers. We find
                 that peer contents are highly clustered according to
                 several metrics of interest. We propose to leverage
                 this property by allowing peers to search for content
                 without server support, by querying suitably identified
                 semantic neighbours. We find via trace-driven
                 simulations that this approach is generally effective,
                 and is even more effective for rare files. If we
                 further allow peers to query both their semantic
                 neighbours, and in turn their neighbours' neighbours,
                 we attain hit rates as high as over 55\% for neighbour
                 lists of size 20.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGOPS Operating Systems Review",
  keywords =     "file sharing; peer-to-peer; simulation; trace",
}

@Book{Hardy:1949:DS,
  author =       "G. H. (Godfrey Harold) Hardy",
  title =        "Divergent series",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xvi + 396",
  year =         "1949",
  LCCN =         "QA295 .H29",
  bibdate =      "Wed Nov 16 08:14:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
}

@Book{Hardy:1975:ITN,
  author =       "Godfrey H. Hardy and Edward M. Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  edition =      "Fourth",
  pages =        "421",
  year =         "1975",
  ISBN =         "0-19-853310-1",
  ISBN-13 =      "978-0-19-853310-8",
  LCCN =         "????",
  bibdate =      "Fri Jun 24 12:32:14 2005",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Hardy:1991:DS,
  author =       "G. H. (Godfrey Harold) Hardy",
  title =        "Divergent series",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  edition =      "Second",
  pages =        "xvi + 396",
  year =         "1991",
  ISBN =         "0-8284-0334-1",
  ISBN-13 =      "978-0-8284-0334-4",
  LCCN =         "QA295 .H29 1991",
  bibdate =      "Wed Nov 16 08:17:27 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
  remark =       "Unaltered reprint of \cite{Hardy:1949:DS}, despite
                 label of second edition.",
  subject =      "Divergent series",
}

@Article{Harremoes:2001:MEF,
  author =       "Peter Harremo{\"e}s and Flemming Tops{\o}e",
  title =        "Maximum Entropy Fundamentals",
  journal =      j-ENTROPY,
  volume =       "3",
  number =       "3",
  pages =        "191--226",
  month =        sep,
  year =         "2001",
  CODEN =        "ENTRFG",
  DOI =          "http://dx.doi.org/10.3390/e3030191",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Thu Feb 28 10:55:45 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.mdpi.com/1099-4300/3/3/191",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  keywords =     "continuity of entropy; entropy loss; exponential
                 family; game theoretical equilibrium; hyperbolic
                 distributions; information topology; maximum entropy;
                 minimum risk; Nash equilibrium code; partition
                 function; Zipf's law",
  remark =       "Open access journal.",
}

@Article{Harremoes:2005:ZLHa,
  author =       "Peter Harremo{\"e}s and Flemming Topsoe",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "3--4",
  pages =        "315--318",
  day =          "1",
  month =        aug,
  year =         "2005",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.endm.2005.07.075",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1571065305051450",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@InCollection{Harremoes:2005:ZLHb,
  author =       "Peter Harremo{\"e}s and Flemming Topsoe",
  editor =       "Rudolf Ahlswede and others",
  booktitle =    "General theory of information transfer and
                 combinatorics.",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  volume =       "21",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "315--318",
  year =         "2005",
  DOI =          "http://dx.doi.org/10.1016/j.endm.2005.07.075",
  bibdate =      "Sat Nov 12 11:07:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Electronic Notes in Discrete Mathematics",
  ZMnumber =     "1158.91482",
  abstract =     "Zipf's law --- or Estoup-Zipf's law --- is an
                 empirical fact of computational linguistics which
                 relates rank and frequency of words in natural
                 languages. The law suggests modelling by distributions
                 of ``hyperbolic type''. We present a satisfactory
                 general definition and an information-theoretical
                 characterization of the resulting hyperbolic
                 distributions. When applied to linguistics this leads
                 to a property of stability and flexibility, explaining
                 that a language can develop towards higher and higher
                 expressive powers without changing its basic
                 structure.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics) 94A15 (General topics of
                 information theory) 94A17 (Measures of information)",
  keywords =     "entropy loss; hyperbolic distributions; Zipf's law",
}

@InCollection{Harremoes:2006:ZLH,
  author =       "P. Harremo{\"e}s and F. Topsoe",
  editor =       "Rudolf Ahlswede and others",
  booktitle =    "General theory of information transfer and
                 combinatorics",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  volume =       "4123",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "788--792",
  year =         "2006",
  DOI =          "http://dx.doi.org/10.1007/11889342_50",
  bibdate =      "Sat Nov 12 11:15:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  ZMnumber =     "1158.91481",
  abstract =     "Zipf's law --- or Estoup-Zipf's law --- is an
                 empirical fact of computational linguistics which
                 relates rank and frequency of words in natural
                 languages. The law suggests modelling by distributions
                 of ``hyperbolic type''. We present a satisfactory
                 general definition and an information-theoretical
                 characterization of the resulting hyperbolic
                 distributions. When applied to linguistics this leads
                 to a property of stability and flexibility, explaining
                 that a language can develop towards higher and higher
                 expressive powers without changing its basic
                 structure.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics) 94A15 (General topics of
                 information theory) 94A17 (Measures of information)",
  keywords =     "entropy loss; hyperbolic distributions; Zipf's law",
}

@Article{Hartshorn:2009:BRB,
  author =       "Kevin Hartshorn",
  title =        "Book Review: {{\booktitle{The fabulous Fibonacci
                 numbers}} by Alfred Posamentier and Ingmar Lehmann}",
  journal =      j-J-MATH-ARTS,
  volume =       "3",
  number =       "2",
  pages =        "113--116",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/17513470902897569",
  ISSN =         "1751-3472 (print), 1751-3480 (electronic)",
  ISSN-L =       "1751-3480",
  bibdate =      "Sat Jan 07 09:43:47 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematics and the Arts",
  onlinedate =   "05 Jun 2009",
}

@Article{Hasan:2002:ADA,
  author =       "Bassam Hasan",
  title =        "Assessing data authenticity with {Benford}'s law",
  journal =      "Information Systems Control Journal",
  volume =       "6",
  pages =        "??--??",
  year =         "2002",
  CODEN =        "ISYJFS",
  ISSN =         "1526-7407",
  bibdate =      "Sat Feb 16 17:45:21 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.isaca.org/",
  remark =       "Journal publication ceased at volume 6 in 2008,
                 according to one library catalog, but volumes up to
                 2013 are available at journal Web site.",
}

@Article{Hassan:2003:EDA,
  author =       "Bassam Hassan",
  title =        "Examining data accuracy and authenticity with leading
                 digit frequency analysis",
  journal =      "Industrial Management + Data Systems",
  volume =       "103",
  number =       "2",
  pages =        "121--125",
  month =        "????",
  year =         "2003",
  CODEN =        "MDSD8F",
  ISSN =         "0263-5577 (print), 1758-5783 (electronic)",
  ISSN-L =       "0263-5577",
  bibdate =      "Fri Nov 25 11:07:59 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hasumi:2007:ITS,
  author =       "Tomohiro Hasumi",
  title =        "Interoccurrence time statistics in the two-dimensional
                 {Burridge--Knopoff} earthquake model",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  number =       "??",
  pages =        "026117",
  day =          "29",
  month =        aug,
  year =         "2007",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.76.026117",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.76.026117",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf--Mandelbrot law",
}

@Book{Havil:2003:GEE,
  author =       "Julian Havil",
  title =        "{Gamma}: Exploring {Euler}'s Constant",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xxiii + 266",
  year =         "2003",
  ISBN =         "0-691-09983-9",
  ISBN-13 =      "978-0-691-09983-5",
  LCCN =         "QA41 .H23 2003",
  bibdate =      "Thu Sep 25 16:52:46 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is the subject of Section 14.2, pages
                 145--155.",
  price =        "US\$29.95",
  URL =          "http://www.loc.gov/catdir/description/prin031/2002192453.html",
  acknowledgement = ack-nhfb,
}

@Article{Havlin:1995:DBZ,
  author =       "Shlomo Havlin",
  title =        "The distance between {Zipf} plots",
  journal =      j-PHYSICA-A,
  volume =       "216",
  number =       "1--2",
  pages =        "148--150",
  day =          "1",
  month =        jun,
  year =         "1995",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/0378-4371(95)00069-J",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037843719500069J",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Book{Heaps:1978:IRC,
  author =       "Harold Stanley Heaps",
  title =        "Information retrieval, computational and theoretical
                 aspects",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 344",
  year =         "1978",
  ISBN =         "0-12-335750-0",
  ISBN-13 =      "978-0-12-335750-2",
  LCCN =         "Z699 .H38",
  bibdate =      "Sat Nov 12 11:36:39 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Library and information science",
  acknowledgement = ack-nhfb,
  remark =       "Heaps's Law is given on pp. 206--208.",
  subject =      "Information storage and retrieval systems",
}

@Article{Hefeeda:2008:TMP,
  author =       "Mohamed Hefeeda and Osama Saleh",
  title =        "Traffic modeling and proportional partial caching for
                 peer-to-peer systems",
  journal =      j-IEEE-TRANS-NETWORKING,
  volume =       "16",
  number =       "6",
  pages =        "1447--1460",
  month =        dec,
  year =         "2008",
  CODEN =        "IEANEP",
  DOI =          "http://dx.doi.org/10.1109/TNET.2008.918081",
  ISSN =         "1063-6692 (print), 1558-2566 (electronic)",
  ISSN-L =       "1063-6692",
  bibdate =      "Fri Mar 6 16:31:04 MST 2009",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
  abstract =     "Peer-to-peer (P2P) file sharing systems generate a
                 major portion of the Internet traffic, and this portion
                 is expected to increase in the future. We explore the
                 potential of deploying proxy caches in different
                 Autonomous Systems (ASes) with the goal of reducing the
                 cost incurred by Internet service providers and
                 alleviating the load on the Internet backbone. We
                 conduct an eight-month measurement study to analyze the
                 P2P traffic characteristics that are relevant to
                 caching, such as object popularity, popularity
                 dynamics, and object size. Our study shows that the
                 popularity of P2P objects can be modeled by a
                 Mandelbrot-Zipf distribution, and that several
                 workloads exist in P2P traffic. Guided by our findings,
                 we develop a novel caching algorithm for P2P traffic
                 that is based on object segmentation, and proportional
                 partial admission and eviction of objects. Our
                 trace-based simulations show that with a relatively
                 small cache size, a byte hit rate of up to 35\% can be
                 achieved by our algorithm, which is close to the byte
                 hit rate achieved by an off-line optimal algorithm with
                 complete knowledge of future requests. Our results also
                 show that our algorithm achieves a byte hit rate that
                 is at least 40\% more, and at most triple, the byte hit
                 rate of the common web caching algorithms. Furthermore,
                 our algorithm is robust in face of aborted downloads,
                 which is a common case in P2P systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE\slash ACM Transactions on Networking",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J771",
  keywords =     "internet measurement; network protocols; peer-to-peer
                 systems; traffic analysis; traffic modeling",
}

@Book{Henriques:2011:WLB,
  author =       "Diana B. Henriques",
  title =        "The wizard of lies: {Bernie Madoff} and the death of
                 trust",
  publisher =    "Times Books/Henry Holt",
  address =      "New York, NY, USA",
  pages =        "xxiv + 419",
  year =         "2011",
  ISBN =         "0-8050-9134-3",
  ISBN-13 =      "978-0-8050-9134-2",
  LCCN =         "HV6692.M33 H46 2011",
  bibdate =      "Fri Mar 22 08:51:50 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Madoff, Bernard L; Swindlers and swindling; United
                 States; Biography; Ponzi schemes; Commercial crimes",
  tableofcontents = "An earthquake on Wall Street \\
                 Becoming bernie \\
                 The hunger for yield \\
                 The big four \\
                 The cash spigot \\
                 What they wanted to believe \\
                 Warning signs \\
                 A near-death experience \\
                 Madoff's world \\
                 The year of living dangerously \\
                 Waking up in the rubble \\
                 Reckoning the damage \\
                 Net winners and net losers \\
                 The sins of the father \\
                 The wheels of justice \\
                 Hope, lost and found",
}

@Article{Herman:1998:TRI,
  author =       "Tom Herman",
  title =        "Tax report: An {IRS} blooper startles thousands of
                 taxpayers",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "1--1",
  day =          "18",
  month =        feb,
  year =         "1998",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  bibdate =      "Fri Mar 22 09:17:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://online.wsj.com/article/SB887753996209804500.html",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Wall Street Journal",
  keywords =     "Benford's Law",
  remark =       "From the article: ``[a taxpayer] was expecting a \$513
                 tax refund. Instead, he recently received a letter from
                 the Internal Revenue Service informing him that he owes
                 the government \$300,000,007.57. \ldots{} about 3,000
                 other people around the nation got similar erroneous
                 notices, each showing a balance due of `three hundred
                 million dollars and change.'\,''",
}

@Article{Hernando:2009:ZLF,
  author =       "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas
                 and C. Vesperinas and A. Plastino",
  title =        "{Zipf}'s law from a {Fisher} variational-principle",
  journal =      j-PHYS-LET-A,
  volume =       "374",
  number =       "1",
  pages =        "18--21",
  day =          "14",
  month =        dec,
  year =         "2009",
  CODEN =        "PYLAAG",
  DOI =          "http://dx.doi.org/10.1016/j.physleta.2009.10.027",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0375960109012894",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  keywords =     "Zipf's Law",
}

@Article{Herzel:1957:SDD,
  author =       "Amato Herzel",
  title =        "Sulla distribuzione della cifre iniziali dei numeri
                 statistici. ({Italian}) [{On} the frequency of initial
                 digits of statistical numbers]",
  journal =      "{Atti dell XV e XVII Riunione, Societa Italiana di
                 Statistica}",
  volume =       "??",
  number =       "??",
  pages =        "205--228",
  year =         "1957",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sun Sep 18 12:00:07 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}

@Article{Hickman:2010:DAC,
  author =       "Matthew Hickman and Stephen Rice",
  title =        "Digital Analysis of Crime Statistics: Does Crime
                 Conform to {Benford's Law}?",
  journal =      j-J-QUANT-CRIMINOL,
  volume =       "26",
  number =       "3",
  pages =        "333--349",
  month =        sep,
  year =         "2010",
  CODEN =        "JQCRE6",
  DOI =          "http://dx.doi.org/10.1007/s10940-010-9094-6",
  ISSN =         "0748-4518 (print), 1573-7799 (electronic)",
  ISSN-L =       "0748-4518",
  bibdate =      "Fri Nov 25 10:30:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Criminology",
  keywords =     "Benford distribution; Benford's law; Crime data; Crime
                 statistics; Data errors; Digital analysis; Fabricated
                 data; First digit; Fraud detection; Uniform crime
                 reports",
}

@Article{Hill:1970:ZLP,
  author =       "Bruce M. Hill",
  title =        "{Zipf}'s law and prior distributions for the
                 composition of a population",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "65",
  number =       "331",
  pages =        "1220--1232",
  month =        sep,
  year =         "1970",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62.35",
  MRnumber =     "0279936 (43 \#5657)",
  MRreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  URL =          "http://www.jstor.org/stable/2284288",
  ZMnumber =     "Zbl 0224.92011",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Hill:1974:RFF,
  author =       "Bruce M. Hill",
  title =        "The rank-frequency form of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "1017--1026",
  month =        dec,
  year =         "1974",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15",
  MRnumber =     "0426242 (54 \#14188)",
  MRreviewer =   "S. M. Samuels",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  ZMnumber =     "Zbl 0301.60011",
  acknowledgement = ack-nhfb,
  classification = "B0240 (Probability and statistics); C1140
                 (Probability and statistics)",
  corpsource =   "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
                 USA",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Bose--Einstein allocation; distribution; random
                 processes; rank frequency form; statistics; Zipf's
                 law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hill:1975:SFZ,
  author =       "Bruce M. Hill and Michael Woodroofe",
  title =        "Stronger forms of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "70",
  number =       "349",
  pages =        "212--219",
  month =        mar,
  year =         "1975",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15 (62D05)",
  MRnumber =     "0440763 (55 \#13633)",
  MRreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  ZMnumber =     "Zbl 0326.92014",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Hill:1988:RNG,
  author =       "Theodore Hill",
  title =        "Random number guessing and the first digit
                 phenomenon",
  journal =      j-PSYCHOL-REP,
  volume =       "62",
  number =       "3",
  pages =        "967--971",
  month =        jun,
  year =         "1988",
  CODEN =        "PYRTAZ",
  DOI =          "http://dx.doi.org/10.2466/pr0.1988.62.3.967",
  ISSN =         "0033-2941 (print), 1558-691X (electronic)",
  ISSN-L =       "0033-2941",
  bibdate =      "Fri Feb 15 06:41:31 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967",
  acknowledgement = ack-nhfb,
  ajournal =     "Psychol. rep.",
  fjournal =     "Psychological Reports",
}

@Article{Hill:1995:BII,
  author =       "Theodore P. Hill",
  title =        "Base-invariance implies {Benford's Law}",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "123",
  number =       "3",
  pages =        "887--895",
  month =        mar,
  year =         "1995",
  CODEN =        "PAMYAR",
  DOI =          "http://dx.doi.org/10.2307/2160815",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "60A10 (28D05)",
  MRnumber =     "1233974 (95d:60006)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2160815",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
}

@Article{Hill:1995:SDP,
  author =       "Theodore P. Hill",
  title =        "The significant-digit phenomenon",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "4",
  pages =        "322--327",
  month =        apr,
  year =         "1995",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2974952",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11K99 (60E99)",
  MRnumber =     "96f:11101",
  MRreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Hill:1995:SDS,
  author =       "Theodore P. Hill",
  title =        "A statistical derivation of the significant-digit
                 law",
  journal =      j-STAT-SCI,
  volume =       "10",
  number =       "4",
  pages =        "354--363",
  year =         "1995",
  CODEN =        "STSCEP",
  ISSN =         "0883-4237",
  ISSN-L =       "0883-4237",
  MRclass =      "60E99 (60A10 62E99)",
  MRnumber =     "1421567 (98a:60021)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 10:09:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "2-P&origin=MSN;
                 http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO",
  ZMnumber =     "Zbl 0955.60509",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science. A Review Journal of the Institute
                 of Mathematical Statistics",
}

@TechReport{Hill:1996:NDT,
  author =       "Theodore P. Hill",
  title =        "A note on distributions of true versus fabricated
                 data",
  type =         "Preprint",
  institution =  "Department of Mathematics, Georgia Institute of
                 Technology",
  address =      "Atlanta, GA, USA",
  pages =        "4",
  year =         "1996",
  bibdate =      "Sat Feb 16 17:47:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr",
  acknowledgement = ack-nhfb,
}

@InCollection{Hill:1997:BL,
  author =       "Theodore Hill",
  editor =       "Michiel Hazewinkel",
  booktitle =    "Encyclopedia of Mathematics, Supplement {I}",
  title =        "{Benford's Law}",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "102--103",
  year =         "1997",
  ISBN =         "90-481-4896-0",
  ISBN-13 =      "978-90-481-4896-7",
  LCCN =         "????",
  bibdate =      "Wed Nov 16 10:29:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hill:1998:FDP,
  author =       "Theodore P. Hill",
  title =        "The First Digit Phenomenon",
  journal =      j-AM-SCI,
  volume =       "86",
  number =       "4",
  pages =        "358--363",
  month =        jul # "\slash " # aug,
  year =         "1998",
  CODEN =        "AMSCAC",
  DOI =          "http://dx.doi.org/10.1511/1998.4.358",
  ISSN =         "0003-0996 (print), 1545-2786 (electronic)",
  ISSN-L =       "0003-0996",
  bibdate =      "Sat Dec 10 11:54:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
                 http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
  abstract =     "A century ago, Simon Newcomb observed an unexpected
                 pattern in the first digits of logarithm tables: The
                 digit $1$ is significantly more likely to occur than
                 $2$, $2$ than $3$, and so on. More than a half-century
                 later, Frank Benford rediscovered the first-digit
                 phenomenon and found that it applied to many tables of
                 numerical data, including the stock market, census
                 statistics and accounting figures. New mathematical
                 insights establish the empirical law developed by
                 Newcomb and Benford as part of modern probability
                 theory, and recent applications include testing of
                 mathematical models, design of computers and detection
                 of fraud in accounting.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  journal-URL =  "http://www.americanscientist.org/issues/past.aspx",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Hill:1999:DFD,
  author =       "Theodore P. Hill",
  title =        "The Difficulty of Faking Data",
  journal =      j-CHANCE,
  volume =       "12",
  number =       "3",
  pages =        "27--31",
  month =        "????",
  year =         "1999",
  CODEN =        "CNDCE4",
  DOI =          "http://dx.doi.org/10.1080/09332480.1999.10542154",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Tue Nov 22 18:54:44 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/",
  keywords =     "Benford's Law",
  xxnote =       "Check: Hurlimann bibliography says v26 pp. 8--13??;
                 that is wrong!",
}

@Article{Hill:1999:PCS,
  author =       "Theodore P. Hill",
  title =        "Le premier chiffre significatif fait sa loi.
                 ({French}) [{The} first significant digit makes its
                 law]",
  journal =      "La Recherche: L'actualit{\'e} des sciences",
  volume =       "2",
  number =       "316",
  pages =        "72--76",
  month =        jan,
  year =         "1999",
  CODEN =        "RCCHBV",
  ISSN =         "0029-5671 (print), 1625-9955 (electronic)",
  ISSN-L =       "0029-5671",
  bibdate =      "Sat Feb 16 17:51:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970",
  acknowledgement = ack-nhfb,
  language =     "French",
  xxjournal =    "La Recherche Hors S{\'e}rie",
}

@InProceedings{Hill:2002:RAB,
  author =       "T. P. Hill",
  editor =       "????",
  booktitle =    "Conference, Leiden University",
  title =        "Recent applications of {Benford}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:55:46 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hill:2005:RDS,
  author =       "Theodore P. Hill and Klaus Sch{\"u}rger",
  title =        "Regularity of digits and significant digits of random
                 variables",
  journal =      j-STOCH-PROC-APPL,
  volume =       "115",
  number =       "10",
  pages =        "1723--1743",
  month =        oct,
  year =         "2005",
  CODEN =        "STOPB7",
  DOI =          "http://dx.doi.org/10.1016/j.spa.2005.05.003",
  ISSN =         "0304-4149 (print), 1879-209X (electronic)",
  ISSN-L =       "0304-4149",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304414905000657",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
  keywords =     "Benford's Law; digit-regular random variable;
                 floating-point numbers; law of least significant
                 digits; nonleading digits; normal numbers; significant
                 digits; significant-digit-regular random variable;
                 trailing digits",
}

@Article{Hill:2011:LEB,
  author =       "Theodore P. Hill",
  title =        "Letter to the Editor: {Benford's Law} Blunders",
  journal =      j-AMER-STAT,
  volume =       "65",
  number =       "2",
  pages =        "141--141",
  month =        may,
  year =         "2011",
  CODEN =        "ASTAAJ",
  DOI =          "http://dx.doi.org/10.1198/tast.2011.10179",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Feb 18 18:34:43 2013",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/pdf/10.1198/tast.2011.11011",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  remark =       "Brief comment on a error in Feller's derivation of
                 Benford's Law, with pointer to a corrected proof in
                 \cite{Berger:2011:BLS}.",
}

@Article{Hisano:2011:PVD,
  author =       "Ryohei Hisano and Didier Sornette and Takayuki
                 Mizuno",
  title =        "Predicted and verified deviations from {Zipf}'s law in
                 ecology of competing products",
  journal =      j-PHYS-REV-E,
  volume =       "84",
  number =       "2",
  pages =        "026117",
  day =          "24",
  month =        aug,
  year =         "2011",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.84.026117",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.84.026117",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "8",
}

@InProceedings{Hjorland:2005:BLS,
  author =       "Birger Hj{\o}rland and Jeppe Nicolaisen",
  editor =       "Fabio Crestani and Ian Ruthven",
  booktitle =    "Context: nature, impact, and role: {5th International
                 Conference on Conceptions of Library and Information
                 Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005;
                 proceedings}",
  title =        "{Bradford}'s law of scattering: ambiguities in the
                 concept of ``subject''",
  volume =       "3507",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "96--106",
  year =         "2005",
  ISBN =         "3-540-26178-8",
  ISBN-13 =      "978-3-540-26178-0",
  LCCN =         "Z672.5 .I5616 2005",
  bibdate =      "Fri Nov 25 11:52:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  bookpages =    "xiii + 250",
}

@Article{Hoare:1986:DFS,
  author =       "G. T. Q. Hoare and E. Wright",
  title =        "The distribution of first significant digits",
  journal =      j-MATH-GAZ,
  volume =       "70",
  number =       "451",
  pages =        "34--37",
  month =        mar,
  year =         "1986",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572",
  ISSN-L =       "0025-5572",
  bibdate =      "Sat Feb 16 17:57:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3615826",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Hobza:2001:NBL,
  author =       "Tom{\'a}{\v{s}} Hobza and Igor Vajda",
  title =        "On the {Newcomb--Benford} law in models of statistical
                 data",
  journal =      "Revista Matem{\'a}tica Complutense",
  volume =       "14",
  number =       "2",
  pages =        "407--420",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "1139-1138, 1696-8220, 1988-2807",
  ISSN-L =       "1139-1138",
  MRclass =      "62E10",
  MRnumber =     "1871305 (2002j:62015)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. Mat. Complut.",
  fjournal =     "Revista Matem{\'a}tica Complutense",
}

@InCollection{Horgan:2009:BL,
  author =       "Jane M. Horgan",
  title =        "{Benford's Law}",
  crossref =     "Horgan:2009:PRI",
  chapter =      "9.4",
  pages =        "142--144",
  year =         "2009",
  bibdate =      "Mon Feb 18 18:46:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hosking:1987:PQE,
  author =       "J. R. M. Hosking and J. R. Wallis",
  title =        "Parameter and Quantile Estimation for the Generalized
                 {Pareto} Distribution",
  journal =      j-TECHNOMETRICS,
  volume =       "29",
  number =       "3",
  pages =        "339--349",
  month =        "????",
  year =         "1987",
  CODEN =        "TCMTA2",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Fri Nov 25 16:39:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
}

