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%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.156",
%%%     date            = "14 August 2024",
%%%     time            = "12:16:28 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             = "https://www.math.utah.edu/~beebe",
%%%     checksum        = "01055 42644 187274 1888797",
%%%     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; Hall--Petch effect; 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
%%%                        480 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
%%%                        medicine, nuclear science, operations
%%%                        research, pathology, physics, plasticity,
%%%                        political analysis, probability, psychology,
%%%                        risk analysis, signal processing, simulation,
%%%                        social sciences, 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.
%%%
%%%                        A simple Benford-based rule of thumb is that
%%%                        about half the values start with digit 1 or
%%%                        2, about 10 percent with 8 or 9, and 5
%%%                        percent with 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 1.156, the year coverage looked like
%%%                        this:
%%%
%%%                             1881 (   1)    1929 (   1)    1977 (   9)
%%%                             1882 (   0)    1930 (   0)    1978 (  11)
%%%                             1883 (   0)    1931 (   1)    1979 (   6)
%%%                             1884 (   0)    1932 (   2)    1980 (   8)
%%%                             1885 (   0)    1933 (   0)    1981 (  12)
%%%                             1886 (   0)    1934 (   1)    1982 (  10)
%%%                             1887 (   0)    1935 (   1)    1983 (   6)
%%%                             1888 (   0)    1936 (   2)    1984 (  16)
%%%                             1889 (   0)    1937 (   1)    1985 (  10)
%%%                             1890 (   0)    1938 (   2)    1986 (  16)
%%%                             1891 (   0)    1939 (   0)    1987 (  18)
%%%                             1892 (   0)    1940 (   0)    1988 (  12)
%%%                             1893 (   0)    1941 (   0)    1989 (  14)
%%%                             1894 (   0)    1942 (   0)    1990 (   9)
%%%                             1895 (   0)    1943 (   1)    1991 (  11)
%%%                             1896 (   1)    1944 (   1)    1992 (  15)
%%%                             1897 (   0)    1945 (   2)    1993 (  11)
%%%                             1898 (   0)    1946 (   1)    1994 (  12)
%%%                             1899 (   0)    1947 (   0)    1995 (  19)
%%%                             1900 (   0)    1948 (   2)    1996 (  23)
%%%                             1901 (   0)    1949 (   2)    1997 (  17)
%%%                             1902 (   0)    1950 (   3)    1998 (  21)
%%%                             1903 (   0)    1951 (   0)    1999 (  28)
%%%                             1904 (   0)    1952 (   1)    2000 (  22)
%%%                             1905 (   0)    1953 (   1)    2001 (  26)
%%%                             1906 (   0)    1954 (   1)    2002 (  34)
%%%                             1907 (   0)    1955 (   1)    2003 (  42)
%%%                             1908 (   0)    1956 (   0)    2004 (  46)
%%%                             1909 (   0)    1957 (   5)    2005 (  68)
%%%                             1910 (   1)    1958 (   1)    2006 (  60)
%%%                             1911 (   0)    1959 (   1)    2007 (  49)
%%%                             1912 (   1)    1960 (   1)    2008 (  54)
%%%                             1913 (   1)    1961 (   2)    2009 (  78)
%%%                             1914 (   1)    1962 (   2)    2010 (  97)
%%%                             1915 (   1)    1963 (   1)    2011 (  88)
%%%                             1916 (   1)    1964 (   1)    2012 (  59)
%%%                             1917 (   1)    1965 (   4)    2013 (  46)
%%%                             1918 (   0)    1966 (   4)    2014 (  52)
%%%                             1919 (   0)    1967 (   3)    2015 (  79)
%%%                             1920 (   1)    1968 (   4)    2016 (  25)
%%%                             1921 (   0)    1969 (  12)    2017 (  12)
%%%                             1922 (   1)    1970 (   8)    2018 (  13)
%%%                             1923 (   0)    1971 (   2)    2019 (   8)
%%%                             1924 (   0)    1972 (   7)    2020 (  16)
%%%                             1925 (   1)    1973 (  10)    2021 (  13)
%%%                             1926 (   1)    1974 (  12)    2022 (  10)
%%%                             1927 (   1)    1975 (  13)    2023 (   9)
%%%                             1928 (   2)    1976 (  13)    2024 (   3)
%%%                             20xx (   1)
%%%
%%%                             Article:       1167
%%%                             Book:            93
%%%                             InCollection:    53
%%%                             InProceedings:   64
%%%                             Manual:           1
%%%                             MastersThesis:    6
%%%                             Misc:            20
%%%                             PhdThesis:        8
%%%                             Proceedings:      8
%%%                             TechReport:      50
%%%                             Unpublished:      3
%%%
%%%                             Total entries: 1473
%%%
%%%                        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
%%%                              https://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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   "\ifx \undefined \polhk      \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" #
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   "\ifx \undefined \url        \input{path.sty} \fi"
}

%%% ====================================================================
%%% 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|https://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-ACTA-PHYS-POL-B       = "Acta Physica Polonica B"}