@Article{Hoyle:2002:MSM,
  author =       "David C. Hoyle and Magnus Rattray and Ray Jupp and
                 Andrew Brass",
  title =        "Making sense of microarray data distributions",
  journal =      j-BIOINFORMATICS,
  volume =       "18",
  number =       "4",
  pages =        "576--584",
  month =        apr,
  year =         "2002",
  ISSN =         "1367-4803 (print), 1367-4811 (electronic)",
  ISSN-L =       "1367-4803",
  bibdate =      "Fri Nov 25 11:16:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  keywords =     "Benford's Law; mRNA transcription data",
}

@Article{Hsu:1948:ESM,
  author =       "E. H. Hs{\"u}",
  title =        "An Experimental Study on ``Mental Numbers'' and a New
                 Application",
  journal =      j-J-GEN-PSYCH,
  volume =       "38",
  number =       "1",
  pages =        "57--67",
  month =        "????",
  year =         "1948",
  CODEN =        "JGPSAY",
  DOI =          "http://dx.doi.org/10.1080/00221309.1948.9711768",
  ISSN =         "0022-1309 (print), 1940-0888 (electronic)",
  ISSN-L =       "0022-1309",
  bibdate =      "Sat Jan 07 09:29:53 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of General Psychology",
  keywords =     "Benford's Law",
  onlinedate =   "06 Jul 2010",
}

@Article{Huang:2001:PLE,
  author =       "Z. F. Huang and S. Solomon",
  title =        "Power, {L{\'e}vy}, exponential and {Gaussian}-like
                 regimes in autocatalytic financial systems",
  journal =      j-EUR-PHYS-J-B,
  volume =       "20",
  number =       "4",
  pages =        "601--607",
  month =        apr,
  year =         "2001",
  CODEN =        "EPJBFY",
  DOI =          "http://dx.doi.org/10.1007/PL00011114",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Thu Feb 28 10:26:53 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/PL00011114",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Huang:2008:IZL,
  author =       "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and
                 Jing-Shiuan Hua",
  title =        "An investigation of {Zipf's Law} for fraud detection
                 {(DSS\# 06-10-1826R(2))}",
  journal =      j-DEC-SUPP-SYS,
  volume =       "46",
  number =       "1",
  pages =        "70--83",
  month =        dec,
  year =         "2008",
  CODEN =        "DSSYDK",
  DOI =          "http://dx.doi.org/10.1016/j.dss.2008.05.003",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923608001073",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Huberman:1999:IGD,
  author =       "Bernardo A. Huberman and Lada A. Adamic",
  title =        "{Internet}: Growth dynamics of the {World-Wide Web}",
  journal =      j-NATURE,
  volume =       "401",
  number =       "6749",
  pages =        "131--131",
  day =          "9",
  month =        sep,
  year =         "1999",
  CODEN =        "NATUAS",
  DOI =          "http://dx.doi.org/10.1038/43604",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Tue Nov 15 09:52:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Zipf's Law",
}

@Article{Hui:2011:BLN,
  author =       "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min",
  title =        "{Benford's Law} in Nuclear Structure Physics",
  journal =      j-CHIN-PHYS-LETT,
  volume =       "28",
  number =       "3",
  pages =        "32101--32104",
  month =        mar,
  year =         "2011",
  CODEN =        "CPLEEU",
  DOI =          "http://dx.doi.org/10.1088/0256-307X/28/3/032101",
  ISSN =         "0256-307X (print), 1741-3540 (electronic)",
  ISSN-L =       "0256-307X",
  bibdate =      "Fri Nov 25 10:37:25 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chinese Physics Letters",
}

@TechReport{Humenberger:2006:BGV,
  author =       "Hans Humenberger",
  title =        "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der
                 ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on
                 the distribution of the first digit of numbers]",
  type =         "Report",
  institution =  "Institut f{\"u}r Mathematik und Angewandte Statistik,
                 Universit{\"a}t f{\"u}r Bodenkultur",
  address =      "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria",
  month =        aug,
  year =         "2006",
  bibdate =      "Sun Feb 17 09:37:40 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Humenberger:2008:EBB,
  author =       "H. Humenberger",
  title =        "{Eine elementarmathematische Begr{\"u}ndung des
                 Benford-Gesetzes}. ({German}) [{An} elementary
                 mathematical derivation of the {Benford Law}]",
  journal =      "Der Mathematikunterricht",
  volume =       "54",
  number =       "??",
  pages =        "24--34",
  month =        "????",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "0025-5807",
  ISSN-L =       "0025-5807",
  bibdate =      "Fri Nov 18 11:59:44 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Hungerbuhler:2007:BGF,
  author =       "Norbert H{\"u}ngerb{\"u}hler",
  title =        "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie
                 die Mathematik Steuers{\"u}ndern das F{\"u}rchten
                 lehrt} [{Benford's Law} on leading digits. Mathematics
                 teaches tax evaders to fear]",
  type =         "Report",
  institution =  "EducETH",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "24",
  day =          "2",
  month =        mar,
  year =         "2007",
  bibdate =      "Fri Nov 18 12:02:21 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
  lastaccess =   "18 November 2011",
  remark =       "This report has several nice figures, including
                 photographs of Newcomb, Benford, and worn pages of log
                 tables, and an amazing plot of the agreement of
                 200,125,088 mathematical constants with Benford's
                 Law.",
}

@Article{Hurlimann:2003:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "A generalized {Benford} law and its application",
  journal =      j-ADV-APPL-STAT,
  volume =       "3",
  number =       "3",
  pages =        "217--228",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0972-3617",
  ISSN-L =       "0972-3617",
  MRclass =      "11K31 (11B73)",
  MRnumber =     "2034405 (2004k:11125)",
  MRreviewer =   "Vydas {\v{C}}ekanavi{\v{c}}ius",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances and Applications in Statistics",
}

@Article{Hurlimann:2004:IPB,
  author =       "Werner H{\"u}rlimann",
  title =        "Integer powers and {Benford}'s law",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "11",
  number =       "1",
  pages =        "39--46",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "1311-8080",
  ISSN-L =       "1314-3395",
  MRclass =      "62E15 (11B83 11K31 62E20)",
  MRnumber =     "2033394 (2005c:62030)",
  MRreviewer =   "I. N. Volodin",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
}

@TechReport{Hurlimann:2006:BLB,
  author =       "Werner H{\"u}rlimann",
  title =        "{Benford's Law} from 1881 to 2006: a bibliography",
  type =         "Report",
  address =      "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
  pages =        "15",
  day =          "5",
  month =        jul,
  year =         "2006",
  bibdate =      "Fri Mar 30 11:32:30 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/pdf/math.ST/0607168",
  abstract =     "On the occasion of the 125-th anniversary of Newcomb's
                 paper, a bibliography of academic work related to
                 Benford's law from its year of origin 1881 to 2006 has
                 been compiled.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "This bibliography lists 325 references on the title
                 subject, with these (years) and counts: (1881) 1,
                 (1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
                 (1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
                 (1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
                 (1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
                 (1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
                 (1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
                 (1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
                 (1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
                 (1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
                 (1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
                 (1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
                 (2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
                 (2005) 34, (2006) 18.",
}

@Article{Hurlimann:2006:GBL,
  author =       "W. Hurlimann",
  title =        "Generalizing {Benford}'s law using power laws:
                 application to integer sequences",
  journal =      "ArXiv Mathematics e-prints",
  month =        jul,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006math......7166H",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0607166",
  keywords =     "Mathematics - Statistics, Mathematics - Number Theory,
                 11B73, 11B83, 11K31, 62E15, 62E17",
}

@Article{Hurlimann:2009:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "Generalizing {Benford}'s law using power laws:
                 application to integer sequences",
  journal =      j-INT-J-MATH-MATH-SCI,
  pages =        "10",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0161-1712",
  ISSN-L =       "0161-1712",
  MRclass =      "60E05 (11B83 62E15)",
  MRnumber =     "2533550 (2010h:60043)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Article ID 970284.",
  URL =          "http://arxiv.org/abs/math/0607166",
  abstract =     "A simple method to derive parametric analytical
                 extensions of Benford's law for first digits of
                 numerical data is proposed. Two generalized Benford
                 distributions are considered, namely the two-sided
                 power Benford distribution and the new Pareto Benford
                 distribution. The fitting capabilities of these
                 generalized Benford distributions are illustrated and
                 compared at some interesting and important integer
                 sequences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
}

@Article{Ioannides:2003:ZLC,
  author =       "Yannis M. Ioannides and Henry G. Overman",
  title =        "{Zipf}'s law for cities: an empirical examination",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "33",
  number =       "2",
  pages =        "127--137",
  day =          "1",
  month =        mar,
  year =         "2003",
  CODEN =        "RSUEDM",
  DOI =          "http://dx.doi.org/10.1016/S0166-0462(02)00006-6",
  ISSN =         "0166-0462 (print), 1879-2308 (electronic)",
  ISSN-L =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0166046202000066",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01660462",
  keywords =     "Zipf's Law",
}

@Article{Ioannidis:2005:WMP,
  author =       "John P. A. Ioannidis",
  title =        "Why Most Published Research Findings Are False",
  journal =      j-PLOS-MED,
  volume =       "2",
  number =       "8",
  pages =        "696--701",
  month =        aug,
  year =         "2005",
  CODEN =        "PMLEAC",
  DOI =          "http://dx.doi.org/10.1371/journal.pmed.0020124",
  ISSN =         "1549-1277 (print), 1549-1676 (electronic)",
  ISSN-L =       "1549-1277",
  bibdate =      "Fri Nov 18 12:42:05 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124",
  abstract =     "There is increasing concern that most current
                 published research findings are false. The probability
                 that a research claim is true may depend on study power
                 and bias, the number of other studies on the same
                 question, and, importantly, the ratio of true to no
                 relationships among the relationships probed in each
                 scientific field. In this framework, a research finding
                 is less likely to be true when the studies conducted in
                 a field are smaller; when effect sizes are smaller;
                 when there is a greater number and lesser preselection
                 of tested relationships; where there is greater
                 flexibility in designs, definitions, outcomes, and
                 analytical modes; when there is greater financial and
                 other interest and prejudice; and when more teams are
                 involved in a scientific field in chase of statistical
                 significance. Simulations show that for most study
                 designs and settings, it is more likely for a research
                 claim to be false than true. Moreover, for many current
                 scientific fields, claimed research findings may often
                 be simply accurate measures of the prevailing bias. In
                 this essay, I discuss the implications of these
                 problems for the conduct and interpretation of
                 research.",
  acknowledgement = ack-nhfb,
  articleno =    "e124",
  fjournal =     "PLoS Medicine",
  remark =       "This article does not discuss Benford's Law, but is
                 related to the use of that law in the detection of
                 fraud in research data. Ioannidis discusses the abuse
                 of statistics for limited experimental data, a topic
                 that receives book-length treatment in
                 \cite{Ziliak:2008:CSS}.",
}

@Article{Ipeirotis:2008:CAH,
  author =       "Panagiotis G. Ipeirotis and Luis Gravano",
  title =        "Classification-aware hidden-web text database
                 selection",
  journal =      j-TOIS,
  volume =       "26",
  number =       "2",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2008",
  CODEN =        "ATISET",
  DOI =          "http://doi.acm.org/10.1145/1344411.1344412",
  ISSN =         "1046-8188",
  ISSN-L =       "0734-2047",
  bibdate =      "Thu Jun 12 16:52:34 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tois/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Many valuable text databases on the web have
                 noncrawlable contents that are ``hidden'' behind search
                 interfaces. Metasearchers are helpful tools for
                 searching over multiple such ``hidden-web'' text
                 databases at once through a unified query interface. An
                 important step in the metasearching process is database
                 selection, or determining which databases are the most
                 relevant for a given user query. The state-of-the-art
                 database selection techniques rely on statistical
                 summaries of the database contents, generally including
                 the database vocabulary and associated word
                 frequencies. Unfortunately, hidden-web text databases
                 typically do not export such summaries, so previous
                 research has developed algorithms for constructing
                 approximate content summaries from document samples
                 extracted from the databases via querying. We present a
                 novel ``focused-probing'' sampling algorithm that
                 detects the topics covered in a database and adaptively
                 extracts documents that are representative of the topic
                 coverage of the database. Our algorithm is the first to
                 construct content summaries that include the
                 frequencies of the words in the database.
                 Unfortunately, Zipf's law practically guarantees that
                 for any relatively large database, content summaries
                 built from moderately sized document samples will fail
                 to cover many low-frequency words; in turn, incomplete
                 content summaries might negatively affect the database
                 selection process, especially for short queries with
                 infrequent words. To enhance the sparse document
                 samples and improve the database selection decisions,
                 we exploit the fact that topically similar databases
                 tend to have similar vocabularies, so samples extracted
                 from databases with a similar topical focus can
                 complement each other. We have developed two database
                 selection algorithms that exploit this observation. The
                 first algorithm proceeds hierarchically and selects the
                 best categories for a query, and then sends the query
                 to the appropriate databases in the chosen categories.
                 The second algorithm uses ``shrinkage,'' a statistical
                 technique for improving parameter estimation in the
                 face of sparse data, to enhance the database content
                 summaries with category-specific words. We describe how
                 to modify existing database selection algorithms to
                 adaptively decide (at runtime) whether shrinkage is
                 beneficial for a query. A thorough evaluation over a
                 variety of databases, including 315 real web databases
                 as well as TREC data, suggests that the proposed
                 sampling methods generate high-quality content
                 summaries and that the database selection algorithms
                 produce significantly more relevant database selection
                 decisions and overall search results than existing
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Information Systems (TOIS)",
  keywords =     "database selection; Distributed information retrieval;
                 web search",
}

@Article{Irmay:1997:RBZ,
  author =       "Shragga Irmay",
  title =        "The relationship between {Zipf}'s law and the
                 distribution of first digits",
  journal =      j-J-APPL-STAT,
  volume =       "24",
  number =       "4",
  pages =        "383--393",
  day =          "1",
  month =        aug,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRclass =      "62E15",
  MRnumber =     "1491308 (98h:62015)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.catchword.co.uk/titles/carfax/02664763/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/02664769723594",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; Zipf's Law",
  xxpages =      "383--394",
}

@Article{Ismail:2004:SES,
  author =       "Sanaa Isma{\"\i}l",
  title =        "A Simple Estimator for the Shape Parameter of the
                 {Pareto} Distribution with Economics and Medical
                 Applications",
  journal =      j-J-APPL-STAT,
  volume =       "31",
  number =       "1",
  pages =        "3--13",
  month =        jan,
  year =         "2004",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Sat Dec 4 12:10:37 MST 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Israeloff:1996:CZD,
  author =       "N. E. Israeloff and M. Kagalenko and K. Chan",
  title =        "Can {Zipf} Distinguish Language From Noise in
                 Noncoding {DNA}?",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "??",
  pages =        "1976--??",
  day =          "11",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.76.1976",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@MastersThesis{Iudica:2012:BLM,
  author =       "Federico Iudica",
  title =        "{Benford's Law}: Mathematical Properties and Forensic
                 Accounting Applications",
  type =         "{Master}'s Thesis",
  school =       "Facolt{\`a} di Impresa e Management, Cattedra di
                 Matematica, Luiss Guido Carli University",
  address =      "Rome, Italy",
  pages =        "iv + 56",
  year =         "2012",
  bibdate =      "Tue Feb 19 05:54:59 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://tesi.eprints.luiss.it/8189/1/iudica-tesi-2012.pdf",
  acknowledgement = ack-nhfb,
  advisor =      "Marco Dall'Aglio",
  language =     "English",
}

@Article{Iyengar:1983:SPL,
  author =       "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R.
                 Uppuluri",
  title =        "String patterns of leading digits",
  journal =      j-APPL-MATH-COMP,
  volume =       "12",
  number =       "4",
  pages =        "321--337",
  month =        jul,
  year =         "1983",
  CODEN =        "AMHCBQ",
  DOI =          "http://dx.doi.org/10.1016/0096-3003(83)90045-0",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Feb 16 18:02:26 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300383900450",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Izsak:2006:MLE,
  author =       "F. Izs{\'a}k",
  title =        "Maximum likelihood estimation for constrained
                 parameters of multinomial distributions --- Application
                 to {Zipf--Mandelbrot} models",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "51",
  number =       "3",
  pages =        "1575--1583",
  day =          "1",
  month =        dec,
  year =         "2006",
  CODEN =        "CSDADW",
  DOI =          "http://dx.doi.org/10.1016/j.csda.2006.05.008",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  MRnumber =     "2307527",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016794730600154X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  keywords =     "Zipf's Law",
}

@Article{Jager:2008:DAD,
  author =       "Hendrik Jager and Pierre Liardet",
  title =        "Distributions arithm{\'e}tiques des d{\'e}nominateurs
                 de convergents de fractions continues. ({French})
                 [Arithmetic distributions of the denominators of
                 continued fractions]",
  journal =      "Proceedings of the Koninklijke Nederlandse Akademie
                 van Wetenschappen, Series A, Indagationes
                 mathematicae",
  volume =       "91",
  number =       "2",
  pages =        "181--197",
  day =          "20",
  month =        jun,
  year =         "2008",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/S1385-7258(88)80026-X",
  ISSN =         "1385-7258 (print), 1878-5972 (electronic)",
  ISSN-L =       "1385-7258",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
  acknowledgement = ack-nhfb,
  fjournal =     "Indagationes Mathematicae (Proceedings)",
  keywords =     "Benford's Law",
  language =     "French",
  xxjournal =    "Indagationes Mathematicae (Proceedings)",
}

@MastersThesis{Jamain:2001:BL,
  author =       "Adrien Jamain",
  title =        "{Benford's Law}",
  type =         "{Master}'s thesis",
  school =       "Department of Mathematics, Imperial College of London
                 and ENSIMAG",
  address =      "London, UK",
  pages =        "????",
  year =         "2001",
  bibdate =      "Sat Feb 16 18:06:41 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Not found in Imperial College Library or COPAC
                 catalogs on 16 February 2013. URL link is broken too.",
  URL =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Jang:2008:CDH,
  author =       "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
                 S. J. Miller",
  title =        "Chains of distributions, hierarchical {Bayesian}
                 models and {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J;
                 http://arxiv.org/abs/0805.4226",
  abstract =     "Kossovsky recently conjectured that the distribution
                 of leading digits of a chain of probability
                 distributions converges to Benford's law as the length
                 of the chain grows. We prove his conjecture in many
                 cases, and provide an interpretation in terms of
                 products of independent random variables and a central
                 limit theorem. An interesting consequence is that in
                 hierarchical Bayesian models priors tend to satisfy
                 Benford's Law as the number of levels of the hierarchy
                 increases, which allows us to develop some simple tests
                 (based on Benford's law) to test proposed models. We
                 give explicit formulas for the error terms as sums of
                 Mellin transforms, which converges extremely rapidly as
                 the number of terms in the chain grows. We may
                 interpret our results as showing that certain Markov
                 chain Monte Carlo processes are rapidly mixing to
                 Benford's law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0805.4226",
  keywords =     "Mathematics - Probability, Mathematics - Statistics
                 Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
  pagecount =    "15",
  primaryclass = "math.PR",
}

@Article{Jang:2009:CDH,
  author =       "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
                 S. J. Miller",
  title =        "Chains of distributions, hierarchical {Bayesian}
                 models and {Benford's Law}",
  journal =      "Journal of Algebra, Number Theory: Advances and
                 Applications",
  volume =       "1",
  number =       "1",
  pages =        "37--60",
  month =        mar,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0972-5555",
  ISSN-L =       "0972-5555",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0805.4226",
  keywords =     "Mathematics - Probability, Mathematics - Statistics
                 Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
  primaryclass = "math.PR",
}

@Article{Jansen:2001:RNP,
  author =       "C. J. M. Jansen and M. M. W. Pollmann",
  title =        "On Round Numbers: Pragmatic Aspects of Numerical
                 Expressions",
  journal =      j-J-QUANT-LINGUISTICS,
  volume =       "8",
  number =       "3",
  pages =        "187--201",
  month =        "????",
  year =         "2001",
  DOI =          "http://dx.doi.org/10.1076/jqul.8.3.187.4095",
  ISSN =         "0929-6174 (print), 1744-5035 (electronic)",
  ISSN-L =       "0929-6174",
  bibdate =      "Sat Jan 07 09:51:05 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095",
  abstract =     "This paper describes and explains some regularities in
                 the frequency of numbers in text. An analysis of number
                 frequencies in text corpora in Dutch, English, German,
                 and French confirms the expectation that frequency is
                 highly dependent on two factors: magnitude and
                 roundness. Roundness (defined as number frequency in an
                 approximation context) proves to be related to three
                 arithmetical properties: `10-ness', `2-ness', and
                 `5-ness'. In predicting the frequency of numbers
                 irrespective of their context `$ 2 1 / 2 $-ness' should
                 be added to these factors, as is suggested in the work
                 of Sigurd (1988). The role of the four number
                 characteristics found in this study can be explained by
                 the preference of the language user for using base
                 numbers, and for doubling and halving quantities.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Linguistics",
  onlinedate =   "09 Aug 2010",
}

@Article{Janvresse:2004:UDB,
  author =       "{\'E}lise Janvresse and Thierry de la Rue",
  title =        "From uniform distributions to {Benford}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "41",
  number =       "4",
  pages =        "1203--1210",
  year =         "2004",
  CODEN =        "JPRBAM",
  DOI =          "http://dx.doi.org/10.1239/jap/1101840566",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "60J20 (60J10)",
  MRnumber =     "2122815 (2006b:60161)",
  MRreviewer =   "Michael Drmota",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566;
                 http://www.jstor.org/stable/4141393;
                 https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf",
  abstract =     "We provide a new, probabilistic explanation for the
                 appearance of Benford's law in everyday-life numbers,
                 by showing that it arises naturally when we consider
                 mixtures of uniform distributions. Then we connect our
                 result to a result of Flehinger, for which we provide a
                 shorter proof, and the speed of convergence.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
}

@Article{Janvresse:2009:BL,
  author =       "Elise Janvresse and Thierry de la Rue",
  title =        "{Benford}'s law",
  journal =      "Butl. Soc. Catalana Mat.",
  volume =       "24",
  number =       "1",
  pages =        "5--12",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0214-316X",
  ISSN-L =       "0214-316X",
  MRclass =      "62-01",
  MRnumber =     "2567485",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translated by Frederic Utzet",
  acknowledgement = ack-nhfb,
  fjournal =     "Butllet{\'\i}n de la Societat Catalana de
                 Matem{\`a}tiques",
}

@Article{Janvresse:2011:AAU,
  author =       "{\'E}lise Janvresse and Thierry {De La Rue}",
  title =        "Averaging along Uniform Random Integers",
  journal =      "ArXiv e-prints",
  year =         "2011",
  bibdate =      "Mon Nov 21 07:06:41 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1103.1719",
  abstract =     "Motivated by giving a meaning to ``The probability
                 that a random integer has initial digit d'', we define
                 a URI-set as a random set E of natural integers such
                 that each n>0 belongs to E with probability 1/n,
                 independently of other integers. This enables us to
                 introduce two notions of densities on natural numbers:
                 The URI-density, obtained by averaging along the
                 elements of $E$, and the local URI-density, which we
                 get by considering the $k$-th element of $E$ and
                 letting $k$ go to infinity. We prove that the elements
                 of $E$ satisfy Benford's law, both in the sense of
                 URI-density and in the sense of local URI-density.
                 Moreover, if $ b_1 $ and $ b_2 $ are two
                 multiplicatively independent integers, then the
                 mantissae of a natural number in base $ b_1 $ and in
                 base $ b_2 $ are independent. Connections of
                 URI-density and local URI-density with other well-known
                 notions of densities are established: Both are stronger
                 than the natural density, and URI-density is equivalent
                 to log-density. We also give a stochastic
                 interpretation, in terms of URI-set, of the $ H_\infty
                 $-density.",
  acknowledgement = ack-nhfb,
}

@Article{Janvresse:2012:AAU,
  author =       "{\'E}lise Janvresse and Thierry {De La Rue}",
  title =        "Averaging along Uniform Random Integers",
  journal =      "Uniform Distribution Theory",
  volume =       "7",
  number =       "2",
  pages =        "35--60",
  month =        "????",
  year =         "2012",
  DOI =          "????",
  ISSN =         "1336-913X",
  ISSN-L =       "1336-913X",
  bibdate =      "Tue Feb 19 05:56:13 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.boku.ac.at/MATH/udt/vol07/no2/03JanRue16-11.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.boku.ac.at/MATH/udt/",
  keywords =     "Benford's Law",
}

@PhdThesis{Janvresse:2012:QCP,
  author =       "{\'E}lise Janvresse",
  title =        "Quelques contributions aux probabilit{\'e}s et {\`a}
                 la th{\'e}orie ergodique. ({French}) [Some
                 contributions to probability theory and ergodic
                 theory]",
  type =         "Document de synth{\`e}se pr{\'e}sent{\'e} pour
                 l'{Habilitation {\`a} Diriger des Recherches}",
  school =       "l'Universit{\'e} de Rouen",
  address =      "Rouen, France",
  pages =        "67",
  day =          "17",
  month =        feb,
  year =         "2012",
  bibdate =      "Tue Feb 19 05:57:33 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.univ-rouen.fr/LMRS/Persopage/Janvresse/hdr_Janvresse.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  language =     "French",
}

@MastersThesis{Jasak:2010:BZR,
  author =       "Zoran Jasak",
  title =        "Benfordov zakon i reinforcement u{\v{c}}enje.
                 ({Bosnian}) [{Benford's Law} and reinforcement
                 learning]",
  type =         "{Magistarski Rad} ({M.Sc.} Thesis)",
  school =       "Prirodno-Matematicki Fakultet, Odsjek za matematiku,
                 Ju Univerzitet u Tuzla",
  address =      "Tuzla, Bosnia and Herzegovina",
  pages =        "124",
  month =        dec,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:48:33 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "action; Adaptive Benford's method; Adaptivna
                 Benfordova metoda; akcija; Benford's law; Benfordov
                 zakon; confidence intervals; contamination level;
                 intervali povjerenja; koli{\v{c}}nik; nivo
                 kontaminacije; Q learning; Q u{\v{c}}enje; quotient;
                 reinforcement learning; reinforcement u{\v{c}}enje;
                 Sarsa; stanje; state",
  language =     "Bosnian",
}

@Article{Jech:1992:LDL,
  author =       "Thomas Jech",
  title =        "The logarithmic distribution of leading digits and
                 finitely additive measures",
  journal =      j-DISCRETE-MATH,
  volume =       "108",
  number =       "1--3",
  pages =        "53--57",
  month =        "????",
  year =         "1992",
  CODEN =        "DSMHA4",
  ISSN =         "0012-365X (print), 1872-681X (electronic)",
  ISSN-L =       "0012-365X",
  bibdate =      "Fri Nov 18 12:12:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete Mathematics",
}

@Article{Jelenkovic:2008:CMS,
  author =       "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang",
  title =        "Characterizing the miss sequence of the {LRU} cache",
  journal =      j-SIGMETRICS,
  volume =       "36",
  number =       "2",
  pages =        "119--121",
  month =        sep,
  year =         "2008",
  CODEN =        "????",
  DOI =          "http://doi.acm.org/10.1145/1453175.1453203",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Wed Aug 25 07:31:09 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Renewed interest in caching systems stems from their
                 wide-spread use for reducing the document download
                 latency over the Internet. Since caches are usually
                 organized in a hierarchical manner, it is important to
                 study the performance properties of tandem caches. The
                 first step in understanding this problem is to
                 characterize the miss stream from one single cache
                 since it represents the input to the next level cache.
                 In this regard, we discover that the miss stream from
                 one single cache is approximated well by the
                 superposition of a number of asymptotically independent
                 renewal processes. Interestingly, when this weakly
                 correlated miss sequence is fed into another cache,
                 this barely observable correlation can lead to
                 measurably different caching performance when compared
                 to the independent reference model. This result is
                 likely to enable the development of a rigorous analysis
                 of the tandem cache performance.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "average-case analysis; cache fault probability;
                 hierarchical caching; least-recently-used caching; web
                 caching; Zipf's law",
}

@Article{Jiang:2010:NMS,
  author =       "Weina Jiang and Anthony T. S. Ho and Helen Treharne
                 and Yun Q. Shi",
  title =        "A Novel Multi-size Block {Benford's Law} Scheme for
                 Printer Identification",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6297",
  pages =        "643--652",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-15702-8_59",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:47:23 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59",
  acknowledgement = ack-nhfb,
  book-DOI =     "http://dx.doi.org/10.1007/978-3-642-15702-8",
  book-URL =     "http://www.springerlink.com/content/978-3-642-15702-8",
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Jiang:2011:BLN,
  author =       "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao",
  title =        "{Benford}'s law in nuclear structure physics",
  journal =      j-CHIN-PHYS-LETT,
  volume =       "28",
  number =       "3",
  pages =        "032101",
  month =        "????",
  year =         "2011",
  CODEN =        "CPLEEU",
  DOI =          "http://dx.doi.org/10.1088/0256-307X/28/3/032101",
  ISSN =         "0256-307X (print), 1741-3540 (electronic)",
  ISSN-L =       "0256-307X",
  bibdate =      "Mon Nov 14 16:16:10 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Chin. Phys. Lett.",
  fjournal =     "Chinese Physics Letters",
  pagecount =    "4",
}

@Article{Jin:2009:AUR,
  author =       "Jang C. Jin",
  title =        "{Asian} University Rankings in International and
                 Development Economics: An Application of {Zipf's Law}",
  journal =      j-REV-INT-ECON,
  volume =       "17",
  number =       "1",
  pages =        "137--143",
  year =         "2009",
  DOI =          "http://dx.doi.org/10.1111/j.1467-9396.2008.00790.x",
  ISSN =         "0965-7576 (print), 1467-9396 (electronic)",
  ISSN-L =       "0965-7576",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Review of International Economics",
}

@Article{Jin:2009:PME,
  author =       "Jang C. Jin",
  title =        "Publications in mathematical economics and
                 econometrics: ranking of {Asian} universities and an
                 application of {Zipf's Law}",
  journal =      "{Asian-Pacific} Economic Literature",
  volume =       "23",
  number =       "2",
  pages =        "116--122",
  year =         "2009",
  DOI =          "http://dx.doi.org/10.1111/j.1467-8411.2009.01233.x",
  ISSN =         "0818-9935 (print), 1467-8411 (electronic)",
  ISSN-L =       "0818-9935",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291467-8411",
}

@Article{Jolion:2001:IBL,
  author =       "Jean-Michel Jolion",
  title =        "Images and {Benford}'s law",
  journal =      j-J-MATH-IMAG-VIS,
  volume =       "14",
  number =       "1",
  pages =        "73--81",
  year =         "2001",
  CODEN =        "JMIVEK",
  DOI =          "http://dx.doi.org/10.1023/A:1008363415314",
  ISSN =         "0924-9907 (print), 1573-7683 (electronic)",
  ISSN-L =       "0924-9907",
  MRclass =      "94A08 (68U10)",
  MRnumber =     "1818436 (2001m:94007)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Imaging and Vision: JMIV",
}

@Article{Jolissaint:2005:LBR,
  author =       "Paul Jolissaint",
  title =        "Loi de {Benford}, relations de r{\'e}currence et
                 suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s
                 Law, recurrence relations, and equidistributed
                 sequences]",
  journal =      j-ELEM-MATH,
  volume =       "60",
  number =       "1",
  pages =        "10--18",
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.4171/EM/2",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRclass =      "11K36 (37A45 60E99)",
  MRnumber =     "2188341 (2006j:11109)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Jolissaint:2009:LBR,
  author =       "Paul Jolissaint",
  title =        "Loi de {Benford}, relations de r{\'e}currence et
                 suites {\'e}quidistribu{\'e}es. {II}. ({French})
                 [{Benford}'s Law, recurrence relations, and
                 equidistributed sequences. {II}]",
  journal =      j-ELEM-MATH,
  volume =       "64",
  number =       "1",
  pages =        "21--36",
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.4171/EM/112",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRclass =      "62E10 (11A63 37A45)",
  MRnumber =     "2471593 (2010f:62032)",
  MRreviewer =   "Denys Pommeret",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Jones:2002:LDR,
  author =       "B. K. Jones",
  title =        "Logarithmic distributions in reliability analysis",
  journal =      j-MICROELECT-RELIABILITY,
  volume =       "42",
  number =       "4--5",
  pages =        "779--786",
  month =        apr # "\slash " # may,
  year =         "2002",
  CODEN =        "MCRLAS",
  DOI =          "http://dx.doi.org/10.1016/S0026-2714(02)00031-8",
  ISSN =         "0026-2714 (print), 1872-941X (electronic)",
  ISSN-L =       "0026-2714",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Benford's Law; Pareto distribution; Zipf's Law",
}

@TechReport{Judge:2006:DPS,
  author =       "George Judge and Laura Schechter",
  title =        "Detecting problems in survey data using {Benford}'s
                 law",
  type =         "Preprint",
  institution =  "University of California at Berkeley and University of
                 Wisconsin at Madison",
  address =      "Berkeley, CA, USA and Madison, WI, USA",
  pages =        "30",
  day =          "1",
  month =        nov,
  year =         "2006",
  bibdate =      "Sat Feb 16 18:12:29 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.aae.wisc.edu/lschechter/benford.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Judge:2009:DPS,
  author =       "G. Judge and L. Schechter",
  title =        "Detecting Problems in Survey Data using {Benford's
                 Law}",
  journal =      j-J-HUM-RESOUR,
  volume =       "44",
  number =       "1",
  pages =        "1--24",
  month =        "Winter",
  year =         "2009",
  CODEN =        "JHREA9",
  DOI =          "http://dx.doi.org/10.3368/jhr.44.1.1",
  ISSN =         "0022-166X (print), 1548-8004 (electronic)",
  ISSN-L =       "0022-166X",
  bibdate =      "Tue Nov 22 18:55:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jhr.uwpress.org/content/44/1/1.abstract;
                 http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Human Resources",
}

@Article{Kafri:2008:SIS,
  author =       "Oded Kafri",
  title =        "Sociological Inequality and the {Second Law}",
  journal =      "ArXiv e-prints",
  year =         "2008",
  bibdate =      "Mon Nov 21 06:41:29 2011",
  bibsource =    "http://dblp.uni-trier.de;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/0805.3206",
  abstract =     "There are two fair ways to distribute particles in
                 boxes. The first way is to divide the particles equally
                 between the boxes. The second way, which is calculated
                 here, is to score fairly the particles between the
                 boxes. The obtained power law distribution function
                 yields an uneven distribution of particles in boxes. It
                 is shown that the obtained distribution fits well to
                 sociological phenomena, such as the distribution of
                 votes in polls and the distribution of wealth and
                 Benford's law.",
  acknowledgement = ack-nhfb,
}

@Article{Kafri:2009:DNE,
  author =       "Oded Kafri",
  title =        "The Distributions in Nature and Entropy Principle",
  journal =      "ArXiv e-prints",
  day =          "28",
  month =        jul,
  year =         "2009",
  bibdate =      "Mon Nov 21 07:26:11 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/0907.4852",
  abstract =     "The derivation of the maximum entropy distribution of
                 particles in boxes yields two kinds of distributions: a
                 ``bell-like'' distribution and a long-tail
                 distribution. The first one is obtained when the ratio
                 between particles and boxes is low, and the second one
                 when the ratio is high. The obtained long tail
                 distribution yields correctly the empirical Zipf law,
                 Pareto's 20:80 rule and Benford's law. Therefore, it is
                 concluded that the long tail and the ``bell-like''
                 distributions are outcomes of the tendency of
                 statistical systems to maximize entropy.",
  acknowledgement = ack-nhfb,
  pagecount =    "19",
}

@Article{Kafri:2009:EPD,
  author =       "Oded Kafri",
  title =        "Entropy Principle in Direct Derivation of {Benford's
                 Law}",
  journal =      "ArXiv e-prints",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K;
                 http://arxiv.org/abs/0901.3047",
  abstract =     "The uneven distribution of digits in numerical data,
                 known as Benford's law, was discovered in 1881. Since
                 then, this law has been shown to be correct in copious
                 numerical data relating to economics, physics and even
                 prime numbers. Although it attracts considerable
                 attention, there is no a priori probabilistic criterion
                 when a data set should or should not obey the law. Here
                 a general criterion is suggested, namely that any file
                 of digits in the Shannon limit (namely, having maximum
                 entropy) has a Benford's law distribution of digits.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0901.3047",
  keywords =     "Computer Science - Discrete Mathematics, Physics -
                 Data Analysis, Statistics and Probability",
  primaryclass = "cs.DM",
}

@InCollection{Kanemitsu:1988:BLF,
  author =       "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard
                 Rauzy and Jau-Shyong Shiue",
  booktitle =    "Probability theory and mathematical statistics
                 ({Kyoto}, 1986)",
  title =        "On {Benford}'s law: the first digit problem",
  volume =       "1299",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "158--169",
  year =         "1988",
  DOI =          "http://dx.doi.org/10.1007/BFb0078471",
  MRclass =      "11K06 (60E99)",
  MRnumber =     "935987 (89d:11059)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Math.",
  acknowledgement = ack-nhfb,
}

@Article{Kanter:1995:MPL,
  author =       "I. Kanter and D. A. Kessler",
  title =        "{Markov} Processes: Linguistics and {Zipf's Law}",
  journal =      j-PHYS-REV-LET,
  volume =       "74",
  number =       "??",
  pages =        "4559--??",
  day =          "29",
  month =        may,
  year =         "1995",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.74.4559",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Katsikas:1990:CDG,
  author =       "A. A. Katsikas and J. S. Nicolis",
  title =        "Chaotic dynamics of generating {Markov} partitions and
                 linguistic sequences mimicking {Zipf}'s law",
  journal =      "Nuovo Cimento D (1)",
  volume =       "12",
  number =       "2",
  pages =        "177--195",
  year =         "1990",
  CODEN =        "NCSDDN",
  DOI =          "http://dx.doi.org/10.1007/BF02450454",
  ISSN =         "0392-6737 (print), 1826-9893 (electronic)",
  ISSN-L =       "0392-6737",
  MRclass =      "92A90 (58F13 92A08 94A15)",
  MRnumber =     "1049338 (90m:92114)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D.
                 Serie 1",
}

@Article{Katsikas:1991:CDG,
  author =       "A. A. Katsikas and J. S. Nicolis",
  title =        "Chaotic Dynamics of Generating {Markov} Partitions,
                 and Linguistic Sequences Mimicking {Zipf}'s Law",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "565",
  pages =        "335--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon May 13 08:51:55 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
}

@Article{Katz:1986:FDP,
  author =       "Talbot M. Katz and Daniel I. A. Cohen",
  title =        "The First Digit Property for Exponential Sequences is
                 Independent of the Underlying Distribution",
  journal =      j-FIB-QUART,
  volume =       "24",
  number =       "1",
  pages =        "2--7",
  month =        feb,
  year =         "1986",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:45 MDT 2011",
  bibsource =    "http://www.fq.math.ca/24-1.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/24-1/katz.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Kawamura:2002:UZL,
  author =       "Kenji Kawamura and Naomichi Hatano",
  title =        "Universality of {Zipf}'s law",
  journal =      j-J-PHYS-SOC-JAP,
  volume =       "71",
  number =       "5",
  pages =        "1211--1213",
  year =         "2002",
  CODEN =        "JUPSAU",
  DOI =          "http://dx.doi.org/10.1143/JPSJ.71.1211",
  ISSN =         "0031-9015 (print), 1347-4073 (electronic)",
  ISSN-L =       "0031-9015",
  bibdate =      "Sat Nov 12 11:00:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jpsj.ipap.jp/",
  ZMnumber =     "1063.60114",
  abstract =     "The aim of the present paper is to propose and
                 simulate a simple and generic model that reproduces
                 Zipf's law. In the proposed model, the time evolution
                 is considered to be a random walk in the logarithmic
                 scale reflecting the company asset distribution and/or
                 the evolution of city populations (e.g. Zipf's law for
                 income distribution asserts that the size and number of
                 companies are in inverse proportional relationship).
                 The paper explains theoretically and shows by numerical
                 simulation that the introduced model of Zipf's law has
                 a very robust behaviour when applied to various natural
                 and social phenomena. The authors do not investigate
                 the famous case of Zipf's law application to the
                 frequency of English words, but they speculate that
                 this case might be also explained within the same time
                 development of the proposed model.",
  acknowledgement = ack-nhfb,
  classmath =    "60J60 (Diffusion processes) 60J70 (Appl. of diffusion
                 theory) 76R50 (Diffusion) 82C24 (Interface problems
                 (dynamic and non-equilibrium))",
  fjournal =     "Journal of the Physical Society of Japan",
  keywords =     "city population evolution; company asset distribution;
                 diffusion; generic model of Zipf's law; natural and
                 social phenomena; random walk in logarithmic scale",
  ZMreviewer =   "Neculai Curteanu (Ia\c si)",
}

@Article{Kaynar:2010:FSM,
  author =       "B. Kaynar and A. Berger and T. P. Hill and A. Ridder",
  title =        "Finite-state {Markov} Chains obey {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        mar,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "60J22, 11K06, 15B51",
  bibdate =      "Tue Nov 15 06:30:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K;
                 http://arxiv.org/abs/1003.0562",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1003.0562",
  keywords =     "Mathematics - Probability",
  primaryclass = "math.PR",
}

@Article{Kechedzhi:2005:RDW,
  author =       "K. E. Kechedzhi and O. V. Usatenko and V. A.
                 Yampol{\cprime}skii",
  title =        "Rank distributions of words in correlated symbolic
                 systems and the {Zipf} law",
  journal =      j-PHYS-REV-E,
  volume =       "72",
  number =       "4",
  pages =        "046138",
  day =          "28",
  month =        oct,
  year =         "2005",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.72.046138",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  MRclass =      "82C31",
  MRnumber =     "2183723 (2006f:82069)",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.72.046138",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "6",
}

@Article{Kemperman:1975:BDM,
  author =       "J. H. B. Kemperman",
  title =        "Bounds on the discrepancy modulo $1$ of a real random
                 variable",
  journal =      j-BULL-INST-MATH-STAT,
  volume =       "4",
  number =       "??",
  pages =        "138--??",
  month =        "????",
  year =         "1975",
  CODEN =        "SMBCVA",
  ISSN =         "0146-3942",
  ISSN-L =       "0146-3942",
  bibdate =      "Sat Nov 12 16:26:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Abstract no. 75t-47.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin --- Institute of Mathematical Statistics",
}

@Article{Kennard:1981:MDF,
  author =       "Robert W. Kennard and John E. Reith",
  title =        "{M32}. On the distribution of first digits",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "97--98",
  month =        "????",
  year =         "1981",
  CODEN =        "CSSCDB",
  DOI =          "http://dx.doi.org/10.1080/03610918108812195",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 07 09:27:42 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  keywords =     "Benford's Law",
  onlinedate =   "27 Jun 2007",
}

@InProceedings{Khosravani:2012:TIB,
  author =       "A. Khosravani and C. Rasinariu",
  title =        "Transformation invariance of {Benford} variables and
                 their numerical modeling",
  crossref =     "Niola:2012:RRA",
  pages =        "57--61",
  year =         "2012",
  bibdate =      "Tue Feb 19 06:01:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.wseas.us/e-library/conferences/2012/SaintMalo/ACMIN/ACMIN-06.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kim:2011:ZAS,
  author =       "SeongKi Kim and HaYoon Song and SangYong Han",
  title =        "{ZipfAllocation}: an algorithm for static allocation
                 of movies in a cluster of video servers",
  journal =      j-SPE,
  volume =       "41",
  number =       "6",
  pages =        "695--716",
  month =        may,
  year =         "2011",
  CODEN =        "SPEXBL",
  DOI =          "http://dx.doi.org/10.1002/spe.1027",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Tue Jun 21 17:09:57 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soft{\-}ware\emdash Prac{\-}tice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "25 Nov 2010",
}

@Article{Kim:2012:BLN,
  author =       "Sangrak Kim",
  title =        "{Benford}'s law in non-equilibrium processes: Droplet
                 collisions case",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "20",
  pages =        "4970--4975",
  day =          "15",
  month =        oct,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2012.05.043",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437112004141",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
}

@InProceedings{Kitsuregawa:1989:EBS,
  author =       "Masaru Kitsuregawa and Masaya Nakayama and Mikio
                 Takagi",
  title =        "The Effect of Bucket Size Tuning in the Dynamic Hybrid
                 {GRACE} Hash Join Method",
  crossref =     "Apers:1989:VLD",
  pages =        "257--266",
  month =        aug,
  year =         "1989",
  CODEN =        "VLDBDP",
  bibdate =      "Sat Jan 25 17:38:12 MST 1997",
  bibsource =    "Compendex database;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/hash.bib",
  abstract =     "In this paper, we show detailed analysis and
                 performance evaluation of the Dynamic Hybrid GRACE Hash
                 Join Method (DHGH Method) when the tuple distribution
                 in buckets is unbalanced. The conventional Hash Join
                 Methods specify the tuple distribution in buckets
                 statically. However it may differ from estimation since
                 join operations are applied with selection operations.
                 When the tuple distribution in buckets is unbalanced,
                 the processing cost of join operation becomes more
                 costly than the ideal case when you use Hybrid Hash
                 Join Method (HH Method). On the other hand, when you
                 use the DHGH Method, the destaging buckets are selected
                 dynamically, gives the same performance as the ideal
                 case even if the tuple distribution in buckets is
                 unbalanced such as Zipf-like distributions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Tokyo",
  affiliationaddress = "Tokyo, Jpn",
  classification = "723",
  journalabr =   "Very Large Data Bases Int Conf Very Large Data Bases",
  keywords =     "Computer Metatheory --- Programming Theory; Computer
                 Programming --- Algorithms; Database Systems; Query
                 Processing; Relational; Relational Algebra; VLDB",
}

@Article{Klar:2010:ZLL,
  author =       "B. Klar and P. R. Parthasarathy and N. Henze",
  title =        "{Zipf} and {Lerch} limit of birth and death
                 processes",
  journal =      j-PROB-ENG-INFO-SCI,
  volume =       "24",
  number =       "1",
  pages =        "129--144",
  year =         "2010",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1017/S0269964809990179",
  ISSN =         "0269-9648 (print), 1469-8951 (electronic)",
  ISSN-L =       "0269-9648",
  MRclass =      "60J27 (91F20)",
  MRnumber =     "2575846 (2010m:60254)",
  bibdate =      "Sat Mar 23 12:53:04 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Probab. Engrg. Inform. Sci.",
  fjournal =     "Probability in the Engineering and Informational
                 Sciences",
  keywords =     "Zipf's Law",
}

@Article{Knudsen:2001:ZLC,
  author =       "Thorbj{\o}rn Knudsen",
  title =        "{Zipf}'s law for cities and beyond: the case of
                 {Denmark}",
  journal =      j-AM-J-ECON-SOCIOL,
  volume =       "60",
  number =       "1",
  pages =        "123--146",
  month =        jan,
  year =         "2001",
  CODEN =        "AJESA3",
  DOI =          "http://dx.doi.org/10.1111/1536-7150.00057",
  ISSN =         "0002-9246 (print), 1536-7150 (electronic)",
  ISSN-L =       "0002-9246",
  bibdate =      "Sat Feb 16 18:14:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3487947",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Journal of Economics and Sociology",
}

@Book{Knuth:1969:SNM,
  author =       "Donald E. Knuth",
  title =        "Semi\-nu\-mer\-i\-cal Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  ISBN =         "0-201-03802-1",
  ISBN-13 =      "978-0-201-03802-6",
  LCCN =         "QA76.5 .K57",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is discussed on pp. 219--229.",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
}

@Book{Knuth:1997:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1997",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See section 4.2.4V, The Fraction Parts, pages
                 254--262, for a discussion of Benford's Law.",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
}

@Article{Kohyama:1984:TIC,
  author =       "Tamotsu Kohyama and Y{\=o}ji Aizawa",
  title =        "Theory of the intermittent chaos. {$ 1 / f $} spectrum
                 and the {Pareto--Zipf} law",
  journal =      j-PROG-THEOR-PHYS,
  volume =       "71",
  number =       "5",
  pages =        "917--929",
  year =         "1984",
  CODEN =        "PTPKAV",
  DOI =          "http://dx.doi.org/10.1143/PTP.71.917",
  ISSN =         "0033-068X (print), 1347-4081 (electronic)",
  ISSN-L =       "0033-068X",
  MRclass =      "58F13 (76F99)",
  MRnumber =     "756214 (86a:58063)",
  MRreviewer =   "Joseph Ford",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
}

@TechReport{Kollath-Romano:2004:DSD,
  author =       "P. Kollath-Romano",
  title =        "On the distribution of significant digits in numbers",
  type =         "Preprint",
  institution =  "Rensselaer Polytechnic Institute",
  address =      "Troy, NY, USA",
  year =         "2004",
  bibdate =      "Sat Feb 16 18:15:19 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Konheim:1965:MDT,
  author =       "Alan G. Konheim",
  title =        "Mantissa Distributions (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "143--144",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  DOI =          "http://dx.doi.org/10.2307/2004111",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Kontorovich:2005:BLV,
  author =       "Alex V. Kontorovich and Steven J. Miller",
  title =        "{Benford}'s law, values of {$L$}-functions and the {$
                 3 x + 1 $} problem",
  journal =      j-ACTA-ARITHMETICA,
  volume =       "120",
  number =       "3",
  pages =        "269--297",
  year =         "2005",
  CODEN =        "AARIA9",
  DOI =          "http://dx.doi.org/10.4064/aa120-3-4",
  ISSN =         "0065-1036 (print), 1730-6264 (electronic)",
  ISSN-L =       "0065-1036",
  MRclass =      "11K06 (11B37 11M06 37A45)",
  MRnumber =     "2188844 (2007c:11085)",
  MRreviewer =   "J. C. Lagarias",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005AcAri.120..269K;
                 http://arxiv.org/abs/math/0412003",
  abstract =     "We show the leading digits of a variety of systems
                 satisfying certain conditions follow Benford's Law. For
                 each system proving this involves two main ingredients.
                 One is a structure theorem of the limiting
                 distribution, specific to the system. The other is a
                 general technique of applying Poisson Summation to the
                 limiting distribution. We show the distribution of
                 values of $L$-functions near the central line and (in
                 some sense) the iterates of the $ 3 x + 1 $ Problem are
                 Benford.",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Arithmetica",
}

@Article{Kossovsky:2006:TBU,
  author =       "Alex Ely Kossovsky",
  title =        "Towards a Better Understanding of the Leading Digits
                 Phenomena",
  journal =      "ArXiv Mathematics e-prints",
  year =         "2006",
  bibdate =      "Mon Nov 21 06:46:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math/0612627",
  abstract =     "This article on leading digits (Benford's Law)
                 contains the following: (i) An attempt at a
                 comprehensive account on the leading digits phenomena,
                 incorporating many of its existing explanations,
                 proofs, and differing points of view. (ii) The finding
                 that leading digits of random numbers derived from a
                 chain of distributions that are linked via parameter
                 selection are logarithmic in the limit as the number of
                 sequences approaches infinity, and that empirically
                 only around 5 or 6 sequences of such a distribution
                 chain are needed to obtain results that are close
                 enough to the logarithmic (i.e., rapid convergence).
                 (iii) An outright exact logarithmic behavior for a
                 2-sequence chain whenever parametrical density is
                 exactly logarithmic. (iv) An account on the existence
                 of singularities in exponential growth rates with
                 regards to the leading digits distributions of their
                 series. (v) An account on several distributions that
                 are intrinsically logarithmic or approximately so. (vi)
                 A conceptual justification of Flehinger's iterated
                 averaging scheme --- an algorithm that was presented
                 without any clear motivation. (vii) A note on the close
                 relationship of Flehinger's scheme and the chain of
                 distribution to Hill's super distribution. (viii) A
                 conceptual argument justifying the scale invariance
                 principle --- a principle invoked in derivations of
                 Benford's law. (ix) A note on the intimate connection
                 between one-sided tail to the right in density
                 distributions and logarithmic leading digit behavior.",
  acknowledgement = ack-nhfb,
  remark =       "On 18 February 2013, the archive has 17 revisions of
                 this article.",
  xxjournal =    "CoRR",
}

@InCollection{Kotz:2004:FDP,
  author =       "Samuel Kotz and N. Balakrishnan and Campbell B. Read
                 and Brani Vidakovic",
  editor =       "Samuel Kotz and N. Balakrishnan and Campbell B. Read
                 and Brani Vidakovic",
  booktitle =    "Encyclopedia of Statistical Sciences",
  title =        "First-Digit Problem",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "??--??",
  year =         "2004",
  DOI =          "http://dx.doi.org/10.1002/0471667196.ess0783.pub2",
  ISBN =         "0-471-66719-6 (e-book)",
  ISBN-13 =      "978-0-471-66719-3 (e-book)",
  bibdate =      "Sun Feb 24 10:49:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InProceedings{Krakar:2008:ABL,
  author =       "Zdravko Krakar and Mario {\v{Z}}gela",
  editor =       "Boris Aurer and Miroslav Ba{\'c}a",
  booktitle =    "Proceedings of the 19th Central European Conference on
                 Information and Intelligent Systems (CECIS 2008)",
  title =        "Application of {Benford's Law} in Payment System
                 Auditing",
  publisher =    "Fakultet organizacije i informatike",
  address =      "Vara{\v{z}}din, Croatia",
  pages =        "187--193",
  year =         "2008",
  bibdate =      "Sun Nov 13 11:14:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krakar:2008:EBL,
  author =       "Zdravko Krakar and Mario {\v{Z}}gela",
  editor =       "Mario Plenkovi{\'c}",
  booktitle =    "Society and Technology 2008",
  title =        "Evaluation of {Benford's Law}: application in stock
                 prices and stock turnover",
  publisher =    "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo",
  address =      "Zagreb, Croatia",
  pages =        "57--71",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Nov 13 11:18:37 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "International Federation of Communication Studies,
                 Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u
                 Zagrebu.",
}

@Article{Krakar:2009:ABL,
  author =       "Mario {\v{Z}}gela and Zdravko Krakar",
  title =        "Application of {Benford's Law} in Payment System
                 Auditing",
  journal =      j-J-INFO-ORG-SCI,
  volume =       "33",
  number =       "1",
  pages =        "39--51",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1846-3312 (print), 1846-9418 (electronic)",
  ISSN-L =       "1846-3312",
  bibdate =      "Sun Nov 13 11:12:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf;
                 http://jios.foi.hr/index.php/jios/article/view/108/66;
                 http://jios.foi.hr/index.php/jios/issue/view/13",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informational and Organizational Sciences",
  journal-URL =  "http://jios.foi.hr/index.php/jios/index",
  xxjournal =    "Journal of Information Ethics and Organisational
                 Science (wrong!)",
}

@Article{Kreifelts:1973:OBG,
  author =       "Thomas Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
                 Basis for a Floating-Point Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "4",
  pages =        "353--363",
  month =        dec,
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/computing.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "See correction \cite{Kreifelts:1975:OBF}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. Numerische Datenverarbeitung, Bonn, West
                 Germany",
  classification = "723; 921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "base; computer programming; floating point arithmetic;
                 mathematical techniques; optimal choice; rounding
                 errors",
  language =     "German",
}

@Article{Kreifelts:1975:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
                 (Berichtigung)} ({German}) {Optimal Basis Choice for a
                 Floating-Point Arithmetic (Correction)}",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "3",
  pages =        "313--314",
  month =        sep,
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/computing.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kreifelts:1973:OBG}.",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@TechReport{Kreiner:2002:FDL,
  author =       "W. A. Kreiner",
  title =        "First digit law",
  type =         "Preprint",
  institution =  "Abteilung Chemische Physik, Arbeitsgruppe
                 Laseranwendungen, Universit{\"a}t Ulm",
  address =      "Ulm, Germany",
  pages =        "7",
  day =          "3",
  month =        may,
  year =         "2002",
  bibdate =      "Sat Feb 16 18:18:49 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; First Digit Law; Newcomb; Statistisches
                 Fraktal",
  language =     "German",
}

@Article{Kreiner:2003:NBL,
  author =       "W. A. Kreiner",
  title =        "On the {Newcomb--Benford} law",
  journal =      j-Z-NATURFORSCH,
  volume =       "58a",
  number =       "11",
  pages =        "618--622",
  month =        "????",
  year =         "2003",
  CODEN =        "ZNTFA2",
  ISSN =         "0372-9516",
  ISSN-L =       "0372-9516",
  bibdate =      "Sat Feb 16 18:19:41 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Naturforschung}",
}

@Article{Krevitt:1972:CSZ,
  author =       "Beth Krevitt and Belver C. Griffith",
  title =        "A comparison of several {Zipf}-type distributions in
                 their goodness of fit to language data",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "23",
  number =       "3",
  pages =        "220--221",
  year =         "1972",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/asi.4630230310",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Kriel:2010:DDM,
  author =       "Eckhardt Kriel",
  title =        "Discussion of {``Data mining journal entries for fraud
                 detection: An exploratory study''}",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "186--188",
  month =        sep,
  year =         "2010",
  CODEN =        "IJAIA7",
  DOI =          "http://dx.doi.org/10.1016/j.accinf.2010.07.009",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089510000400",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
}

@Article{Kristiansen:2004:BTZ,
  author =       "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
                 Skjeltorp",
  title =        "Braid theory and {Zipf} relation used in dynamics of
                 magnetic microparticles",
  journal =      j-ECONOM-LETT,
  volume =       "30",
  number =       "1",
  pages =        "2387--2388",
  day =          "1",
  month =        may,
  year =         "2004",
  CODEN =        "ECLEDS",
  DOI =          "http://dx.doi.org/10.1016/j.jmmm.2003.12.1288",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304885303019127",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Kristiansen:2004:EOZ,
  author =       "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
                 Skjeltorp",
  title =        "Experimental observation of {Zipf--Mandelbrot}
                 relation",
  journal =      j-PHYSICA-A,
  volume =       "335",
  number =       "3--4",
  pages =        "413--420",
  day =          "15",
  month =        apr,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2003.12.024",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "82D10 (76T99 82-05)",
  MRnumber =     "2044153",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437103011804",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Kristiansen:2006:BTZ,
  author =       "K. de Lange Kristiansen and G. Helgesen and A. T.
                 Skjeltorp",
  title =        "Braid theory and {Zipf--Mandelbrot} relation used in
                 microparticle dynamics",
  journal =      j-EUR-PHYS-J-B,
  volume =       "51",
  number =       "3",
  pages =        "363--371",
  month =        jun,
  year =         "2006",
  CODEN =        "EPJBFY",
  DOI =          "http://dx.doi.org/10.1140/epjb/e2006-00241-7",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Sat Sep 8 18:31:14 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
}

@Article{Krugman:1996:CMU,
  author =       "Paul Krugman",
  title =        "Confronting the Mystery of Urban Hierarchy",
  journal =      j-J-JPN-INT-ECON,
  volume =       "10",
  number =       "4",
  pages =        "399--418",
  month =        dec,
  year =         "1996",
  CODEN =        "JJIEBD",
  DOI =          "http://dx.doi.org/10.1006/jjie.1996.0023",
  ISSN =         "0889-1583 (print), 1095-8681 (electronic)",
  ISSN-L =       "0889-1583",
  bibdate =      "Wed Feb 27 06:15:55 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0889158396900234",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the {Japanese} and International
                 Economies",
  keywords =     "Zipf's Law",
}

@Book{Krugman:1996:SOE,
  author =       "Paul R. Krugman",
  title =        "The Self-Organizing Economy",
  publisher =    "Blackwell Publishers",
  address =      "Cambridge, MA, USA",
  pages =        "vi + 122",
  year =         "1996",
  ISBN =         "1-55786-699-6 (paperback)",
  ISBN-13 =      "978-1-55786-699-8 (paperback)",
  LCCN =         "HB199 .K75 1996",
  bibdate =      "Wed Feb 27 07:08:14 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Economics; Self-organizing systems",
}

@Article{Kuipers:1969:RPR,
  author =       "L. Kuipers",
  title =        "Remark on a Paper by {R. L. Duncan} Concerning the
                 Uniform Distribution Mod $1$ of the Sequence of the
                 Logarithms of the {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "5",
  pages =        "465--466",
  month =        dec,
  year =         "1969",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:21 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-5.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Kuipers:1973:RPD,
  author =       "L. Kuipers and Jau-shyong Shiue",
  title =        "Remark on a Paper by {Duncan} and {Brown} on the
                 Sequence of Logarithms of Certain Recursive Sequences",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "3",
  pages =        "292--293",
  month =        oct,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:42 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-3.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  note =         "See \cite{Brown:1970:MOU}.",
  URL =          "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Book{Kuipers:1974:UDS,
  author =       "Lauwerens Kuipers and Harald Niederreiter",
  title =        "Uniform distribution of sequences",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 390",
  year =         "1974",
  ISBN =         "0-471-51045-9",
  ISBN-13 =      "978-0-471-51045-1",
  LCCN =         "QA292 .K84",
  bibdate =      "Sat Nov 12 15:42:53 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "``A Wiley-Interscience publication.''.",
  subject =      "Sequences (Mathematics); Uniform distribution
                 (Probability theory)",
}

@Book{Kuipers:2006:UDS,
  author =       "Lauwerens Kuipers and Harald Niederreiter",
  title =        "Uniform distribution of sequences",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xviii + 390",
  year =         "2006",
  ISBN =         "0-486-45019-8 (paperback)",
  ISBN-13 =      "978-0-486-45019-3 (paperback)",
  LCCN =         "QA292 .K84 2006",
  bibdate =      "Sat Nov 12 15:42:53 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html;
                 http://www.loc.gov/catdir/toc/fy0612/2005056064.html",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in \cite{Kuipers:1974:UDS}.",
  subject =      "Sequences (Mathematics); Uniform distribution
                 (Probability theory)",
}

@Article{Kulikova:2004:OSS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "One-sided stable distributions and {Benford}'s law",
  journal =      "Teor. Veroyatn. Primen.",
  volume =       "49",
  number =       "1",
  pages =        "178--184",
  year =         "2004",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1137/S0040585X97980944",
  ISSN =         "0040-361X",
  ISSN-L =       "0040-361X",
  MRclass =      "60E07 (60F05)",
  MRnumber =     "2141338 (2005m:60028)",
  MRreviewer =   "S{\'a}ndor Cs{\"o}rg{\H{o}}",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
                 Veroyatnoste{\u\i} i ee Primeneniya",
}

@Article{Kulikova:2005:CAS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "Completely Asymmetric Stable Laws and {Benford's
                 Law}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "49",
  number =       "1",
  pages =        "163--169",
  month =        mar,
  year =         "2005",
  CODEN =        "TPRBAU",
  DOI =          "http://dx.doi.org/10.1137/S0040585X97980944",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Thu Jul 7 19:15:48 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/98094",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of probability and its applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Kulikova:2005:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H. F. D.} ({$H$}-function distribution) and the
                 {Benford} law. {I}",
  journal =      "Teor. Veroyatn. Primen.",
  volume =       "50",
  number =       "2",
  pages =        "366--371",
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1137/S0040585X97981706",
  ISSN =         "0040-361X",
  ISSN-L =       "0040-361X",
  MRclass =      "60E07 (60F05)",
  MRnumber =     "2221718 (2007b:60029)",
  MRreviewer =   "S{\'a}ndor Cs{\"o}rg{\H{o}}",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
                 Veroyatnoste{\u\i} i ee Primeneniya",
}

@Article{Kulikova:2006:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H.F.D.} ({$H$}-function Distribution) and {Benford's
                 Law}. {I}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "50",
  number =       "2",
  pages =        "311--315",
  month =        jan,
  year =         "2006",
  CODEN =        "TPRBAU",
  DOI =          "http://dx.doi.org/10.1137/S0040585X97981706",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Wed May 19 18:14:51 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of probability and its applications",
  journal-URL =  "http://epubs.siam.org/tvp",
}

@InCollection{Kumar:2003:BLA,
  author =       "Kuldeep Kumar and Sukanto Bhattacharya",
  editor =       "Cheng-Few Lee",
  booktitle =    "Advances in Financial Planning and Forecasting",
  title =        "{Benford}'s law and its application in financial fraud
                 detection",
  volume =       "11",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "57--70",
  year =         "2003",
  ISBN =         "0-7623-1016-2",
  ISBN-13 =      "978-0-7623-1016-6",
  ISSN =         "1046-5847",
  LCCN =         "????",
  bibdate =      "Wed Nov 23 16:45:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  bookpages =    "ix + 177",
}

@Article{Kumar:2007:DDD,
  author =       "Kuldeep Kumar and Sukanto Bhattacharya",
  title =        "Detecting the dubious digits: {Benford}'s law in
                 forensic accounting",
  journal =      j-SIGNIF,
  volume =       "4",
  number =       "2",
  pages =        "81--83",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1111/j.1740-9713.2007.00234.x",
  ISSN =         "1740-9705 (print), 1740-9713 (electronic)",
  ISSN-L =       "1740-9705",
  MRnumber =     "2380610",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://onlinelibrary.wiley.com/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Significance ({Oxford, England})",
  onlinedate =   "7 Jun 2007",
}

@Article{Kunoff:1987:FDP,
  author =       "Sharon Kunoff",
  title =        "{$ N! $} has the First Digit Property",
  journal =      j-FIB-QUART,
  volume =       "25",
  number =       "4",
  pages =        "365--367",
  month =        nov,
  year =         "1987",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:01:00 MDT 2011",
  bibsource =    "http://www.fq.math.ca/25-4.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Lagarias:1985:PG,
  author =       "Jeffrey C. Lagarias",
  title =        "The $ 3 x + 1 $ Problem and Its Generalizations",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "92",
  number =       "1",
  pages =        "3--23",
  month =        jan,
  year =         "1985",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11K55 (11K31)",
  MRnumber =     "86i:11043",
  MRreviewer =   "A. D. Pollington",
  bibdate =      "Mon Jun 28 12:37:47 MDT 1999",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
  keywords =     "Benford's Law",
}

@Article{Lagarias:1992:PTS,
  author =       "J. C. Lagarias and A. Weiss",
  title =        "The $ 3 x + 1 $ Problem: Two Stochastic Models",
  journal =      j-ANN-APPL-PROBAB,
  volume =       "2",
  number =       "1",
  pages =        "229--261",
  month =        feb,
  year =         "1992",
  CODEN =        "????",
  ISSN =         "1050-5164",
  ISSN-L =       "1050-5164",
  bibdate =      "Fri Jun 6 11:35:34 MDT 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/annapplprobab.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.aoap/1177005779",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Applied Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoap/;
                 http://www.jstor.org/journals/10505164.html;",
}

@Article{Lagarias:2005:BLF,
  author =       "J. C. Lagarias and K. Soundararajan",
  title =        "{Benford}'s law for the $ 3 x + 1 $ function",
  journal =      "ArXiv Mathematics e-prints",
  month =        sep,
  year =         "2005",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005math......9175L;
                 http://arxiv.org/abs/math/0509175",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0509175",
  keywords =     "Mathematics - Number Theory, Mathematics -
                 Probability",
}

@Article{Lagarias:2006:BLF,
  author =       "Jeffrey C. Lagarias and K. Soundararajan",
  title =        "{Benford}'s law for the $ 3 x + 1 $ function",
  journal =      "J. London Math. Soc. (2)",
  volume =       "74",
  number =       "2",
  pages =        "289--303",
  year =         "2006",
  CODEN =        "JLMSAK",
  DOI =          "http://dx.doi.org/10.1112/S0024610706023131",
  ISSN =         "0024-6107 (print), 1469-7750 (electronic)",
  ISSN-L =       "0024-6107",
  MRclass =      "37A45",
  MRnumber =     "2269630 (2007h:37007)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
}

@Article{Lang:1989:UAB,
  author =       "Sheau-Dong Lang and James R. Driscoll and Jiann H.
                 Jou",
  title =        "A Unified Analysis of Batched Searching of Sequential
                 and Tree-Structured Files",
  journal =      j-TODS,
  volume =       "14",
  number =       "4",
  pages =        "604--618",
  month =        dec,
  year =         "1989",
  CODEN =        "ATDSD3",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  MRclass =      "68P10 (68P20)",
  MRnumber =     "1 073 204",
  bibdate =      "Sat Apr 14 10:34:48 MDT 2001",
  bibsource =    "Database/Graefe.bib; Database/Wiederhold.bib;
                 http://www.acm.org/pubs/toc/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf;
                 http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/;
                 http://www.acm.org/pubs/toc/Abstracts/tods/76908.html",
  abstract =     "A direct and unified approach is used to analyze the
                 efficiency of batched searching of sequential and
                 tree-structured files. The analysis is applicable to
                 arbitrary search distributions, and closed-form
                 expressions are obtained for the expected batched
                 searching cost and savings. In particular, we consider
                 a search distribution satisfying Zipf's law for
                 sequential files and four types of uniform (random)
                 search distribution for sequential and tree-structured
                 files. These results unify and extend earlier research
                 on batched searching and estimating block accesses for
                 database systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Florida Univ., Orlando, FL, USA",
  annote =       "closed-form expressions for the number of accesses
                 needed given arbitrary search distributions.",
  fjournal =     "ACM Transactions on Database Systems",
  generalterms = "Algorithms; Design; Performance; Theory",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
  keywords =     "algorithms; design; performance; theory",
  subject =      "{\bf H.3.3}: Information Systems, INFORMATION STORAGE
                 AND RETRIEVAL, Information Search and Retrieval, Search
                 process. {\bf H.3.2}: Information Systems, INFORMATION
                 STORAGE AND RETRIEVAL, Information Storage, File
                 organization. {\bf H.2.2}: Information Systems,
                 DATABASE MANAGEMENT, Physical Design, Access methods.",
}

@Article{Lansey:2009:ISR,
  author =       "Jonathan C. Lansey and Bruce Bukiet",
  title =        "{Internet} Search Result Probabilities: {Heaps' Law}
                 and Word Associativity",
  journal =      j-J-QUANT-LINGUISTICS,
  volume =       "16",
  number =       "1",
  pages =        "40--66",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/09296170802514153",
  ISSN =         "0929-6174 (print), 1744-5035 (electronic)",
  ISSN-L =       "0929-6174",
  bibdate =      "Sat Jan 07 09:36:17 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153",
  abstract =     "We study the number of internet search results
                 returned from multi-word queries based on the number of
                 results returned when each word is searched for
                 individually. We derive a model to describe search
                 result values for multi-word queries using the total
                 number of pages indexed by Google and by applying the
                 Zipf power law to the words per page distribution on
                 the internet and Heaps' law for unique word counts.
                 Based on data from 351 word pairs each with exactly one
                 hit when searched for together, and a Zipf law
                 coefficient determined in other studies, we approximate
                 the Heaps' law coefficient for the indexed worldwide
                 web (about 8 billion pages) to be $ \beta = 0.52 $.
                 Previous studies used under 20,000 pages. We
                 demonstrate through examples how the model can be used
                 to analyse automatically the relatedness of word pairs
                 assigning each a value we call ``strength of
                 associativity''. We demonstrate the validity of our
                 method with word triplets and through two experiments
                 conducted 8 months apart. We then use our model to
                 compare the index sizes of competing search giants
                 Yahoo and Google.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Linguistics",
  keywords =     "Benford's Law; Heaps' Law; Zipf's Law",
  onlinedate =   "25 Feb 2009",
  remark =       "From page 65: ``We mention that tests we have
                 conducted show that internet searches for random
                 numbers return approximately log-normally distributed
                 results and sorting by first digits yields results that
                 follow Benford's law (1938).''",
}

@Article{Lanza:2000:UDA,
  author =       "R. B. Lanza",
  title =        "Using digital analysis to detect fraud: Review of the
                 {DATAS\reg} statistical analysis tool",
  journal =      j-J-FORENSIC-ACCOUNT,
  volume =       "1",
  number =       "??",
  pages =        "291--296",
  month =        "????",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "1524-5586",
  bibdate =      "Tue Nov 22 10:47:45 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.rtedwards.com/journals/JFA/",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@Article{Lanza:2003:FSP,
  author =       "Richard B. Lanza",
  title =        "Fear Not the Software: Proactively Detecting
                 Occupational Fraud Using Computer Audit Reports",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep # "\slash " # feb,
  year =         "2003",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:14:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294967868",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Lanza:2004:CBS,
  author =       "Richard B. Lanza",
  title =        "Comparing Best Software for Fraud Examinations: Fraud
                 Data Interrogation Tools",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        nov # "\slash" # dec,
  year =         "2004",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:17:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294967837",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Lee:2010:SAR,
  author =       "Joanne Lee and Wendy K. Tam Cho and George G. Judge",
  title =        "{Stigler}'s approach to recovering the distribution of
                 first significant digits in natural data sets",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "2",
  pages =        "82--88",
  day =          "15",
  month =        jan,
  year =         "2010",
  CODEN =        "SPLTDC",
  DOI =          "http://dx.doi.org/10.1016/j.spl.2009.09.015",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715209003563",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  keywords =     "Benford's Law",
}

@Article{Leemis:2000:SDS,
  author =       "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
                 Evans",
  title =        "Survival Distributions Satisfying {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "54",
  number =       "4",
  pages =        "236--241",
  month =        nov,
  year =         "2000",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRclass =      "62E15 (62N05)",
  MRnumber =     "1803620",
  bibdate =      "Fri Jan 27 18:16:34 MST 2012",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326510;
                 http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amstat.org/publications/tas/Leemis.htm;
                 http://www.jstor.org/stable/2685773",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Lefort:1982:LOA,
  author =       "B. Lefort",
  title =        "{L}'Emploi des Outils au Cours de Taches d'Entretien
                 et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of
                 Tools in Maintenance Tasks and the {Zipf--Mandelbrot
                 Law}]",
  journal =      j-TRAV-HUM,
  volume =       "45",
  number =       "2",
  pages =        "307--316",
  month =        "????",
  year =         "1982",
  CODEN =        "TRHUAH",
  ISSN =         "0041-1868 (print), 2104-3663 (electronic)",
  ISSN-L =       "0041-1868",
  bibdate =      "Mon Sep 10 07:17:32 MDT 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/40657805",
  acknowledgement = ack-nhfb,
  fjournal =     "Le Travail Humain",
  language =     "French",
}

@Article{Lehner:2004:DVG,
  author =       "B. Lehner and P. Doll",
  title =        "Development and validation of a global database of
                 lakes",
  journal =      j-J-HYDROL,
  volume =       "296",
  number =       "1--4",
  pages =        "1--22",
  day =          "20",
  month =        aug,
  year =         "2004",
  CODEN =        "JHYDA7",
  DOI =          "http://dx.doi.org/10.1016/j.jhydrol.2004.03.028",
  ISSN =         "0022-1694 (print), 1879-2707 (electronic)",
  ISSN-L =       "0022-1694",
  bibdate =      "Fri Mar 22 08:54:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022169404001404",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Journal of Hydrology",
  keywords =     "Benford's Law",
}

@InProceedings{Lei:2000:EIN,
  author =       "Skylar Lei and Michael Smith and Giancarlo Succi",
  title =        "Empirical investigation of a novel approach to check
                 the integrity of software engineering measuring
                 processes",
  crossref =     "ACM:2000:PIC",
  pages =        "773--773",
  year =         "2000",
  DOI =          "http://dx.doi.org/10.1145/337180.337629",
  bibdate =      "Sat Feb 16 18:28:12 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Leimkuhler:1980:EFB,
  author =       "Ferdinand F. Leimkuhler",
  title =        "An Exact Formulation of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "36",
  number =       "4",
  pages =        "285--292",
  month =        "????",
  year =         "1980",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/eb026699",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:14:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "An exact, discrete formulation of Bradford's law
                 describing the distribution of articles in journals is
                 derived by showing that Bradford's law is a special
                 case of the Zipf--Mandelbrot `rank frequency' law. A
                 relatively simple method is presented for fitting the
                 model to empirical data and estimating the number of
                 journals and articles in a subject collection. This
                 method is demonstrated with an example application.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Leinicke:2006:FFN,
  author =       "Linda M. Leinicke and Joyce A. Ostrosky and W. Max
                 Rexroad",
  title =        "Fighting fraud by the numbers: Digital analysis
                 primer",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2006",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:13:02 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294967620",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Lemons:1986:NTD,
  author =       "Don S. Lemons",
  title =        "On the number of things and the distribution of first
                 digits",
  journal =      j-AMER-J-PHYSICS,
  volume =       "54",
  number =       "9",
  pages =        "816--817",
  month =        sep,
  year =         "1986",
  CODEN =        "AJPIAS",
  DOI =          "http://dx.doi.org/10.1119/1.14453",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Wed Nov 23 12:03:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ajp.aapt.org/",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  keywords =     "Benford's Law",
  remark =       "Lemons gives a derivation of Benford's Law that does
                 not assume scale invariance, unlike other widely-cited
                 derivations
                 \cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.",
}

@Article{Levene:2001:ZLW,
  author =       "Mark Levene and Jos{\'e} Borges and George Loizou",
  title =        "{Zipf}'s law for {Web} surfers",
  journal =      j-KNOWL-INFO-SYS,
  volume =       "3",
  number =       "1",
  pages =        "120--129",
  year =         "2001",
  CODEN =        "KISNCR",
  DOI =          "http://dx.doi.org/10.1007/PL00011657",
  ISSN =         "0219-1377",
  bibdate =      "Sat Nov 12 11:00:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0991.68622",
  abstract =     "One of the main activities of Web users, known as
                 `surfing', is to follow links. Lengthy navigation often
                 leads to disorientation when users lose track of the
                 context in which they are navigating and are unsure how
                 to proceed in terms of the goal of their original
                 query. Studying navigation patterns of Web users is
                 thus important, since it can lead us to a better
                 understanding of the problems users face when they are
                 surfing. We derive Zipf's rank frequency law (i.e., an
                 inverse power law) from an absorbing Markov chain model
                 of surfers' behavior assuming that less probable
                 navigation trails are, on average, longer than more
                 probable ones. In our model the probability of a trail
                 is interpreted as the relevance (or `value') of the
                 trail. We apply our model to two scenarios: in the
                 first the probability of a user terminating the
                 navigation session is independent of the number of
                 links he has followed so far, and in the second the
                 probability of a user terminating the navigation
                 session increases by a constant each time the user
                 follows a link. We analyze these scenarios using two
                 sets of experimental data sets showing that, although
                 the first scenario is only a rough approximation of
                 surfers' behavior, the data is consistent with the
                 second scenario and can thus provide an explanation of
                 surfers' behavior.",
  acknowledgement = ack-nhfb,
  classmath =    "68U99 (Computing methodologies) 68P15 (Database
                 theory) 68P20 (Information storage and retrieval)",
  fjournal =     "Knowledge and Information Systems",
  keywords =     "Markov chain; Web navigation; Zipf's law",
}

@Article{Ley:1994:TPB,
  author =       "Eduadro Ley and Hal R. Varian",
  title =        "Are there psychological barriers in the {Dow--Jones}
                 index?",
  journal =      j-APPL-FINANC-ECON,
  volume =       "4",
  number =       "3",
  pages =        "217--224",
  month =        "????",
  year =         "1994",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/758526902",
  ISSN =         "0960-3107 (print), 1466-4305 (electronic)",
  ISSN-L =       "0960-3107",
  bibdate =      "Sat Feb 16 18:29:52 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/758526902",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Financial Economics",
}

@Article{Ley:1996:PDU,
  author =       "Eduardo Ley",
  title =        "On the Peculiar Distribution of the {U.S.} Stock
                 Indexes' Digits",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "4",
  pages =        "311--313",
  month =        nov,
  year =         "1996",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 15:09:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2684926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Leydesdorff:2006:CPL,
  author =       "Loet Leydesdorff and Stephen Bensman",
  title =        "Classification and power laws: the logarithmic
                 transformation",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "57",
  number =       "11",
  pages =        "1470--1486",
  month =        sep,
  year =         "2006",
  CODEN =        "JASIEF",
  DOI =          "http://dx.doi.org/10.1002/asi.20467",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Sat Feb 16 18:31:04 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  keywords =     "Benford's Law",
}

@Article{Li:1992:RTE,
  author =       "W. Li",
  title =        "Random texts exhibit {Zipf}'s-law-like word frequency
                 distribution",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "38",
  number =       "6",
  pages =        "1842--1845",
  month =        "????",
  year =         "1992",
  CODEN =        "IETTAW",
  DOI =          "http://dx.doi.org/10.1109/18.165464",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Fri Nov 18 12:32:19 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
}

@Article{Li:2002:ZLI,
  author =       "Wentian Li and Yaning Yang",
  title =        "{Zipf's Law} in Importance of Genes for Cancer
                 Classification Using Microarray Data",
  journal =      j-J-THEOR-BIOL,
  volume =       "219",
  number =       "4",
  pages =        "539--551",
  day =          "21",
  month =        dec,
  year =         "2002",
  CODEN =        "JTBIAP",
  DOI =          "http://dx.doi.org/10.1006/jtbi.2002.3145",
  ISSN =         "0022-5193 (print), 1095-8541 (electronic)",
  ISSN-L =       "0022-5193",
  MRclass =      "92C40 (92D10)",
  MRnumber =     "2044066",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022519302931450",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225193",
  keywords =     "Zipf's Law",
}

@Article{Li:2004:DBL,
  author =       "Zhi-peng Li and Lin Cong and Hua-jia Wang",
  title =        "Discussion on {Benford's Law} and its Application",
  journal =      "ArXiv e-prints",
  pages =        "1--13",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 16:17:04 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2004math......8057L;
                 http://arxiv.org/abs/math/0408057",
  abstract =     "The probability that a number in many naturally
                 occurring tables of numerical data has first
                 significant digit $d$ is predicted by Benford's Law $
                 {\rm Prob} (d) = \log_{10} (1 + {\displaystyle {1 \over
                 d}}), d = 1, 2, \ldots, 9 $. Illustrations of Benford's
                 Law from both theoretical and real-life sources on both
                 science and social science areas are shown in detail
                 with some novel ideas and generalizations developed
                 solely by the authors of this paper. Three tests,
                 Chi-Square test, total variation distance, and maximum
                 deviations are adopted to examine the fitness of the
                 datasets to Benford's distribution. Finally,
                 applications of Benford's Law are summarized and
                 explored to reveal the power of this mathematical
                 principle.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "math/0408057",
}

@Article{Li:2005:ZLP,
  author =       "Yujian Li and Chuangbai Xiao",
  title =        "{Zipf}'s law probably existing in protein sequences",
  journal =      "J. Beijing Univ. Technol.",
  volume =       "31",
  number =       "4",
  pages =        "366--368",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Nov 12 11:10:06 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1084.92019",
  abstract =     "In order to analyze whether Zipf's law in linguistics
                 exists in protein sequences, this paper uses $ 1.735 \,
                 7 \times 10^4 $ protein sequences labeled with
                 secondary structures which are selected from the DSSP
                 database. The segments of successive amino acid
                 residues with a same code of secondary structure are
                 defined as words. The results show that the
                 distribution of words emerging frequency follows Zipf's
                 law with the exponent $ 0.981 $.",
  acknowledgement = ack-nhfb,
  classmath =    "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics
                 to biology): 92D20 (Protein sequences, DNA sequences)",
  language =     "Chinese. English summary",
  xxremark =     "Which journal is this? Beijing gong ye da xue xue bao
                 = Journal of Beijing Polytechnic University (ISSN
                 0254-0037), or Beijing ke ji da xue xue bao = Journal
                 of University of Science and Technology, Beijing (ISSN
                 1001-053X), or something different?",
}

@Misc{Li:2011:ZLB,
  author =       "Wentian Li",
  title =        "{Zipf's Law} bibliography",
  howpublished = "Web site.",
  month =        aug,
  year =         "2011",
  bibdate =      "Fri Nov 25 08:58:21 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The site holds 870 references (in untagged
                 reference-list form) up to 11 August 2011.",
  URL =          "http://www.nslij-genetics.org/wli/zipf/",
  acknowledgement = ack-nhfb,
  lastaccess =   "25 November 2011",
}

@Article{LimKaiJie:2012:CES,
  author =       "Shawn {Lim Kai Jie} and Mohandas Kalaichelvan",
  title =        "A Critical Evaluation of the Significance of Round
                 Numbers in {European} Equity Markets in Light of the
                 Predictions from {Benford's Law}",
  journal =      "International Research Journal of Finance and
                 Economics",
  volume =       "95",
  number =       "??",
  pages =        "196--210",
  day =          "28",
  month =        aug,
  year =         "2012",
  DOI =          "????",
  ISSN =         "1450-2887",
  bibdate =      "Tue Feb 19 06:04:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://mpra.ub.uni-muenchen.de/40960/;
                 http://mpra.ub.uni-muenchen.de/40960/1/IRJFE_95_15.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Lindsay:2004:DFD,
  author =       "D. H. Lindsay and P. S. Foote and A. Campbell and D.
                 R. Reilly",
  title =        "Detecting fraud in the data using automatic
                 intervention detection",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2004",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sat Feb 16 18:32:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Book{Lines:1986:NYT,
  author =       "Malcolm E. Lines",
  title =        "A number for your thoughts: facts and speculations
                 about numbers from {Euclid} to the latest computers",
  publisher =    pub-ADAM-HILGER,
  address =      pub-ADAM-HILGER:adr,
  pages =        "vi + 214",
  year =         "1986",
  ISBN =         "0-85274-495-1 (paperback)",
  ISBN-13 =      "978-0-85274-495-6 (paperback)",
  LCCN =         "QA241 .L617 1986",
  bibdate =      "Wed Nov 23 11:34:02 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html",
  acknowledgement = ack-nhfb,
  remark =       "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law
                 of Benford''.",
  subject =      "number theory",
}

@Article{Lipovetsky:2009:PLD,
  author =       "Stan Lipovetsky",
  title =        "{Pareto} $ 80 / 20 $ law: derivation via random
                 partitioning",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "40",
  number =       "2",
  pages =        "271--277",
  month =        "????",
  year =         "2009",
  CODEN =        "IJMEBM",
  DOI =          "http://dx.doi.org/10.1080/00207390802213609",
  ISSN =         "0020-739X (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  bibdate =      "Sat Jan 07 09:22:31 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609",
  abstract =     "The Pareto 80/20 Rule, also known as the Pareto
                 principle or law, states that a small number of causes
                 (20\%) is responsible for a large percentage (80\%) of
                 the effect. Although widely recognized as a heuristic
                 rule, this proportion has not been theoretically based.
                 The article considers derivation of this 80/20 rule and
                 some other standard quotients from the mean and its
                 interval estimation for the total value defined by the
                 product of two variables in the random partitioning
                 model.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  onlinedate =   "19 Feb 2009",
}

@Article{Liu:2008:MNS,
  author =       "Cheng-Shi Liu",
  title =        "Maximal non-symmetric entropy leads naturally to
                 {Zipf}'s law",
  journal =      j-FRACTALS,
  volume =       "16",
  number =       "1",
  pages =        "99--101",
  year =         "2008",
  CODEN =        "FRACEG",
  DOI =          "http://dx.doi.org/10.1142/S0218348X08003788",
  ISSN =         "0218-348X",
  ISSN-L =       "0218-348X",
  MRclass =      "94A17 (94A15)",
  MRnumber =     "2399875 (2009c:94027)",
  MRreviewer =   "Yasuichi Horibe",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fractals. Complex Geometry, Patterns, and Scaling in
                 Nature and Society",
}

@Article{Liu:2010:CIE,
  author =       "Hongyan Liu and Xiaoyu Wang and Yinghui Yang",
  title =        "Comments on {``An integrated efficient solution for
                 computing frequent and top-$k$ elements in data
                 streams''}",
  journal =      j-TODS,
  volume =       "35",
  number =       "2",
  pages =        "15:1--15:??",
  month =        apr,
  year =         "2010",
  CODEN =        "ATDSD3",
  DOI =          "http://doi.acm.org/10.1145/1735886.1735894",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  bibdate =      "Wed Apr 28 13:44:08 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tods/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Metwally:2006:IES}.",
  abstract =     "We investigate a well-known algorithm, {\em
                 Space-Saving\/} [Metwally et al. 2006], which has been
                 proven efficient and effective at mining frequent
                 elements in data streams. We discovered an error in one
                 of the theorems in Metwally et al. [2006]. Experiments
                 are conducted to illustrate the error.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Database Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
  keywords =     "approximate queries; data streams; frequent elements;
                 top-$k$ elements; Zipfian distributions",
}

@Article{Liu:2011:BLC,
  author =       "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren",
  title =        "{Benford}'s law and cross-sections of {$ A(n, \alpha)
                 B $} reactions",
  journal =      j-EUR-PHYS-J-A,
  volume =       "47",
  pages =        "78",
  month =        jun,
  year =         "2011",
  CODEN =        "EPJAFV",
  DOI =          "http://dx.doi.org/10.1140/epja/i2011-11078-3",
  ISSN =         "1434-6001 (print), 1434-601X (electronic)",
  ISSN-L =       "1434-6001",
  bibdate =      "Mon Nov 14 18:00:32 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011EPJA...47...78L",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal A: Hadrons and Nuclei",
  journal-URL =  "http://www.springerlink.com/content/1434-6001",
}

@Book{Livio:2002:GRS,
  author =       "Mario Livio",
  title =        "The golden ratio: the story of phi, the world's most
                 astonishing number",
  publisher =    "Broadway Books",
  address =      "New York, NY, USA",
  pages =        "viii + 294",
  year =         "2002",
  ISBN =         "0-7679-0815-5",
  ISBN-13 =      "978-0-7679-0815-3",
  LCCN =         "QA466 .L58 2002",
  bibdate =      "Tue Jul 08 12:29:44 2003",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is treated on pages 231--237.",
  price =        "US\$24.95, CAN\$37.95",
  acknowledgement = ack-nhfb,
}

@Article{Logan:1978:FDP,
  author =       "Jonothan L. Logan and Samuel A. Goudsmit",
  title =        "The First Digit Phenomenon",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "122",
  number =       "4",
  pages =        "193--197",
  day =          "18",
  month =        aug,
  year =         "1978",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 30 11:20:35 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper contains derivations of both Stigler's Law
                 and Benford's Law, and receives strong criticism in
                 \cite{Raimi:1985:FDP}. This paper contains an important
                 historical note that is recorded in entry
                 \cite{Benford:1938:LAN}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
                 http://www.jstor.org/stable/986530",
  abstract =     "Forty years ago an article appeared in these
                 Proceedings, which has since then attracted much
                 attention of mathematicians and some physicists. It was
                 written by Frank Benford, a physicist from the General
                 Electric Company at Schenectady. He had examined a
                 large number of numerical tables, the kind that are
                 printed in almanacs, and in scientific and technical
                 handbooks. He noticed a most unusual and unexpected
                 property of many of these tables. Consider, for
                 example, the numbers representing the populations of
                 states or all the countries in the world, or their
                 areas, their budgets, their numbers of hospital beds,
                 etc. One would expect that on the average just as many
                 of these entries would begin with the digit $1$ as with
                 $2$ or $3$ or $4$, and so on. But Benford noticed that
                 small values of the first digits occur far more
                 often.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@Article{Lolbert:2008:NEG,
  author =       "Tam{\'a}s Lolbert",
  title =        "On the non-existence of a general {Benford}'s law",
  journal =      "Mathematical Social Sciences",
  volume =       "55",
  number =       "2",
  pages =        "103--106",
  month =        mar,
  year =         "2008",
  CODEN =        "MSOSDD",
  DOI =          "http://dx.doi.org/10.1016/j.mathsocsci.2007.09.001",
  ISSN =         "0165-4896 (print), 1879-3118 (electronic)",
  ISSN-L =       "0165-4896",
  MRclass =      "60A10 (60E10)",
  MRnumber =     "2391902",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165489607000935",
  abstract =     "Benford's law states that in randomly collected
                 numbers certain digits are more often leading digits
                 than others. More formally: the general law states that
                 the mantissae follow the logarithmic distribution in
                 any base. Benford's law was recognized by many
                 mathematicians so that several possible explanations
                 have been derived, but several questions are still
                 open. Applications are widespread, for example an
                 auditing technique (the so-called digital analysis),
                 which is employed around the world by internal revenue
                 services to detect tax fraud, is based on this
                 phenomenon.\par

                 In this paper it will be shown that there exists no
                 probability measure that would obey Benford's law for
                 any base, but if the set of possible bases does not
                 exceed a given upper limit, most real-life
                 distributions obey, or can be transformed to obey
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Social Sciences",
}

@Article{Losee:2001:TDB,
  author =       "Robert M. Losee",
  title =        "Term dependence: a basis for {Luhn} and {Zipf}
                 models",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "52",
  number =       "12",
  pages =        "1019--1025",
  year =         "2001",
  CODEN =        "JASIEF",
  DOI =          "http://dx.doi.org/10.1002/asi.1155",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}

@Article{Lotka:1926:FDS,
  author =       "Alfred J. Lotka",
  title =        "The Frequency Distribution of Scientific
                 Productivity",
  journal =      j-J-WASH-ACAD-SCI,
  volume =       "16",
  number =       "12",
  pages =        "317--323",
  month =        dec,
  year =         "1926",
  CODEN =        "JWASA3",
  ISSN =         "0043-0439",
  ISSN-L =       "0043-0439",
  bibdate =      "Thu Nov 24 14:36:11 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This is the earliest known publication on the
                 phenomenon known as Zipf's Law, here applied to
                 publication counts of chemists and physicists. Lotka's
                 Law (a term possibly first used in
                 \cite{Zipf:1949:HBP}) says that the number of authors
                 producing $n$ publications is about $ 1 / n^2 $ of the
                 number producing only one. This `law' seems to have
                 been misunderstood and misapplied in other fields; see
                 \cite{Potter:1981:LLR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Washington Academy of Sciences",
  keywords =     "Lotka's Law",
}

@TechReport{Lowe:1999:FDL,
  author =       "Tomas Lowe and Sally Murphy and Justin Hayward",
  title =        "The First Digit Law",
  type =         "Report",
  number =       "??",
  institution =  "Department of Computing, Imperial College",
  address =      "London, UK",
  month =        jun,
  year =         "1999",
  bibdate =      "Wed Nov 23 16:59:50 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf;
                 http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html",
  acknowledgement = ack-nhfb,
  lastaccess =   "23 November 2011",
}

@Article{Lu:2005:CZL,
  author =       "Tim Lu and Christine M. Costello and Peter J. P.
                 Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl
                 and Stefan Schreiber",
  title =        "Can {Zipf}'s law be adapted to normalize
                 microarrays?",
  journal =      "BMC Bioinformatics",
  volume =       "6",
  number =       "??",
  pages =        "37--49",
  month =        "????",
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1186/1471-2105-6-37",
  ISSN =         "1471-2105",
  ISSN-L =       "1471-2105",
  bibdate =      "Sat Feb 16 18:38:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.biomedcentral.com/1471-2105/6/37",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lu:2005:DFH,
  author =       "Fletcher Lu and J. Efrim Boritz",
  title =        "Detecting Fraud in Health Insurance Data: Learning to
                 Model Incomplete {Benford's Law} Distributions",
  crossref =     "Gama:2005:MLE",
  pages =        "633--640",
  year =         "2005",
  DOI =          "http://dx.doi.org/10.1007/11564096_63",
  bibdate =      "Tue Nov 15 08:55:45 2011",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@InCollection{Lu:2006:AFD,
  author =       "Fletcher Lu and J. Efrim Boritz and Dominic Covvey",
  booktitle =    "Advances in artificial intelligence",
  title =        "Adaptive fraud detection using {Benford}'s law",
  volume =       "4013",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "347--358",
  year =         "2006",
  DOI =          "http://dx.doi.org/10.1007/11766247_30",
  MRnumber =     "2280590",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@InProceedings{Lu:2006:BCF,
  author =       "F. Lu and J. E. Boritz",
  editor =       "????",
  booktitle =    "{Uncertainty in Artificial Intelligence: Proceedings
                 of the 22nd Conference}",
  title =        "Building a case for fraud using {Benford}'s law with
                 reinforcement learning",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Sat Feb 16 18:34:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lu:2010:BLP,
  author =       "Ocean Fan Lu and David E. Giles",
  title =        "{Benford's Law} and psychological barriers in certain
                 {eBay} auctions",
  journal =      j-APPL-ECON-LETT,
  volume =       "17",
  number =       "10",
  pages =        "1005--1008",
  month =        "????",
  year =         "2010",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/13504850802631814",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Sat Jan 07 09:10:23 2012",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814",
  abstract =     "Using generalizations of Benford's Law we test for the
                 absence of psychological barriers at various price
                 levels in eBay auctions for professional football
                 tickets. Our empirical results indicate that this
                 hypothesis cannot be rejected.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  onlinedate =   "16 Jun 2009",
}

@Article{Lu:2013:DZH,
  author =       "Linyuan L{\"u} and Zi-Ke Zhang and Tao Zhou",
  title =        "Deviation of {Zipf}'s and {Heaps' Laws} in Human
                 Languages with Limited Dictionary Sizes",
  journal =      j-SCI-REP,
  volume =       "3",
  number =       "??",
  pages =        "1--7",
  month =        "????",
  year =         "2013",
  CODEN =        "SRCEC3",
  DOI =          "http://dx.doi.org/10.1038/srep01082",
  ISSN =         "2045-2322",
  bibdate =      "Tue Feb 26 07:39:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/srep/2013/130130/srep01082/full/srep01082.html",
  accepted =     "21 December 2012",
  acknowledgement = ack-nhfb,
  articleno =    "1082",
  fjournal =     "Scientific Reports",
  onlinedate =   "30 January 2013",
  received =     "11 June 2012",
}

@Article{Luque:2008:FDF,
  author =       "Bartolo Luque and Lucas Lacasa",
  title =        "The first digit frequencies of primes and {Riemann}
                 zeta zeros tend to uniformity following a
                 size-dependent generalized {Benford}'s law",
  journal =      "ArXiv e-prints",
  month =        nov,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See published paper \cite {Luque:2009:FDF}.",
  URL =          "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L;
                 http://arxiv.org/abs/0811.3302",
  abstract =     "Prime numbers seem to distribute among the natural
                 numbers with no other law than that of chance, however
                 its global distribution presents a quite remarkable
                 smoothness. Such interplay between randomness and
                 regularity has motivated scientists of all ages to
                 search for local and global patterns in this
                 distribution that eventually could shed light into the
                 ultimate nature of primes. In this work we show that a
                 generalization of the well known first-digit Benford's
                 law, which addresses the rate of appearance of a given
                 leading digit $d$ in data sets, describes with
                 astonishing precision the statistical distribution of
                 leading digits in the prime numbers sequence. Moreover,
                 a reciprocal version of this pattern also takes place
                 in the sequence of the nontrivial Riemann zeta zeros.
                 We prove that the prime number theorem is, in the last
                 analysis, the responsible of these patterns. Some new
                 relations concerning the prime numbers distribution are
                 also deduced, including a new approximation to the
                 counting function $ \pi (n) $. Furthermore, some
                 relations concerning the statistical conformance to
                 this generalized Benford's law are derived. Some
                 applications are finally discussed.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0811.3302",
  keywords =     "Mathematics - Number Theory, Mathematics -
                 Probability, Mathematics - Statistics",
  pagecount =    "20",
  primaryclass = "math.NT",
}

@Article{Luque:2009:FDF,
  author =       "Bartolo Luque and Lucas Lacasa",
  title =        "The first digit frequencies of prime numbers and
                 {Riemann} zeta zeros",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "465",
  number =       "2107",
  pages =        "2197--2216",
  day =          "8",
  month =        jul,
  year =         "2009",
  CODEN =        "PRLAAZ",
  DOI =          "http://dx.doi.org/10.1098/rspa.2009.0126",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  bibdate =      "Mon Feb 25 10:44:43 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, \& Engineering Sciences",
  keywords =     "Benford's Law",
  onlinedate =   "22 April 2009",
}

@InProceedings{Lyons:2011:NSF,
  author =       "M. Lyons and E. Carl-Ludwig Siegel",
  booktitle =    "APS March Meeting Abstracts",
  title =        "{NON-Shor} Factorization via {BEQS BEC}: {Watkins}
                 Number-Theory ``Pure''-Mathematics $ \cup $ with
                 Statistical-Physics: {Benford} Log-Law Inversion to
                 {ONLY} {BEQS} digit $ d = 0 $ {BEC}!!!",
  publisher =    "American Physical Society",
  address =      "????",
  pages =        "K1142",
  month =        mar,
  year =         "2011",
  bibdate =      "Mon Nov 14 18:08:39 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L",
  acknowledgement = ack-nhfb,
}

@Article{Ma:2005:CBL,
  author =       "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel
                 and J. Wang and T. Keutgen and Z. Majka and M. Murray
                 and L. Qin and P. Smith and R. Alfaro and J. Cibor and
                 M. Cinausero and Y. El Masri and D. Fabris and E.
                 Fioretto and A. Keksis and M. Lunardon and A. Makeev
                 and N. Marie and E. Martin and A. Martinez-Davalos and
                 A. Menchaca-Rocha and G. Nebbia and G. Prete and V.
                 Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis
                 and P. Staszel and M. Veselsky and G. Viesti and E. M.
                 Winchester and S. J. Yennello",
  title =        "Critical behavior in light nuclear systems:
                 Experimental aspects",
  journal =      j-PHYS-REV-C,
  volume =       "71",
  number =       "5",
  pages =        "054606",
  day =          "26",
  month =        may,
  year =         "2005",
  CODEN =        "PRVCAN",
  DOI =          "http://dx.doi.org/10.1103/PhysRevC.71.054606",
  ISSN =         "0556-2813 (print), 1089-490X, 1538-4497",
  ISSN-L =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevC.71.054606",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  journal-URL =  "http://prc.aps.org/browse",
  keywords =     "Zipf's Law",
}

@InCollection{Macaulay:1922:PLG,
  author =       "F. R. Macaulay",
  editor =       "W. C. Mitchell",
  booktitle =    "Income in the {United States}: Its Amount and
                 Distribution: 1909--1919",
  title =        "{Pareto}'s law and the general problem of mathematical
                 describing the frequency of distribution of income",
  publisher =    "National Bureau of Economic Research",
  address =      "New York, NY, USA",
  pages =        "??--??",
  year =         "1922",
  LCCN =         "????",
  bibdate =      "Fri Nov 25 09:06:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Macon:1950:DFD,
  author =       "N. Macon and L. Moser",
  title =        "On the distribution of first digits of powers",
  journal =      "Scripta Mathematica",
  volume =       "16",
  number =       "??",
  pages =        "290--291",
  month =        "????",
  year =         "1950",
  CODEN =        "????",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  bibdate =      "Sat Nov 12 16:28:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica",
}

@Article{Mahdian:2010:BBM,
  author =       "Babak Mahdian and Stanislav Saic",
  title =        "A bibliography on blind methods for identifying image
                 forgery",
  journal =      j-SIGNAL-PROCESS-IMAGE-COMMUN,
  volume =       "25",
  number =       "6",
  pages =        "389--399",
  month =        jul,
  year =         "2010",
  CODEN =        "SPICEF",
  DOI =          "http://dx.doi.org/10.1016/j.image.2010.05.003",
  ISSN =         "0923-5965 (print), 1879-2677 (electronic)",
  ISSN-L =       "0923-5965",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0923596510000536",
  acknowledgement = ack-nhfb,
  fjournal =     "Signal Processing: Image Communication",
  keywords =     "Benford's Law",
}

@Article{Maia:1984:UBL,
  author =       "M. J. F. Maia and M. D. Maia",
  title =        "On the Unity of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "40",
  number =       "3",
  pages =        "206--216",
  month =        "????",
  year =         "1984",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/eb026765",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:11:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@Article{Maillart:2008:ETZ,
  author =       "T. Maillart and D. Sornette and S. Spaeth and G. von
                 Krogh",
  title =        "Empirical Tests of {Zipf's Law} Mechanism in Open
                 Source {Linux} Distribution",
  journal =      j-PHYS-REV-LET,
  volume =       "101",
  number =       "21",
  pages =        "218701",
  day =          "19",
  month =        nov,
  year =         "2008",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.101.218701",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 http://www.math.utah.edu/pub/tex/bib/linux.bib;
                 http://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "4",
}

@Article{Makse:1995:MUG,
  author =       "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene
                 Stanley",
  title =        "Modelling urban growth patterns",
  journal =      j-NATURE,
  volume =       "377",
  number =       "6550",
  pages =        "608--612",
  day =          "19",
  month =        oct,
  year =         "1995",
  CODEN =        "NATUAS",
  DOI =          "http://dx.doi.org/10.1038/377608a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Feb 27 06:06:25 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Berlin (Germany) population; London (UK) population;
                 Zipf's Law",
}

@Article{Malacarne:2001:QED,
  author =       "L. C. Malacarne and R. S. Mendes and E. K. Lenzi",
  title =        "$q$-exponential distribution in urban agglomeration",
  journal =      j-PHYS-REV-E,
  volume =       "65",
  number =       "??",
  pages =        "017106",
  day =          "21",
  month =        dec,
  year =         "2001",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.65.017106",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.65.017106",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf--Mandelbrot law",
}

@Article{Malcai:1999:PLD,
  author =       "Ofer Malcai and Ofer Biham and Sorin Solomon",
  title =        "Power-law distributions and {L{\'e}vy}-stable
                 intermittent fluctuations in stochastic systems of many
                 autocatalytic elements",
  journal =      j-PHYS-REV-E,
  volume =       "60",
  number =       "2",
  pages =        "1299--1303",
  month =        aug,
  year =         "1999",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.60.1299",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:25:38 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.60.1299",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
}

@Article{Malevergne:2011:TPA,
  author =       "Yannick Malevergne and Vladilen Pisarenko and Didier
                 Sornette",
  title =        "Testing the {Pareto} against the lognormal
                 distributions with the uniformly most powerful unbiased
                 test applied to the distribution of cities",
  journal =      j-PHYS-REV-E,
  volume =       "83",
  number =       "3",
  pages =        "036111",
  day =          "22",
  month =        mar,
  year =         "2011",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.83.036111",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.83.036111",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Pareto distribution; Zipf's Law",
  pagecount =    "11",
}

@InProceedings{Manaris:2002:PTR,
  author =       "B. Manaris and T. Purewal and C. McCormick",
  editor =       "{IEEE}",
  booktitle =    "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002,
                 Embassy Suites Hotel, Columbia, South Carolina, USA",
  title =        "Progress Towards Recognizing and Classifying Beautiful
                 Music with Computers: {MIDI}-Encoded Music and the
                 {Zipf-Mandelbrot Law}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--57",
  year =         "2002",
  DOI =          "http://dx.doi.org/10.1109/.2002.995557",
  ISBN =         "0-7803-7252-2",
  ISBN-13 =      "978-0-7803-7252-8",
  LCCN =         "TK7801 .I56 2002",
  bibdate =      "Mon Feb 18 10:40:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=7814",
  acknowledgement = ack-nhfb,
  bookpages =    "xviii + 482",
}

@InProceedings{Manaris:2003:EMZ,
  author =       "Bill Manaris and Dallas Vaughan and Christopher Wagner
                 and Juan Romero and Robert B. Davis",
  title =        "Evolutionary Music and the {Zipf--Mandelbrot Law}:
                 Developing Fitness Functions for Pleasant Music",
  crossref =     "Raidl:2003:AEC",
  pages =        "522--534",
  year =         "2003",
  bibdate =      "Mon Feb 18 10:49:54 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Manaris:2005:ZLM,
  author =       "Bill Manaris and Juan Romero and Penousal Machado and
                 Dwight Krehbiel and Timothy Hirzel and Walter Pharr and
                 Robert B. Davis",
  title =        "{Zipf}'s law, music classification, and aesthetics",
  journal =      j-COMP-MUSIC-J,
  volume =       "29",
  number =       "1",
  pages =        "55--69",
  month =        "Spring",
  year =         "2005",
  CODEN =        "CMUJDY",
  ISSN =         "0148-9267 (print), 1531-5169 (electronic)",
  ISSN-L =       "0148-9267",
  bibdate =      "Sat Feb 16 18:40:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html;
                 http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Music Journal",
  keywords =     "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law",
}

@InProceedings{Manaris:2006:IES,
  author =       "Bill Manaris and Luca Pellicoro and George Pothering
                 and Harland Hodges",
  editor =       "????",
  booktitle =    "{2006 IASTED International Conference on Artificial
                 Intelligence and Applications (AIA 2006), February
                 13--16, 2006, Innsbruck, Austria}",
  title =        "Investigating {Esperanto}'s statistical proportions
                 relative to other languages using neural networks and
                 {Zipf}'s law",
  publisher =    "Acta Press",
  address =      "????",
  pages =        "1--7",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 18:41:37 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mandelbrot:1953:ITS,
  author =       "Beno{\^\i}t B. Mandelbrot",
  editor =       "Willis Jackson",
  booktitle =    "{Communication theory: papers read at a Symposium on
                 ``Applications of Communication Theory'' held at the
                 Institution of Electrical Engineers, London, September
                 22nd--26th 1952}",
  title =        "An Informational Theory of the Statistical Structure
                 of Languages",
  publisher =    pub-BUTTERWORTHS,
  address =      pub-BUTTERWORTHS:adr,
  pages =        "486--502",
  year =         "1953",
  LCCN =         "Q350 .S92 1952",
  bibdate =      "Wed Nov 16 09:37:30 2011",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://lccn.loc.gov/53004215;
                 http://www.nytimes.com/2010/10/17/us/17mandelbrot.html",
  acknowledgement = ack-nhfb,
  bookpages =    "xii + 532",
  remark =       "The paper is incorrectly referenced as a book in
                 \cite{Baek:2011:ZLU}. Mandelbrot got his Master of
                 Science in Aeronautics at CalTech in 1948, and his
                 Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in
                 1952 in Paris, so perhaps this is a translation of his
                 thesis work.",
}

@Article{Mandelbrot:1959:NCS,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "A note on a class of skew distribution functions:
                 analysis and critique of a paper by {H. A. Simon}",
  journal =      j-INF-CONTROL,
  volume =       "2",
  number =       "??",
  pages =        "90--99",
  month =        apr,
  year =         "1959",
  CODEN =        "IFCNA4",
  DOI =          "http://dx.doi.org/10.1016/S0019-9958(59)90098-1",
  ISSN =         "0019-9958 (print), 1878-2981 (electronic)",
  ISSN-L =       "0019-9958",
  bibdate =      "Wed Nov 16 09:45:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Simon:1955:CSD}.",
  abstract =     "This note is a discussion of H. A. Simon's model
                 (1955) concerning the class of frequency distributions
                 generally associated with the name of G. K. Zipf. The
                 main purpose is to show that Simon's model is
                 analytically circular in the case of the linguistic
                 laws of Estoup--Zipf and Willis--Yule. Insofar as the
                 economic law of Pareto is concerned, Simon has himself
                 noted that his model is a particular case of that of
                 Champernowne; this is correct, with some reservation. A
                 simplified version of Simon's model is included.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information and Control",
}

@Article{Mandelbrot:1960:PLL,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "The {Pareto--Levy} law and the distribution of
                 income",
  journal =      j-INT-ECON-REV,
  volume =       "1",
  number =       "??",
  pages =        "79--106",
  month =        "????",
  year =         "1960",
  CODEN =        "INERAE",
  ISSN =         "0020-6598 (print), 1468-2354 (electronic)",
  ISSN-L =       "0020-6598",
  bibdate =      "Wed Nov 23 11:07:01 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ingenta.com/journals/browse/bpl/iere",
  acknowledgement = ack-nhfb,
  fjournal =     "International Economic Review",
}

@TechReport{Mandelbrot:1962:SNR,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "Statistics of natural resources and the law of
                 {Pareto}",
  type =         "Research Note",
  number =       "NC-146",
  institution =  "IBM",
  address =      "Yorktown Heights, NY, USA",
  day =          "29",
  month =        jun,
  year =         "1962",
  bibdate =      "Mon Sep 10 17:35:59 2012",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Manin:2008:ZLA,
  author =       "Dmitrii Y. Manin",
  title =        "{Zipf's Law} and Avoidance of Excessive Synonymy",
  journal =      j-COGN-SCI,
  volume =       "32",
  number =       "7",
  pages =        "1075--1098",
  year =         "2008",
  CODEN =        "COGSD5",
  DOI =          "http://dx.doi.org/10.1080/03640210802020003",
  ISSN =         "0364-0213 (print), 1551-6709 (electronic)",
  ISSN-L =       "0364-0213",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognitive Science",
  keywords =     "Semantics; Synonymy; Word frequency; Word meaning;
                 Zipf's law",
}

@Article{Manoochehrnia:2010:BLA,
  author =       "P. Manoochehrnia and F. Rachidi and M. Rubinstein and
                 W. Schulz and G. Diendorfer",
  title =        "{Benford's Law} and Its Application to Lightning
                 Data",
  journal =      j-IEEE-TRANS-ELECTROMAGN-COMPAT,
  volume =       "52",
  number =       "4",
  pages =        "956--961",
  month =        nov,
  year =         "2010",
  CODEN =        "IEMCAE",
  DOI =          "http://dx.doi.org/10.1109/TEMC.2010.2067218",
  ISSN =         "0018-9375 (print), 1558-187X (electronic)",
  ISSN-L =       "0018-9375",
  bibdate =      "Mon Nov 21 22:24:43 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electromagnetic Compatibility",
}

@Article{Manrubia:1998:IMU,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
  title =        "Intermittency model for urban development",
  journal =      j-PHYS-REV-E,
  volume =       "58",
  number =       "1",
  pages =        "295--302",
  month =        jul,
  year =         "1998",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.58.295",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:42:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.58.295",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Manrubia:1999:SMP,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
  title =        "Stochastic multiplicative processes with reset
                 events",
  journal =      j-PHYS-REV-E,
  volume =       "59",
  number =       "5",
  pages =        "4945--4948",
  month =        may,
  year =         "1999",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.59.4945",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:25:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.59.4945",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "5",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's law",
}

@Article{Manrubia:1999:TDS,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette and
                 Ricard V. Sol{\'e}",
  title =        "Transient Dynamics and Scaling Phenomena in Urban
                 Growth",
  journal =      j-FRACTALS,
  volume =       "7",
  number =       "1",
  pages =        "1--8",
  month =        mar,
  year =         "1999",
  CODEN =        "FRACEG",
  DOI =          "http://dx.doi.org/10.1142/S0218348X99000025",
  ISSN =         "0218-348X",
  ISSN-L =       "0218-348X",
  bibdate =      "Wed Feb 27 07:11:42 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025",
  acknowledgement = ack-nhfb,
  fjournal =     "Fractals",
  keywords =     "Zipf's Law",
}

@Article{Mansury:2007:EZL,
  author =       "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s",
  title =        "The emergence of {Zipf's Law} in a system of cities:
                 an agent-based simulation approach",
  journal =      j-J-ECON-DYN-CONTROL,
  volume =       "31",
  number =       "7",
  pages =        "2438--2460",
  day =          "15",
  month =        jul,
  year =         "2007",
  CODEN =        "JEDCDH",
  DOI =          "http://dx.doi.org/10.1016/j.jedc.2006.08.002",
  ISSN =         "0165-1889 (print), 1879-1743 (electronic)",
  ISSN-L =       "0165-1889",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165188906001527",
  ZMnumber =     "1163.91504",
  abstract =     "This paper develops a spatial agent-based model to
                 generate a system of cities that exhibits the
                 statistical properties of the Zipf's Law. The numerical
                 results suggest that the combination of bounded
                 rationality and maximum heterogeneity of agents can
                 produce a generic power-law relationship in the size
                 distribution of cities, but does not always generate
                 the Zipf's Law. We found sufficient conditions on the
                 probability distribution of spatial reach to generate
                 the Zipf's Law associated with unit power coefficient.
                 Our model also indicates that the Zipf's Law breaks
                 down unless the extent of agglomeration economies
                 overwhelms the negative disagglomerating forces.",
  acknowledgement = ack-nhfb,
  classmath =    "91B72 (Spatial models)",
  fjournal =     "Journal of Economic Dynamics and Control",
  keywords =     "complex systems; power laws; spatial agent based
                 models; Zipf's Law",
}

@Article{Mantegna:1994:LFN,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C. K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "Linguistic Features of Noncoding {DNA} Sequences",
  journal =      j-PHYS-REV-LET,
  volume =       "73",
  number =       "??",
  pages =        "3169--??",
  day =          "5",
  month =        dec,
  year =         "1994",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.73.3169",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Mantegna:1995:SAC,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C.-K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "Systematic analysis of coding and noncoding {DNA}
                 sequences using methods of statistical linguistics",
  journal =      j-PHYS-REV-E,
  volume =       "52",
  number =       "??",
  pages =        "2939--??",
  day =          "1",
  month =        sep,
  year =         "1995",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.52.2939",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.52.2939",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Marchi:2006:AAS,
  author =       "Scott Marchi and James Hamilton",
  title =        "Assessing the Accuracy of Self-Reported Data: an
                 Evaluation of the Toxics Release Inventory",
  journal =      "Journal of Risk and Uncertainty",
  volume =       "32",
  number =       "1",
  pages =        "57--76",
  month =        jan,
  year =         "2006",
  CODEN =        "JRUNEN",
  DOI =          "http://dx.doi.org/10.1007/s10797-006-6666-3",
  ISSN =         "0895-5646 (print), 1573-0476 (electronic)",
  ISSN-L =       "0895-5646",
  bibdate =      "Fri Nov 25 11:25:49 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marsili:1998:IIL,
  author =       "Matteo Marsili and Yi-Cheng Zhang",
  title =        "Interacting Individuals Leading to {Zipf's Law}",
  journal =      j-PHYS-REV-LET,
  volume =       "80",
  number =       "??",
  pages =        "2741--??",
  day =          "23",
  month =        mar,
  year =         "1998",
  CODEN =        "PRLTAO",
  DOI =          "http://dx.doi.org/10.1103/PhysRevLett.80.2741",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Maslov:2005:GTS,
  author =       "V. P. Maslov",
  title =        "On a general theorem of set theory that leads to the
                 {Gibbs}, {Bose--Einstein}, and {Pareto} distributions
                 and to the {Zipf--Mandelbrot} law for the stock
                 market",
  journal =      j-MAT-ZAMETKI,
  volume =       "78",
  number =       "6",
  pages =        "870--877",
  year =         "2005",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1007/s11006-005-0186-9",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "91B28 (90C29)",
  MRnumber =     "2249037 (2007b:91077)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Article{Maslov:2005:RZLa,
  author =       "V. P. Maslov",
  title =        "Refining {Zipf}'s law for frequency dictionaries",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "405",
  number =       "5",
  pages =        "591--594",
  year =         "2005",
  CODEN =        "DANKAS",
  ISSN =         "0869-5652",
  ISSN-L =       "0869-5652",
  MRclass =      "94A15 (60C05)",
  MRnumber =     "2340762",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
                 Nauk",
}

@Article{Maslov:2005:RZLb,
  author =       "V. P. Maslov",
  title =        "Refinement of {Zipf}'s law for frequency
                 dictionaries",
  journal =      j-DOKL-MATH,
  volume =       "72",
  number =       "3",
  pages =        "942--945",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "1064-5624 (print), 1531-8362 (electronic)",
  ISSN-L =       "1064-5624",
  bibdate =      "Sat Nov 12 11:05:14 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1206.82009",
  acknowledgement = ack-nhfb,
  classmath =    "82B10 (Quantum equilibrium statistical mechanics
                 (general)) 68T50 (Natural language processing) 68Q45
                 (Formal languages)",
  fjournal =     "Doklady Mathematics",
  keywords =     "Bose--Einstein statistics",
  language =     "English. Russian original",
}

@Article{Maslov:2005:ZML,
  author =       "V. P. Maslov",
  title =        "The {Zipf--Mandelbrot} law: quantization and an
                 application to the stock market",
  journal =      j-RUSS-J-MATH-PHYS,
  volume =       "12",
  number =       "4",
  pages =        "483--488",
  year =         "2005",
  CODEN =        "RJMPEL",
  ISSN =         "1061-9208",
  ISSN-L =       "1061-9208",
  MRclass =      "91B28 (82B99)",
  MRnumber =     "2201312 (2006i:91053)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Russian Journal of Mathematical Physics",
}

@Article{Maslov:2006:BGA,
  author =       "V. P. Maslov",
  title =        "{Bose} gas of anharmonic oscillators and a refinement
                 of {Zipf}'s law",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "148",
  number =       "3",
  pages =        "495--496",
  year =         "2006",
  CODEN =        "TMFZAL",
  DOI =          "http://dx.doi.org/10.1007/s11232-006-0117-2",
  ISSN =         "0564-6162",
  ISSN-L =       "0564-6162",
  MRclass =      "82B10",
  MRnumber =     "2283664",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
}

@Article{Maslov:2006:NAD,
  author =       "V. P. Maslov",
  title =        "Negative asymptotic dimension, a new condensate, and
                 their relation to the quantized {Zipf} law",
  journal =      j-MAT-ZAMETKI,
  volume =       "80",
  number =       "6",
  pages =        "856--863",
  year =         "2006",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1007/s11006-006-0203-7",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "82B10 (20F69 53C23 81S10 91F20)",
  MRnumber =     "2311613 (2008e:82005)",
  MRreviewer =   "Artur E. Ruuge",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Article{Maslov:2006:RZM,
  author =       "V. P. Maslov",
  title =        "A refinement of the {Zipf--Mandelbrot} law and
                 lacunarity in an ideal gas",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "147",
  number =       "3",
  pages =        "511--512",
  year =         "2006",
  CODEN =        "TMFZAL",
  DOI =          "http://dx.doi.org/10.1007/s11232-006-0083-8",
  ISSN =         "0564-6162",
  ISSN-L =       "0564-6162",
  MRclass =      "82B10",
  MRnumber =     "2254729 (2007d:82007)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
}

@Article{Maslov:2006:ZLR,
  author =       "V. P. Maslov and T. V. Maslova",
  title =        "On {Zipf}'s law and rank distributions in linguistics
                 and semiotics",
  journal =      j-MAT-ZAMETKI,
  volume =       "80",
  number =       "5",
  pages =        "718--732",
  year =         "2006",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1007/s11006-006-0189-1",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "60C05 (62-07 62P99)",
  MRnumber =     "2311586 (2008g:60027)",
  MRreviewer =   "Konstantin E. Feldman",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "Zbl 1134.62086",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
}

@Article{Maslov:2007:PTZ,
  author =       "V. P. Maslov",
  title =        "Phase transitions of the zeroth kind and the
                 quantization of the {Zipf} law",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "150",
  number =       "1",
  pages =        "118--142",
  year =         "2007",
  CODEN =        "TMFZAL",
  DOI =          "http://dx.doi.org/10.1007/s11232-007-0008-1",
  ISSN =         "0564-6162",
  ISSN-L =       "0564-6162",
  MRclass =      "82B26 (82B03)",
  MRnumber =     "2325869 (2008g:82037)",
  MRreviewer =   "N. N. Ganikhodjaev",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
}

@Article{Maslova:2006:ZLM,
  author =       "T. V. Maslova",
  title =        "{Zipf}'s law and {Maslov}'s formula as applied to
                 semiotic systems",
  journal =      j-DOKL-MATH,
  volume =       "74",
  number =       "3",
  pages =        "917--920",
  year =         "2006",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1134/S1064562406060330",
  ISSN =         "1064-5624 (print), 1531-8362 (electronic)",
  ISSN-L =       "1064-5624",
  bibdate =      "Sat Nov 12 11:13:35 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "pre05824774",
  acknowledgement = ack-nhfb,
  classmath =    "62E20 (Asymptotic distribution theory in statistics)
                 82B03 (Foundations of equilibrium statistical
                 mechanics)",
  fjournal =     "Doklady Mathematics",
  language =     "English. Russian original",
}

@Article{Maslova:2006:ZLV,
  author =       "T. V. Maslova",
  title =        "On the {Zipf} law and the {V. P. Maslov} formula for
                 semiotic systems",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "411",
  number =       "6",
  pages =        "754--757",
  year =         "2006",
  CODEN =        "DANKAS",
  ISSN =         "0869-5652",
  ISSN-L =       "0869-5652",
  MRclass =      "62E20 (82B03)",
  MRnumber =     "2451374",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
                 Nauk",
}

@Article{Masse:2011:SWD,
  author =       "B. Mass{\'e} and D. Schneider",
  title =        "A survey on weighted densities and their connection
                 with the first digit phenomenon",
  journal =      j-ROCKY-MOUNTAIN-J-MATH,
  volume =       "41",
  number =       "5",
  pages =        "1395--1415",
  month =        "????",
  year =         "2011",
  CODEN =        "RMJMAE",
  DOI =          "http://dx.doi.org/10.1216/RMJ-2011-41-5-1395",
  ISSN =         "0035-7596 (print), 1945-3795 (electronic)",
  ISSN-L =       "0035-7596",
  bibdate =      "Mon Feb 18 18:47:30 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rmmc.asu.edu/abstracts/rmj/vol41-5/surv-masspag1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Rocky Mountain Journal of Mathematics",
  keywords =     "Benford's law; first digit phenomenon; hierarchy;
                 mantissa; weighted density",
}

@Article{Masse:2012:RNS,
  author =       "Bruno Mass{\'e} and Dominique Schneider",
  title =        "Random number sequences and the first digit
                 phenomenon",
  journal =      j-ELECTRON-J-PROBAB,
  volume =       "17",
  pages =        "86:1--86:17",
  year =         "2012",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1214/EJP.v17-1900",
  ISSN =         "1083-6489",
  ISSN-L =       "1083-6489",
  bibdate =      "Mon Sep 1 19:06:47 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/ejp.bib;
                 http://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://ejp.ejpecp.org/article/view/1900",
  abstract =     "The sequences of mantissa of positive integers and of
                 prime numbers are known not to be distributed as
                 Benford's law in the sense of the natural density. We
                 show that we can correct this defect by selecting the
                 integers or the primes by means of an adequate random
                 process and we investigate the rate of convergence. Our
                 main tools are uniform bounds for deterministic and
                 random trigonometric polynomials. We then adapt the
                 random process to prove the same result for logarithms
                 and iterated logarithms of integers. Finally we show
                 that, in many cases, the mantissa law of the $n$ th
                 randomly selected term converges weakly to the
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Probability",
  journal-URL =  "http://ejp.ejpecp.org/",
  keywords =     "Benford's law; density; mantissa; weak convergence",
}

@Article{Matthews:1999:PO,
  author =       "Robert Matthews",
  title =        "The Power of One",
  journal =      j-NEW-SCIENTIST,
  volume =       "163",
  number =       "2194",
  pages =        "27--30",
  day =          "10",
  month =        jul,
  year =         "1999",
  CODEN =        "NWSCAL",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Mon Nov 14 16:04:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fortunecity.com/emachines/e11/86/one.html;
                 http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  xxISSN =       "0262-4079, 0028-6664",
}

@Article{McAllister:2003:ARE,
  author =       "James W. McAllister",
  title =        "Algorithmic randomness in empirical data",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "34",
  number =       "3",
  pages =        "633--646",
  month =        sep,
  year =         "2003",
  CODEN =        "SHPSB5",
  DOI =          "http://dx.doi.org/10.1016/S0039-3681(03)00047-5",
  ISSN =         "0039-3681 (print), 1879-2510 (electronic)",
  ISSN-L =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:57 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See replies
                 \cite{Twardy:2005:EDS,McAllister:2005:ACE}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0039368103000475",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00393681",
}

@Article{McAllister:2005:ACE,
  author =       "James W. McAllister",
  title =        "Algorithmic compression of empirical data: reply to
                 {Twardy}, {Gardner}, and {Dowe}",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "36",
  number =       "2",
  pages =        "403--410",
  month =        jun,
  year =         "2005",
  CODEN =        "SHPSB5",
  DOI =          "http://dx.doi.org/10.1016/j.shpsa.2005.04.005",
  ISSN =         "0039-3681 (print), 1879-2510 (electronic)",
  ISSN-L =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:58 MST 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0039368105000221",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00393681",
}

@Article{McCowan:2005:AUZ,
  author =       "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F.
                 Hanser",
  title =        "The appropriate use of {Zipf}'s law in animal
                 communication studies",
  journal =      j-ANIM-BEHAV,
  volume =       "69",
  number =       "1",
  pages =        "F1--F7",
  day =          "20",
  month =        jan,
  year =         "2005",
  CODEN =        "ANBEA8",
  DOI =          "http://dx.doi.org/10.1016/j.anbehav.2004.09.002",
  ISSN =         "0003-3472 (print), 1095-8282 (electronic)",
  ISSN-L =       "0003-3472",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S000334720400346X",
  acknowledgement = ack-nhfb,
  fjournal =     "Animal Behaviour",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00033472",
  keywords =     "Zipf's Law",
}

@Book{McGrayne:2011:TWH,
  author =       "Sharon Bertsch McGrayne",
  title =        "The theory that would not die: how {Bayes}' rule
                 cracked the {Enigma} code, hunted down {Russian}
                 submarines, and emerged triumphant from two centuries
                 of controversy",
  publisher =    pub-YALE,
  address =      pub-YALE:adr,
  pages =        "xiii + 320",
  year =         "2011",
  ISBN =         "0-300-16969-8",
  ISBN-13 =      "978-0-300-16969-0",
  LCCN =         "QA279.5 .M415 2011",
  bibdate =      "Wed May 11 14:42:54 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "Bayes' rule appears to be a straightforward, one-line
                 theorem: by updating our initial beliefs with objective
                 new information, we get a new and improved belief. To
                 its adherents, it is an elegant statement about
                 learning from experience. To its opponents, it is
                 subjectivity run amok. In the first-ever account of
                 Bayes' rule for general readers, Sharon Bertsch
                 McGrayne explores this controversial theorem and the
                 human obsessions surrounding it. She traces its
                 discovery by an amateur mathematician in the 1740s
                 through its development into roughly its modern form by
                 French scientist Pierre Simon Laplace. She reveals why
                 respected statisticians rendered it professionally
                 taboo for 150 years --- at the same time that
                 practitioners relied on it to solve crises involving
                 great uncertainty and scanty information, even breaking
                 Germany's Enigma code during World War II, and explains
                 how the advent of off-the-shelf computer technology in
                 the 1980s proved to be a game-changer. Today, Bayes'
                 rule is used everywhere from DNA de-coding to Homeland
                 Security. Drawing on primary source material and
                 interviews with statisticians and other scientists, The
                 Theory That Would Not Die is the riveting account of
                 how a seemingly simple theorem ignited one of the
                 greatest controversies of all time.",
  acknowledgement = ack-nhfb,
  remark =       "This book has important comments on the battles among
                 Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
                 Pearson, supplementing the extensive discussion of
                 those conflicts in \cite{Ziliak:2008:CSS}.",
  subject =      "Bayesian statistical decision theory; history; science
                 / history; mathematics / history and philosophy",
}

@Article{McKee:1980:POR,
  author =       "Arnold F. McKee",
  title =        "The {Pareto} Optimum: Reconcilable with Social
                 Thought?",
  journal =      "International Journal of Social Economics",
  volume =       "7",
  number =       "7",
  pages =        "366--375",
  month =        "????",
  year =         "1980",
  CODEN =        "ISLEBC",
  DOI =          "http://dx.doi.org/10.1108/eb013878",
  ISSN =         "0306-8293 (print), 1758-6712 (electronic)",
  ISSN-L =       "0306-8293",
  bibdate =      "Fri Nov 25 07:01:57 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{McLaughlin:1984:DFI,
  author =       "William I. McLaughlin and Sylvia A. Lundy",
  title =        "Digit Functions of Integer Sequences",
  journal =      j-FIB-QUART,
  volume =       "22",
  number =       "2",
  pages =        "105--115",
  month =        may,
  year =         "1984",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:30 MDT 2011",
  bibsource =    "http://www.fq.math.ca/22-2.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@InProceedings{Mebane:2006:DAE,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2006 Annual Meeting of the Midwest Political Science
                 Association, April 20--23, Palmer House, Chicago}",
  title =        "Detecting Attempted Election Theft: Vote Counts,
                 Voting Machines and {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "i + 50",
  day =          "19",
  month =        apr,
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:14:14 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/mw06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2006:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{Election Fraud Conference, Salt Lake City, Utah,
                 September 29--30, 2006}",
  title =        "Election Forensics: The Second-digit {Benford's Law}
                 Test and Recent {American Presidential} Elections",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Feb 15 18:22:27 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www-personal.umich.edu/~wmebane/fraud06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2006:EFV,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2006 Summer Meeting of the Political Methodology
                 Society, UC-Davis, July 20--22, 2006}",
  title =        "Election Forensics: Vote Counts and {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "ii + 48",
  day =          "18",
  month =        jul,
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:01:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/pm06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2007:SD,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2007 Summer Meeting of the Political Methodology
                 Society, Pennsylvania State University, July 18--21,
                 2007}",
  title =        "Statistics for Digits",
  publisher =    "????",
  address =      "????",
  pages =        "1--21",
  day =          "2",
  month =        jul,
  year =         "2007",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:03:01 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/pm07.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InProceedings{Mebane:2008:EFO,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{The American Electoral Process conference, Center for
                 the Study of Democratic Politics, Princeton University,
                 May 1--3, 2008}",
  title =        "Election Forensics: Outlier and Digit Tests in
                 {America} and {Russia}",
  publisher =    "????",
  address =      "????",
  pages =        "i + 26",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:08:23 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/aep2008.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2008:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "R. Michael Alvarez and Thad E. Hall and Susan D.
                 Hyde",
  booktitle =    "{The Art and Science of Studying Election Fraud:
                 Detection, Prevention, and Consequences}",
  title =        "Election Forensics: The Second-digit {Benford's Law}
                 Test and Recent {American Presidential} Elections",
  publisher =    "Brookings Institution",
  address =      "Washington, DC, USA",
  pages =        "ii + 30",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:04:22 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Preprint dated 3 November 2006.",
  URL =          "http://www.umich.edu/~wmebane/fraud06.pdf",
  acknowledgement = ack-nhfb,
  remark =       "An earlier version of this paper was presented at the
                 Election Fraud Conference, Salt Lake City, Utah,
                 September 29--30, 2006.",
}

@InProceedings{Mebane:2010:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2010 Summer Meeting of the Political Methodology
                 Society, University of Iowa, July 22--24, 2010}",
  title =        "Election Fraud or Strategic Voting? {Can} Second-digit
                 Tests Tell the Difference?",
  publisher =    "????",
  address =      "????",
  pages =        "1--49",
  year =         "2010",
  ISBN =         "????",
  ISBN-13 =      "????",
  bibdate =      "Sat Feb 16 11:56:47 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/pm10.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Mebane:2010:FPE,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Fraud in the 2009 presidential election in {Iran}?",
  journal =      j-CHANCE,
  volume =       "23",
  number =       "1",
  pages =        "6--15",
  month =        mar,
  year =         "2010",
  CODEN =        "CNDCE4",
  DOI =          "http://dx.doi.org/10.1007/s00144-010-0003-4",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Mon Feb 18 17:50:18 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.springerlink.com/content/0337v415563q0753/abstract/",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/",
  xxnote =       "Publisher archive at
                 \path=http://amstat.tandfonline.com/loi/ucha20= is
                 missing volumes 18 (2005)--24 (2011). Those volumes are
                 available at
                 \path=http://link.springer.com/journal/144=",
}

@TechReport{Mebane:2010:MSD,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Memo on second-digit tests done on precinct counts for
                 {Democratic Senate} primary in {South Carolina}, 2010",
  type =         "Report",
  institution =  "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  day =          "12",
  month =        jun,
  year =         "2010",
  bibdate =      "Sat Feb 16 12:06:16 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Mebane:2011:CBL,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Comment on {Benford's Law} and the Detection of
                 Election Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "269--272",
  day =          "18",
  month =        "Summer",
  year =         "2011",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1093/pan/mpr024",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Fri Nov 25 11:00:46 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Deckert:2011:BLD}.",
  URL =          "http://pan.oxfordjournals.org/content/19/3/269.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
}

@Article{Mellor:2006:GKZ,
  author =       "Andy Mellor",
  title =        "Book Review: {G. K. Zipf, \booktitle The
                 Psycho-biology of Language (1935) MIT Press, Cambridge,
                 MA}",
  journal =      j-SYSTEM,
  volume =       "34",
  number =       "3",
  pages =        "455--457",
  day =          "20",
  month =        sep,
  year =         "2006",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1016/j.system.2006.07.004",
  ISSN =         "0346-251X (print), 1879-3282 (electronic)",
  ISSN-L =       "0346-251X",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0346251X06000674",
  acknowledgement = ack-nhfb,
  fjournal =     "System",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0346251X",
  keywords =     "Zipf's Law",
}

@Article{Mercik:1999:SAI,
  author =       "Szymon Mercik and Karina Weron and Zuzanna Siwy",
  title =        "Statistical analysis of ionic current fluctuations in
                 membrane channels",
  journal =      j-PHYS-REV-E,
  volume =       "60",
  number =       "6",
  pages =        "7343--7348",
  day =          "1",
  month =        dec,
  year =         "1999",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.60.7343",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.60.7343",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Metwally:2006:IES,
  author =       "Ahmed Metwally and Divyakant Agrawal and Amr {El
                 Abbadi}",
  title =        "An integrated efficient solution for computing
                 frequent and top-$k$ elements in data streams",
  journal =      j-TODS,
  volume =       "31",
  number =       "3",
  pages =        "1095--1133",
  month =        sep,
  year =         "2006",
  CODEN =        "ATDSD3",
  DOI =          "http://doi.acm.org/10.1145/1166074.1166084",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  bibdate =      "Tue Oct 17 05:41:01 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tods/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comments in \cite{Liu:2010:CIE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Database Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
}

@Article{Michel:2011:QAC,
  author =       "Jean-Baptiste Michel and Yuan Kui Shen and Aviva
                 Presser Aiden and Adrian Veres and Matthew K. Gray and
                 {The Google Books Team} and Joseph P. Pickett and Dale
                 Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant
                 and Steven Pinker and Martin A. Nowak and Erez
                 Lieberman Aiden",
  title =        "Quantitative Analysis of Culture Using Millions of
                 Digitized Books",
  journal =      j-SCIENCE,
  volume =       "331",
  number =       "6014",
  pages =        "176--182",
  day =          "14",
  month =        jan,
  year =         "2011",
  CODEN =        "SCIEAS",
  DOI =          "http://dx.doi.org/10.1126/science.1199644",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Fri Dec 09 11:06:28 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/331/6014/176.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "Zipf's law",
  remark =       "This papers reports results from a large study of
                 cultural phenomena, fame, and word usage from 4\% of
                 all books ever printed. Among the findings is this
                 quote from the first page: ``we estimated the number of
                 words in the English lexicon as 544,000 in 1900,
                 597,000 in 1950, and 1,022,000 in 2000. The lexicon is
                 enjoying a period of enormous growth: The addition of $
                 \approx 8500 $ words/year has increased the size of the
                 language by over 70\% during the past 50 years.'' From
                 page 177: ``Consistent with Zipf's famous law, a large
                 fraction of the words in our lexicon (63\%) were in
                 this lowest-frequency bin. As a result, we estimated
                 that 52\% of the English lexicon --- the majority of
                 the words used in English books --- consists of lexical
                 `dark matter' undocumented in standard references
                 (12).''",
}

@Article{Miller:1957:SEI,
  author =       "George A. Miller",
  title =        "Some Effects of Intermittent Silence",
  journal =      j-AMER-J-PSYCHOLOGY,
  volume =       "70",
  number =       "2",
  pages =        "311--314",
  month =        jun,
  year =         "1957",
  CODEN =        "AJPCAA",
  ISSN =         "0002-9556 (print), 1939-8298 (electronic)",
  ISSN-L =       "0002-9556",
  bibdate =      "Tue Nov 15 09:40:05 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/1419346",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Journal of Psychology",
  keywords =     "Zipf's Law",
}

@TechReport{Miller:2004:STB,
  author =       "Steven J. Miller",
  title =        "Some thoughts on {Benford}'s law",
  type =         "Preprint",
  institution =  "Williams College",
  address =      "Williamstown, MA 01267 USA",
  year =         "2004",
  bibdate =      "Sat Feb 16 18:43:46 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf",
  acknowledgement = ack-nhfb,
  remark =       "URL not found on 17 February 2013; perhaps in ReCALL
                 2004 proceedings",
}

@Article{Miller:2005:BLV,
  author =       "S. J. Miller and A. Kontorovich",
  title =        "{Benford}'s law, values of {$L$}-functions and the $ 3
                 x + 1 $ problem",
  journal =      j-ACTA-ARITHMETICA,
  volume =       "120",
  number =       "3",
  pages =        "269--297",
  month =        "????",
  year =         "2005",
  CODEN =        "AARIA9",
  DOI =          "http://dx.doi.org/10.4064/aa120-3-4",
  ISSN =         "0065-1036 (print), 1730-6264 (electronic)",
  ISSN-L =       "0065-1036",
  MRclass =      "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65,
                 46F12)",
  bibdate =      "Tue Feb 26 06:11:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Arithmetica",
}

@Book{Miller:2006:IMN,
  author =       "Steven J. Miller and Ramin Takloo-Bighash",
  title =        "An Invitation to Modern Number Theory",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xx + 503",
  year =         "2006",
  ISBN =         "0-691-12060-9 (hardcover)",
  ISBN-13 =      "978-0-691-12060-7 (hardcover)",
  LCCN =         "QA241 .M5344 2006",
  bibdate =      "Fri Mar 22 08:57:57 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Number theory",
  tableofcontents = "Part 1. Basic Number Theory \\
                 1. Mod p Arithmetic, Group Theory and Cryptography \\
                 2. Arithmetic Functions \\
                 3. Zeta and L-Functions \\
                 4. Solutions to Diophantine Equations \\
                 Part 2. Continued Fractions and Approximations \\
                 5. Algebraic and Transcendental Numbers \\
                 6. The Proof of Roth's Theorem \\
                 7. Introduction to Continued Fractions \\
                 Part 3. Probabilistic Methods and Equidistribution \\
                 8. Introduction to Probability \\
                 9. Applications of Probability: Benford's Law and
                 Hypothesis Testing \\
                 10. Distribution of Digits of Continued Fractions \\
                 11. Introduction to Fourier Analysis \\
                 12. f n k g and Poissonian Behavior \\
                 Part 4. The Circle Method \\
                 13. Introduction to the Circle Method \\
                 14. Circle Method: Heuristics for Germain Primes \\
                 Part 5. Random Matrix Theory and L-Functions \\
                 15. From Nuclear Physics to L-Functions \\
                 16. Random Matrix Theory: Eigenvalue Densities \\
                 17. Random Matrix Theory: Spacings between Adjacent
                 Eigenvalues \\
                 18. The Explicit Formula and Density Conjectures \\
                 Appendix A. Analysis Review \\
                 Appendix B. Linear Algebra Review \\
                 Appendix C. Hints and Remarks on the Exercises \\
                 Appendix D. Concluding Remarks",
}

@Article{Miller:2006:MCL,
  author =       "S. J. Miller and M. J. Nigrini",
  title =        "The {Modulo 1 Central Limit Theorem} and {Benford's
                 Law} for Products",
  journal =      "International Journal of Algebra",
  volume =       "3",
  number =       "3",
  pages =        "119--130",
  month =        jul,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "1312-8868",
  ISSN-L =       "1312-8868",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006math......7686M;
                 http://arxiv.org/abs/math/0607686",
  abstract =     "We derive a necessary and sufficient condition for the
                 sum of $M$ independent continuous random variables
                 modulo $1$ to converge to the uniform distribution in $
                 L^1 ([0, 1]) $, and discuss generalizations to discrete
                 random variables. A consequence is that if $ X_1,
                 \ldots {}, X_M $ are independent continuous random
                 variables with densities $ f_1, \ldots {}, f_M $, for
                 any base $B$ as $ M \to \infty $ for many choices of
                 the densities the distribution of the digits of $ X_1 *
                 \cdots {} * X_M $ converges to Benford's law base $B$.
                 The rate of convergence can be quantified in terms of
                 the Fourier coefficients of the densities, and provides
                 an explanation for the prevalence of Benford behavior
                 in many diverse systems.",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0607686",
  keywords =     "Mathematics - Probability, Mathematics - Classical
                 Analysis and ODEs, 60F05, 60F25, 11K06 (Primary),
                 42A10, 42A61, 62E15 (Secondary)",
}

@Article{Miller:2006:OSB,
  author =       "S. J. Miller and M. J. Nigrini",
  title =        "Order Statistics and {Benford's Law}",
  journal =      "ArXiv Mathematics e-prints",
  month =        jan,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006math......1344M",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0601344",
  keywords =     "Mathematics - Probability, Mathematics - Number
                 Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16
                 (Secondary)",
}

@Article{Miller:2008:MCL,
  author =       "Steven J. Miller and Mark J. Nigrini",
  title =        "The modulo $1$ central limit theorem and {Benford}'s
                 law for products",
  journal =      "International Journal of Algebra",
  volume =       "2",
  number =       "1--4",
  pages =        "119--130",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "1312-8868",
  ISSN-L =       "1312-8868",
  MRclass =      "60F05 (11K06 42A10)",
  MRnumber =     "2417189 (2009e:60053)",
  MRreviewer =   "Gutti J. Babu",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Algebra",
  fjournal =     "International Journal of Algebra",
}

@Article{Miller:2008:OSB,
  author =       "Steven J. Miller and Mark J. Nigrini",
  title =        "Order statistics and {Benford}'s law",
  journal =      j-INT-J-MATH-MATH-SCI,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "0161-1712",
  ISSN-L =       "0161-1712",
  MRclass =      "62G30 (62E10)",
  MRnumber =     "2461421 (2010c:62168)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Article ID 382948.",
  URL =          "http://arxiv.org/abs/math/0601344",
  abstract =     "Fix a base $B$ and let zeta have the standard
                 exponential distribution; the distribution of digits of
                 zeta base $B$ is known to be very close to Benford's
                 Law. If there exists a $C$ such that the distribution
                 of digits of $C$ times the elements of some set is the
                 same as that of zeta, we say that set exhibits shifted
                 exponential behavior base $B$ (with a shift of $ \log_B
                 C \bmod 1 $ ). Let $ X_1, \ldots {}, X_N $ be
                 independent identically distributed random variables.
                 If the $ X_i $'s are drawn from the uniform
                 distribution on $ [0, L] $, then as $ N \to \infty $
                 the distribution of the digits of the differences
                 between adjacent order statistics converges to shifted
                 exponential behavior (with a shift of $ \log_B L / N
                 \bmod 1 $ ). By differentiating the cumulative
                 distribution function of the logarithms modulo 1,
                 applying Poisson Summation and then integrating the
                 resulting expression, we derive rapidly converging
                 explicit formulas measuring the deviations from
                 Benford's Law. Fix a delta in $ (0, 1) $ and choose $N$
                 independent random variables from any compactly
                 supported distribution with uniformly bounded first and
                 second derivatives and a second order Taylor series
                 expansion at each point. The distribution of digits of
                 any $ N^\delta $ consecutive differences {\em and\/}
                 all $ N - 1 $ normalized differences of the order
                 statistics exhibit shifted exponential behavior. We
                 derive conditions on the probability density which
                 determine whether or not the distribution of the digits
                 of all the un-normalized differences converges to
                 Benford's Law, shifted exponential behavior, or
                 oscillates between the two, and show that the Pareto
                 distribution leads to oscillating behavior.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  pagecount =    "19",
}

@Article{Mir:2011:LLD,
  author =       "Tariq Ahmad Mir",
  title =        "Law of the leading digits and the ideological struggle
                 for numbers",
  journal =      "ArXiv e-prints",
  pages =        "11",
  year =         "2011",
  bibdate =      "Mon Nov 21 07:02:48 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1104.3948",
  abstract =     "Benford's law states that the occurrence of
                 significant digits in many data sets is not uniform but
                 tends to follow a logarithmic distribution such that
                 the smaller digits appear as first significant digits
                 more frequently than the larger ones. We investigate
                 here numerical data on the country-wise adherent
                 distribution of seven major world religions i.e.,
                 Christianity, Islam, Buddhism, Hinduism, Sikhism,
                 Judaism and Baha'ism to see if the proportion of the
                 leading digits occurring in the distribution conforms
                 to Benford's law. We find that the adherent data of all
                 the religions, except Christianity, excellently does
                 conform to Benford's law. Furthermore, unlike the
                 adherent data on Christianity, the significant digit
                 distribution of the three major Christian denominations
                 i.e. Catholicism, Protestantism and Orthodoxy obeys the
                 law. Thus in spite of their complexity general laws can
                 be established for the evolution of the religious
                 groups.",
  acknowledgement = ack-nhfb,
}

@Article{Mir:2012:LDD,
  author =       "T. A. Mir",
  title =        "The leading digit distribution of the worldwide
                 illicit financial flows",
  journal =      "ArXiv e-prints",
  year =         "2012",
  bibdate =      "Tue Feb 19 06:07:33 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1201.3432",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Mir:2012:LLD,
  author =       "Tariq Ahmad Mir",
  title =        "The law of the leading digits and the world
                 religions",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "3",
  pages =        "792--798",
  day =          "1",
  month =        feb,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2011.09.001",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Mon Nov 21 07:04:12 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437111007175",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A: Statistical Mechanics and its
                 Applications",
}

@Article{Mitchell:2008:TST,
  author =       "James G. Mitchell and Laurent Seuront",
  title =        "Towards a seascape topology {II}: {Zipf} analysis of
                 one-dimensional patterns",
  journal =      j-J-MAR-SYST,
  volume =       "69",
  number =       "3--4",
  pages =        "328--338",
  month =        feb,
  year =         "2008",
  CODEN =        "JMASE5",
  DOI =          "http://dx.doi.org/10.1016/j.jmarsys.2006.03.026",
  ISSN =         "0924-7963 (print), 1879-1573 (electronic)",
  ISSN-L =       "0924-7963",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0924796307000632",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Marine Systems",
  keywords =     "Zipf's Law",
}

@Article{Mitzenmacher:2003:BHG,
  author =       "Michael Mitzenmacher",
  title =        "A Brief History of Generative Models for Power Law and
                 Lognormal Distributions",
  journal =      j-INTERNET-MATH,
  volume =       "1",
  number =       "2",
  pages =        "226--251",
  month =        dec,
  year =         "2003",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/15427951.2004.10129088",
  ISSN =         "1542-7951 (print), 1944-9488 (electronic)",
  ISSN-L =       "1542-7951",
  bibdate =      "Thu Nov 24 13:38:13 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.im/1089229510;
                 http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf;
                 http://www.tandfonline.com/toc/uinm20/1/2",
  acknowledgement = ack-nhfb,
  ajournal =     "Internet Math.",
  fjournal =     "Internet Mathematics",
  keywords =     "Fibonacci sequence; lognormal distribution; monkeys
                 typing randomly; Pareto distribution; power-law
                 distribution; Yule distribution; Zipf's Law",
  remark =       "This is a survey article with a six-page bibliography
                 of earlier work, and a clear description of the
                 differences between lognormal and power-law
                 distributions, which otherwise look similar on log-log
                 plots. Lognormal distributions have finite means and
                 moments, while power-law distributions may have
                 infinite means and/or moments, depending on the
                 exponent. The preprint at author's Web site (last URL)
                 contains additional material on the acrimonious debate
                 between Beno{\^\i}t Mandelbrot and Herbert A. Simon
                 (see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and
                 other references in Mitzenmacher's paper) on the
                 derivation and modeling of Zipf's Law distributions.",
}

@Article{Mizuno:2008:PLE,
  author =       "Takayuki Mizuno and Masahiro Toriyama and Takao Terano
                 and Misako Takayasu",
  title =        "{Pareto} law of the expenditure of a person in
                 convenience stores",
  journal =      j-PHYSICA-A,
  volume =       "387",
  number =       "15",
  pages =        "3931--3935",
  year =         "2008",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2008.01.059",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B82",
  MRnumber =     "2586890",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
}

@Article{Mochty:2002:AMI,
  author =       "L. Mochty",
  title =        "{Die Aufdeckung von Manipulationen im Rechnungswesen
                 --- Was leistet das Benford's Law?}. ({German}) [{The}
                 disclosure of accounting manipulations --- what does
                 {Benford's Law} mean?]",
  journal =      "Die Wirtschaftspr{\"u}fung",
  volume =       "14",
  number =       "??",
  pages =        "725--736",
  month =        "????",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "0043-6313",
  ISSN-L =       "0043-6313",
  bibdate =      "Thu Nov 17 19:20:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Mohanty:1979:MMQ,
  author =       "Siba N. Mohanty",
  title =        "Models and Measurements for Quality Assessment of
                 Software",
  journal =      j-COMP-SURV,
  volume =       "11",
  number =       "3",
  pages =        "251--275",
  month =        sep,
  year =         "1979",
  CODEN =        "CMSVAN",
  DOI =          "http://doi.acm.org/10.1145/356778.356783",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:25:12 MDT 2008",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib;
                 http://www.acm.org/pubs/contents/journals/surveys/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.",
  acknowledgement = ack-nhfb,
  annote =       "Several software quality assessment methods which span
                 the software life cycle are discussed. The quality of a
                 system design can be estimated by measuring the system
                 entropy function or the system work function. The
                 quality improvement due to reconfiguration can be
                 determined by calculating system entropy loading
                 measures. Software science and Zipf's law are shown to
                 be useful for estimating program length and
                 implementation time.",
  country =      "USA",
  date =         "11/10/79",
  descriptors =  "Software; design; software engineering; reliability;
                 measurement; model; fundamentals in statistics;
                 performance evaluation;",
  enum =         "2189",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  references =   "65",
}

@Article{Mohanty:1980:SFW,
  author =       "Siba Mohanty",
  title =        "Surveyor's Forum: {Working} on Interpretations",
  journal =      j-COMP-SURV,
  volume =       "12",
  number =       "2",
  pages =        "256--256",
  month =        jun,
  year =         "1980",
  CODEN =        "CMSVAN",
  DOI =          "http://doi.acm.org/10.1145/356810.356818",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:27:10 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Molchanov:2004:BEL,
  author =       "Stanislav Molchanov and Xian Wang",
  title =        "On the {Benford}'s empirical law",
  journal =      "Random Oper. Stochastic Equations",
  volume =       "12",
  number =       "3",
  pages =        "201--210",
  year =         "2004",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1163/1569397042222495",
  ISSN =         "0926-6364 (print), 1569-397X (electronic)",
  ISSN-L =       "0926-6364",
  MRclass =      "11K16 (11B39 60B15)",
  MRnumber =     "2084074 (2005h:11162)",
  MRreviewer =   "A. N. Philippou",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Random Operators and Stochastic Equations",
}

@TechReport{Moller:2009:MQA,
  author =       "M. M{\"o}ller",
  title =        "Measuring the Quality of Auditing Services with the
                 Help of {Benford's Law} -- An Empirical Analysis and
                 Discussion of this Methodical Approach",
  type =         "Report",
  number =       "??",
  institution =  "Institute for Accounting and Control, University of
                 Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "25",
  day =          "24",
  month =        apr,
  year =         "2009",
  bibdate =      "Tue Nov 22 20:40:12 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ssrn.com/abstract=1529307",
  abstract =     "The so-called Benford's Law describes regularity in
                 the distribution of digits of randomly selected
                 numbers, which states that the relative frequency of
                 the leading digits reduces in a systematic manner from
                 the digit 1 to the digit 9. This distribution
                 hypothesis is being discussed in recent times as an
                 audit instrument in order to gain insights into
                 possible conscious and inadvertent errors in data
                 records. The present paper analyses the closing
                 accounts of 1,373 annual financial statements of
                 companies listed on the German DAX and compares these
                 with the Benford's distribution hypothesis. It can be
                 seen in the process that data pertaining to financial
                 accounts, which have not been audited by the so-called
                 ``Big 4'' audit firms, but by smaller external
                 auditors, deviate to a significant extent from the
                 regularity of Benford's Law, which appears to make the
                 use of Benford's Law suitable as a benchmark to assess
                 the quality of the audit.",
  acknowledgement = ack-nhfb,
}

@Article{Montemurro:2001:BZM,
  author =       "Marcelo A. Montemurro",
  title =        "Beyond the {Zipf--Mandelbrot} law in quantitative
                 linguistics",
  journal =      j-PHYSICA-A,
  volume =       "300",
  number =       "3--4",
  pages =        "567--578",
  day =          "15",
  month =        nov,
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "http://dx.doi.org/10.1016/S0378-4371(01)00355-7",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437101003557",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  keywords =     "Zipf's Law",
}

@Article{Montroll:1983:NOD,
  author =       "Elliott W. Montroll and Michael F. Shlesinger",
  title =        "On $ 1 / f $ noise and other distributions with long
                 tails",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "79",
  number =       "10",
  pages =        "3380--3383",
  day =          "15",
  month =        may,
  year =         "1983",
  CODEN =        "PNASA6",
  DOI =          "http://dx.doi.org/10.1073/pnas.79.10.3380",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  bibdate =      "Thu Feb 28 11:03:24 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.pnas.org/content/79/10/3380.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/search",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Book{Moon:1936:SBI,
  author =       "Parry Moon",
  title =        "The Scientific Basis of Illuminating Engineering",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xi + 608",
  year =         "1936",
  LCCN =         "TH7703 .M65",
  bibdate =      "Mon Nov 14 10:11:54 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "See pages 420ff.",
}

@Article{Moret:2006:NBL,
  author =       "M. A. Moret and V. de Senna and M. G. Pereira and G.
                 F. Zebende",
  title =        "{Newcomb--Benford} Law in Astrophysical Sources",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "17",
  number =       "11",
  pages =        "1597--1604",
  month =        "????",
  year =         "2006",
  CODEN =        "IJMPEO",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  ISSN-L =       "0129-1831",
  bibdate =      "Mon Nov 14 17:37:59 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
}

@Article{Moret:2009:GSA,
  author =       "M. A. Moret and V. de Senna and M. C. Santana and G.
                 F. Zebende",
  title =        "Geometric Structural Aspects of Proteins and
                 {Newcomb--Benford Law}",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "20",
  number =       "12",
  pages =        "1981--1988",
  month =        "????",
  year =         "2009",
  CODEN =        "IJMPEO",
  DOI =          "http://dx.doi.org/10.1142/S0129183109014874",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  ISSN-L =       "0129-1831",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
  keywords =     "Hydrophobicity, protein packing, complex systems, Time
                 series analysis, Systems obeying scaling laws, Binary
                 and multiple stars",
}

@Article{Morrison:2010:MG,
  author =       "Kent E. Morrison",
  title =        "The Multiplication Game",
  journal =      j-MATH-MAG,
  volume =       "83",
  number =       "??",
  pages =        "100--110",
  month =        apr,
  year =         "2010",
  CODEN =        "MAMGA8",
  DOI =          "????",
  ISSN =         "0025-570X",
  ISSN-L =       "0025-570X",
  bibdate =      "Mon Feb 18 17:51:50 2013",
  bibsource =    "http://www.maa.org/pubs/mag_apr10_toc.html;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@TechReport{Morrow:2006:BLF,
  author =       "John Morrow",
  title =        "{Benford's Law}, Families of Distributions and a Test
                 Basis",
  type =         "Report",
  institution =  "University of Wisconsin--Madison",
  address =      "Madison, WI, USA",
  month =        "????",
  year =         "2006",
  bibdate =      "Tue Nov 22 20:44:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Revised draft of 9 October 2010.",
  URL =          "http://www.johnmorrow.info/projects/benford/benfordMain.pdf",
  acknowledgement = ack-nhfb,
  lastaccess =   "22 November 2011",
}

@PhdThesis{Morters:2001:BGV,
  author =       "Peter M{\"o}rters",
  title =        "{Benford's Gesetz {\"u}ber die Verteilung der
                 Ziffern}. (German) [{Benford}'s law on the distribution
                 of digits]",
  type =         "{Habilitationsvorlesung}",
  school =       "????",
  address =      "Kaiserslauten, Germany, and Bath, UK",
  pages =        "4",
  month =        "????",
  year =         "2001",
  bibdate =      "Sat Feb 16 18:47:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://people.bath.ac.uk/maspm/benford.ps",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Mosimann:1995:DFC,
  author =       "James E. Mosimann and Claire V. Wiseman and Ruth E.
                 Edelman",
  title =        "Data Fabrication: Can People Generate Random Digits?",
  journal =      j-ACCOUNT-RES,
  volume =       "4",
  number =       "1",
  pages =        "31--55",
  month =        "????",
  year =         "1995",
  CODEN =        "ARQAEZ",
  ISSN =         "0898-9621 (print), 1545-5815 (electronic)",
  ISSN-L =       "0898-9621",
  bibdate =      "Sat Dec 10 11:56:38 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountability in Research",
  keywords =     "Benford's Law",
  remark =       "The abstract ends with: ``The difficulty that people
                 have in creating random error digits supports the
                 utility of examining such digits in investigations of
                 scientific misconduct.''",
}

@Article{Mosteller:1967:DSR,
  author =       "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
  title =        "The Distribution of Sums of Rounded Percentages",
  journal =      j-DEMOGRAPHY,
  volume =       "4",
  number =       "2",
  pages =        "850--858",
  month =        jun,
  year =         "1967",
  CODEN =        "????",
  ISSN =         "0070-3370 (print), 1533-7790 (electronic)",
  ISSN-L =       "0070-3370",
  bibdate =      "Thu Nov 24 08:03:16 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See \cite{Diaconis:1979:RP} for further work.",
  URL =          "http://muse.jhu.edu/journals/dem/;
                 http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
                 http://www.jstor.org/stable/2060324",
  abstract =     "When percentages are computed for counts in several
                 categories or for several positive measurements0 each
                 taken as a fraction of their sum, the rounded
                 percentages often fail to add to 100 percent. We
                 investigate how frequently this failure occurs and what
                 the distributions of sums of rounded percentages are
                 for (1) an empirical set of data, (2) the multinomial
                 distribution in small samples, (3) spacings between
                 points dropped on an interval --- the broken-stick
                 model; and (4) for simulation for several categories.
                 The several methods produce similar distributions.We
                 find that the probability that the sum of rounded
                 percentages adds to exactly 100 percent is certain for
                 two categories, about three-fourths for three
                 categories, about two-thirds for four categories, and
                 about [Formula: see text] for larger numbers of
                 categories, c, on the average when categories are not
                 improbable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Demography",
  pubmedid =     "21318695",
}

@Article{Moura:2006:ZLB,
  author =       "Newton J. Moura Jr. and Marcelo B. Ribeiro",
  title =        "{Zipf} law for {Brazilian} cities",
  journal =      j-J-THEOR-BIOL,
  volume =       "219",
  number =       "4",
  pages =        "441--448",
  day =          "15",
  month =        jul,
  year =         "2006",
  CODEN =        "JTBIAP",
  DOI =          "http://dx.doi.org/10.1016/j.physa.2005.11.038",
  ISSN =         "0022-5193 (print), 1095-8541 (electronic)",
  ISSN-L =       "0022-5193",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437105012422",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225193",
  keywords =     "Zipf's Law",
}

@PhdThesis{Muller:2003:AZP,
  author =       "Mathias M{\"u}ller",
  title =        "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der
                 Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}.
                 ({German}) [Applications of the digit analysis in the
                 audit practice with a focus on {Benford's Law}]",
  type =         "{Diplomarbeit}",
  school =       "Wirtschaftsuniversit{\"a}t Wien",
  address =      "Wien, Austria",
  pages =        "v + 75",
  month =        "????",
  year =         "2003",
  bibdate =      "Sat Feb 16 18:44:50 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://permalink.obvsg.at/wuw/AC03895842",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Muller:2011:HAS,
  author =       "Hans Christian M{\"u}ller",
  title =        "How an arcane statistical law could have prevented the
                 {Greek} disaster",
  journal =      "Economics Intelligence",
  volume =       "??",
  number =       "??",
  pages =        "??",
  day =          "28",
  month =        jul,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sun Nov 20 10:04:08 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/",
  abstract =     "If we had known what we know today, Greece would not
                 have been able to enter the Euro area. The
                 macroeconomic data the country reported to Eurostat in
                 Luxembourg were heavily tweaked. Unfortunately,
                 however, this only became clear years after it was too
                 late.",
  acknowledgement = ack-nhfb,
}

@Article{Murphy:1973:LLH,
  author =       "Larry J. Murphy",
  title =        "{Lotka's Law} in the Humanities?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "24",
  number =       "6",
  pages =        "461--462",
  month =        nov # "\slash " # dec,
  year =         "1973",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/asi.4630240607",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:09:40 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Nabeshima:2004:ZLP,
  author =       "Terutaka Nabeshima and Yukio-Pegio Gunji",
  title =        "{Zipf}'s law in phonograms and {Weibull} distribution
                 in ideograms: comparison of {English} with {Japanese}",
  journal =      j-BIOSYSTEMS,
  volume =       "73",
  number =       "2",
  pages =        "131--139",
  day =          "20",
  month =        feb,
  year =         "2004",
  CODEN =        "BSYMBO",
  DOI =          "http://dx.doi.org/10.1016/j.biosystems.2003.11.002",
  ISSN =         "0303-2647 (print), 1872-8324 (electronic)",
  ISSN-L =       "0303-2647",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0303264703002260",
  acknowledgement = ack-nhfb,
  fjournal =     "Biosystems (A6E)",
  keywords =     "Zipf's Law",
}

@Article{Nadarajah:2007:CPG,
  author =       "Saralees Nadarajah and Samuel Kotz",
  title =        "On the convolution of {Pareto} and gamma
                 distributions",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "51",
  number =       "12",
  pages =        "3650--3654",
  day =          "22",
  month =        aug,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1389-1286 (print), 1872-7069 (electronic)",
  ISSN-L =       "1389-1286",
  bibdate =      "Sat Apr 2 08:42:20 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/13891286",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Networks",
  journal-URL =  "http://www.sciencedirect.com/science/journal/13891286",
}

@Article{Nagasaka:1984:BL,
  author =       "Kenji Nagasaka",
  title =        "On {Benford}'s law",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "36",
  number =       "2",
  pages =        "337--352",
  year =         "1984",
  CODEN =        "AISXAD",
  DOI =          "http://dx.doi.org/10.1007/BF02481974",
  ISSN =         "0020-3157 (print), 1572-9052 (electronic)",
  ISSN-L =       "0020-3157",
  MRclass =      "60F99 (11K06 11K36 62E99)",
  MRnumber =     "758506 (86a:60052)",
  MRreviewer =   "L. Kuipers",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Ann. Inst. Statist. Math.",
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
}

@Article{Nagasaka:1987:BLL,
  author =       "Kenji Nagasaka and Jau-Shyong Shiue",
  title =        "{Benford}'s law for linear recurrence sequences",
  journal =      "Tsukuba J. Math.",
  volume =       "11",
  number =       "2",
  pages =        "341--351",
  year =         "1987",
  CODEN =        "????",
  ISSN =         "0387-4982",
  ISSN-L =       "0387-4982",
  MRclass =      "60E99 (11B37)",
  MRnumber =     "926460 (88m:60047)",
  MRreviewer =   "L. Kuipers",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tsukuba Journal of Mathematics",
}

@InCollection{Nagasaka:1990:BLL,
  author =       "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong
                 Shiue",
  booktitle =    "Number theory, {Vol}.\ {I} ({Budapest}, 1987)",
  title =        "{Benford}'s law: the logarithmic law of first digit",
  volume =       "51",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "361--391",
  year =         "1990",
  MRclass =      "11K06",
  MRnumber =     "1058225 (92b:11048)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Colloq. Math. Soc. J{\'a}nos Bolyai",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nagasaka:2005:BLD,
  author =       "Kenji Nagasaka",
  editor =       "G. Barat and H. Daud{\'e} and M. Laurent and P.
                 Liardet and S. Louboutin and A. Thomas",
  booktitle =    "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July
                 4--8, 2005, Universit{\'e} de Provence and
                 Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS
                 Marseilles, France}",
  title =        "{Benford}'s law with different basis",
  publisher =    "????",
  address =      "????",
  pages =        "1--2",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 18:49:26 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://atlas-conferences.com/c/a/r/e/47.htm",
  acknowledgement = ack-nhfb,
}

@Article{Naldi:2003:CIZ,
  author =       "M. Naldi",
  title =        "Concentration indices and {Zipf}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "78",
  number =       "3",
  pages =        "329--334",
  month =        mar,
  year =         "2003",
  CODEN =        "ECLEDS",
  DOI =          "http://dx.doi.org/10.1016/S0165-1765(02)00251-3",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "91B82",
  MRnumber =     "1959355",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176502002513",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Nebel:2012:DHG,
  author =       "J.-C. Nebel and S. Pezzulli",
  title =        "Distribution of Human Genes Observes {Zipf's Law}",
  journal =      "Kingston University Research \& Innovation Reports
                 (KURIR)",
  volume =       "8",
  number =       "??",
  pages =        "1--9",
  month =        "????",
  year =         "2012",
  DOI =          "????",
  ISSN =         "1749-5652",
  ISSN-L =       "1749-5652",
  bibdate =      "Tue Feb 19 06:09:05 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://staffnet.kingston.ac.uk/~ku33185/Papers/PDFformat/Kurir12.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://kurir.kingston.ac.uk/",
  remark =       "Kingston University, London, UK. Year 2012 volume is
                 not yet online on 19 February 2013.",
}

@Book{Newbold:2010:SBE,
  author =       "Paul Newbold and William L. Carlson and Betty Thorne",
  title =        "Statistics for Business and Economics",
  publisher =    "Pearson",
  address =      "Boston, MA, USA",
  edition =      "Seventh",
  pages =        "986 + 16",
  year =         "2010",
  ISBN =         "0-13-507248-4",
  ISBN-13 =      "978-0-13-507248-6",
  LCCN =         "QA276.18 .N49 2010",
  bibdate =      "Fri Mar 22 09:03:48 MDT 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Book{Newbold:2013:SBE,
  author =       "Paul Newbold and William L. (William Lee) Carlson and
                 Betty Thorne",
  title =        "Statistics for Business and Economics",
  publisher =    "Pearson Education",
  address =      "Harlow, Essex, UK",
  edition =      "Eighth",
  pages =        "792",
  year =         "2013",
  ISBN =         "0-273-76706-2",
  ISBN-13 =      "978-0-273-76706-0",
  LCCN =         "HF1017 .N48 2013",
  bibdate =      "Fri Mar 22 09:03:53 MDT 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Commercial statistics; Economics; Statistical methods;
                 Statistics",
}

@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the frequency of use of the different digits
                 in natural numbers",
  journal =      j-AM-J-MATH,
  volume =       "4",
  number =       "1--4",
  pages =        "39--40",
  year =         "1881",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  bibdate =      "Thu Feb 15 16:35:24 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2369148",
  abstract =     "That the ten digits do not occur with equal frequency
                 must be evident to any one making much use of
                 logarithmic tables, and noticing how much faster the
                 first pages wear out than the last ones. The first
                 significant figure is oftener 1 than any other digit,
                 and the frequency diminishes up to 9.",
  acknowledgement = ack-nhfb,
  author-dates = "March 12, 1835--July 11, 1909",
  fjournal =     "American Journal of Mathematics",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 40: ``The law of probability of the occurrence
                 of numbers is such that all mantissas of their
                 logarithms are equally probable.''. The article
                 contains no references to earlier work.",
  remark-2 =     "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are
                 the earliest citations of Newcomb's work that I have
                 yet found in connection with Benford's Law.",
  xxURL =        "http://en.wikipedia.org/wiki/Simon_Newcomb",
}

@Article{Newman:1996:ASC,
  author =       "M. E. J. Newman and Kim Sneppen",
  title =        "Avalanches, scaling, and coherent noise",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "6",
  pages =        "6226--6231",
  month =        dec,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "http://dx.doi.org/10.1103/PhysRevE.54.6226",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:44:51 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.6226",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Book{Newman:2002:ME,
  author =       "M. E. J. (Mark E. J.) Newman and Richard G. Palmer",
  title =        "Modeling extinction",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xii + 102",
  year =         "2002",
  ISBN =         "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)",
  ISBN-13 =      "978-0-19-515946-2 (paperback), 978-0-19-515945-5
                 (hardcover)",
  LCCN =         "QH78 .N48 2002",
  bibdate =      "Thu Feb 28 10:36:25 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Santa Fe Institute studies in the sciences of
                 complexity",
  acknowledgement = ack-nhfb,
  keywords =     "power law; Zipf's law",
  subject =      "Extinction (Biology); Statistical methods;
                 Mathematical models",
}

@Article{Newman:2005:PLP,
  author =       "M. E. J. Newman",
  title =        "Power laws, {Pareto} distributions and {Zipf}'s law",
  journal =      j-CONTEMP-PHYS,
  volume =       "46",
  number =       "5",
  pages =        "323--351",
  month =        sep,
  year =         "2005",
  CODEN =        "CTPHAF",
  DOI =          "http://dx.doi.org/10.1080/00107510500052444",
  ISSN =         "0010-7514 (print), 1366-5812 (electronic)",
  ISSN-L =       "0010-7514",
  bibdate =      "Fri Jul 09 16:33:18 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "When the probability of measuring a particular value
                 of some quantity varies inversely as a power of that
                 value, the quantity is said to follow a power law, also
                 known variously as Zipf's law or the Pareto
                 distribution. Power laws appear widely in physics,
                 biology, earth and planetary sciences, economics and
                 finance, computer science, demography and the social
                 sciences. For instance, the distributions of the sizes
                 of cities, earthquakes, forest fires, solar flares,
                 moon craters and people's personal fortunes all appear
                 to follow power laws. The origin of power-law behaviour
                 has been a topic of debate in the scientific community
                 for more than a century. Here we review some of the
                 empirical evidence for the existence of power-law forms
                 and the theories proposed to explain them.",
  acknowledgement = ack-nhfb,
  fjournal =     "Contemporary physics",
  keywords =     "Benford's Law; critical phenomena; Legendre beta
                 function; Pareto distribution; percolation; phase
                 transitions; power-law distributions; random walks;
                 Riemann zeta function; scale-free distributions; Yule
                 process; Zipf's Law",
  remark =       "This article is an excellent survey of continuous and
                 discrete distributions that follow a power law, and
                 some that do not. It is well worth reading.",
  subject =      "astrophysics; atomic and nuclear physics; chemical
                 physics; computational physics; condensed matter
                 physics; environmental physics; experimental physics;
                 general physics; particle and high energy physics;
                 plasma physics; space science; theoretical physics",
}

@Article{Nguyen:2003:DPL,
  author =       "H. T. Nguyen and V. Kreinovich and L. Longpre",
  title =        "Dirty pages of logarithm tables, lifetime of the
                 universe, and subjective (fuzzy) probabilities on
                 finite and infinite intervals",
  journal =      j-IEEE-TRANS-FUZZY-SYSTEMS,
  volume =       "1",
  pages =        "67--73",
  year =         "2003",
  CODEN =        "IEFSEV",
  DOI =          "http://dx.doi.org/10.1109/FUZZ.2003.1209339",
  ISSN =         "1063-6706 (print), 1941-0034 (electronic)",
  ISSN-L =       "1063-6706",
  bibdate =      "Sat Feb 16 18:51:15 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The 12th IEE International Conference on Fuzzy
                 Systems. FUZZ'03",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Fuzzy Systems",
  xxnote =       "Is this the listed journal, or a conference paper??",
}

@Article{Nguyen:2004:DPL,
  author =       "Hung T. Nguyen and Vladik Kreinovich and Luc
                 Longpr{\'e}",
  title =        "Dirty Pages of Logarithm Tables, Lifetime of the
                 Universe, and (Subjective) Probabilities on Finite and
                 Infinite Intervals",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "10",
  number =       "2",
  pages =        "83--106",
  month =        apr,
  year =         "2004",
  CODEN =        "RCOMF8",
  DOI =          "http://dx.doi.org/10.1023/B:REOM.0000015848.19449.12",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon Feb 6 07:42:05 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/rc.bib",
  URL =          "http://link.springer.com/article/10.1023/B%3AREOM.0000015848.19449.12/;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83-106",
  acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}

@Article{Ni:2008:BLH,
  author =       "D. Ni and Z. Ren",
  title =        "{Benford}'s law and half-lives of unstable nuclei",
  journal =      j-EUR-PHYS-J-A,
  volume =       "38",
  pages =        "251--255",
  month =        dec,
  year =         "2008",
  CODEN =        "EPJAFV",
  DOI =          "http://dx.doi.org/10.1140/epja/i2008-10680-8",
  ISSN =         "1434-6001 (print), 1434-601X (electronic)",
  ISSN-L =       "1434-6001",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008EPJA...38..251N",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal A: Hadrons and Nuclei",
  journal-URL =  "http://www.springerlink.com/content/1434-6001",
}

@Article{Ni:2009:BLD,
  author =       "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren",
  title =        "{Benford's Law} and $ \beta $-Decay Half-Lives",
  journal =      j-COMM-THEOR-PHYS,
  volume =       "51",
  number =       "4",
  pages =        "713--716",
  month =        apr,
  year =         "2009",
  CODEN =        "CTPHDI",
  DOI =          "http://dx.doi.org/10.1088/0253-6102/51/4/25",
  ISSN =         "0253-6102",
  ISSN-L =       "0253-6102",
  bibdate =      "Sun Nov 13 11:01:52 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N;
                 http://stacks.iop.org/0253-6102/51/i=4/a=25",
  abstract =     "The experimental values of 2059 $ \beta $-decay
                 half-lives are systematically analyzed and
                 investigated. We have found that they are in
                 satisfactory agreement with Benford's law, which states
                 that the frequency of occurrence of each figure, 1--9,
                 as the first significant digit in a surprisingly large
                 number of different data sets follows a logarithmic
                 distribution favoring the smaller ones. Benford's
                 logarithmic distribution of $ \beta $-decay half-lives
                 can be explained in terms of Newcomb's justification of
                 Benford's law and empirical exponential law of $ \beta
                 $-decay half-lives. Moreover, we test the calculated
                 values of 6721 $ \beta $-decay half-lives with the aid
                 of Benford's law. This indicates that Benford's law is
                 useful for theoretical physicists to test their methods
                 for calculating $ \beta $-decay half-lives.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in theoretical physics",
}

@Article{Nicholls:1987:EZP,
  author =       "Paul Travis Nicholls",
  title =        "Estimation of {Zipf} parameters",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "38",
  number =       "6",
  pages =        "443--445",
  year =         "1987",
  CODEN =        "AISJB6",
  DOI =          "http://dx.doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO;2-E",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
}

@Article{Nicolaisen:2007:PPB,
  author =       "Jeppe Nicolaisen and Birger Hj{\o}rland",
  title =        "Practical potentials of {Bradford}'s law: a critical
                 examination of the received view",
  journal =      j-J-DOC,
  volume =       "63",
  number =       "3",
  pages =        "359--377",
  month =        "????",
  year =         "2007",
  CODEN =        "JDOCAS",
  DOI =          "http://dx.doi.org/10.1108/00220410710743298",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 11:58:03 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
}

@InCollection{Nicolis:1988:PBZ,
  author =       "John S. Nicolis",
  booktitle =    "Synergetics, order and chaos ({Madrid}, 1987)",
  title =        "On the parallel between {Zipf}'s law and {$ 1 / f $}
                 processes in chaotic systems possessing coexisting
                 attractors",
  publisher =    "World Sci. Publ.",
  address =      "Teaneck, NJ, USA",
  pages =        "723--734",
  year =         "1988",
  MRclass =      "58F13 (00A69)",
  MRnumber =     "1115922 (92g:58087)",
  MRreviewer =   "Dieter H. Mayer",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nicolis:1989:CDM,
  author =       "G. Nicolis and C. Nicolis and John S. Nicolis",
  title =        "Chaotic dynamics, {Markov} partitions, and {Zipf}'s
                 law",
  journal =      j-J-STAT-PHYS,
  volume =       "54",
  number =       "3--4",
  pages =        "915--924",
  month =        feb,
  year =         "1989",
  CODEN =        "JSTPSB",
  DOI =          "http://dx.doi.org/10.1007/BF01019781",
  ISSN =         "0022-4715 (print), 1572-9613 (electronic)",
  ISSN-L =       "0022-4715",
  MRclass =      "58F13 (58F14 58F20)",
  MRnumber =     "988565 (90b:58184)",
  MRreviewer =   "Shi Hai Li",
  bibdate =      "Thu Aug 28 18:40:55 MDT 2014",
  bibsource =    "http://link.springer.com/journal/10955;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=54&issue=3;
                 http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01019781",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Physics",
  journal-URL =  "http://link.springer.com/journal/10955",
}

@Article{Nicolis:1989:PBZ,
  author =       "John S. Nicolis and Ichiro Tsuda",
  title =        "On the parallel between {Zipf}'s law and {$ 1 / f $}
                 processes in chaotic systems possessing coexisting
                 attractors",
  journal =      j-PROG-THEOR-PHYS,
  vo