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

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

@String{j-ADV-MATH              = "Advances in Mathematics"}

@String{j-ADV-QUANTUM-CHEM      = "Advances in Quantum Chemistry"}

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

@String{j-AEROBIOLOGIA          = "Aerobiologia"}

@String{j-AM-DOC                = "American Documentation"}

@String{j-AM-J-APPL-SCI         = "American Journal of Applied Sciences"}

@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-PHYS              = "Annals of Physics"}

@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-ARCH-HIST-EXACT-SCI   = "Archive for History of Exact Sciences"}

@String{j-ARKHIMEDES            = "Arkhimedes"}

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

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

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

@String{j-ATMOS-ENV             = "Atmospheric Environment"}

@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-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-BMC-BIOINFORMATICS    = "BMC Bioinformatics"}

@String{j-BOLL-UNIONE-MAT-ITAL  = "Bollettino della Unione matematica italiana"}

@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-CHEM-PHYS-LETT        = "Chemical Physics Letters"}

@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-COLLNET-J-SCIENTOMETRICS-INF-MANAGE = "Collnet Journal of
                                  Scientometrics and Information Management"}

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

@String{j-COMM-NONLIN-SCI-NUM-SIM = "Communications in Nonlinear Science and
                                  Numerical Simulation"}

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

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

@String{j-COMMUN-DESIGN-Q-REVIEW = "Communication Design Quarterly Review"}

@String{j-COMMUN-MATH-STAT      = "Communications in Mathematics and Statistics"}

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

@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}

@String{j-COMP-ARCH-NEWS        = "ACM SIGARCH Computer Architecture News"}

@String{j-COMP-COMM             = "Computer Communications"}

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

@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-AIDED-DES      = "Computer-Aided Design"}

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

@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-CRYPTOLOGIA           = "Cryptologia"}

@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-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
                                  Computer Science"}

@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-ESAIM-PROBAB-STATIST  = "ESAIM: Probability and Statistics"}

@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-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
                                  Processing"}

@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-FUT-GEN-COMP-SYS      = "Future Generation Computer Systems"}

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

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

@String{j-ICARUS-IJSSS          = "Icarus: International Journal of Solar
                                  System Studies"}

@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-SPECTRUM         = "IEEE Spectrum"}

@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-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization
                                   and Computer Graphics"}

@String{j-IMA-J-APPL-MATH       = "IMA Journal of Applied Mathematics"}

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

@String{j-IMAGE-VIS-COMPUT      = "Image and Vision Computing"}

@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-INFO-SYS              = "Information systems"}

@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-PLAST           = "International Journal of Plasticity"}

@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-NUMBER-THEORY   = "International Journal of Number Theory"}

@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-SCI-ENG-RESEARCH = "International Journal of Scientific and
                                  Engineering Research"}

@String{j-INT-J-STAT-PROBAB     = "International Journal of Statistics
                                  and Probability"}

@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-ECONOMETRICS   = "Journal of Applied Econometrics"}

@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-ASSOC-INF-SCI-TECHNOL = "Journal of the Association for Information
                                  Science and Technology"}

@String{j-J-ASTROPHYS-ASTRON    = "Journal of Astrophysics and Astronomy"}

@String{j-J-BUS-ECON-STAT       = "Journal of Business \& Economic Statistics"}

@String{j-J-CLIN-PATHOL         = "Journal of Clinical Pathology"}

@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-DIFFER-EQU          = "Journal of Differential Equations"}

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

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

@String{j-J-DYN-DIFFER-EQU      = "Journal of Dynamics and Differential Equations"}

@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-PHYS           = "Journal of Mathematical Physics"}

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

@String{j-J-MOL-BIOL            = "Journal of Molecular Biology"}

@String{j-J-NETW-COMPUT-APPL    = "Journal of Network and Computer
                                  Applications"}

@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-A-GENERAL = "Journal of the Royal Statistical
                                  Society. Series A (General)"}

@String{j-J-R-STAT-SOC-SER-A-STAT-SOC = "Journal of the Royal
                                  Statistical Society. Series A
                                  (Statistics in 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-RISK-UNCERT         = "Journal of Risk and Uncertainty"}

@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                   Simulation"}

@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-SYST-SOFTW          = "The Journal of systems and software"}

@String{j-J-SUPERCOMPUTING      = "The Journal of Supercomputing"}

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

@String{j-J-THEOR-PROBAB        = "Journal of Theoretical Probability"}

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

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

@String{j-JOCCH                 = "Journal on Computing and Cultural
                                  Heritage (JOCCH)"}

@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-MATH-SOC-SCI          = "Mathematical Social Sciences"}

@String{j-MATH-USSR-IZV         = "Mathematics of the {USSR} --- Izvestiya"}

@String{j-METAB-CLIN-EXP        = "Metabolism, Clinical and Experimental"}

@String{j-METRIKA               = "Metrika"}

@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-NAMS                  = "Notices of the American Mathematical Society"}

@String{j-NATURE                = "Nature"}

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

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

@String{j-NUCL-MED              = "Journal of Nuclear Medicine"}

@String{j-NUCLEAR-INSTR-METH-PHYS-RES-A = "Nuclear instruments and methods in
                                  physics research. Section A, Accelerators,
                                  spectrometers, detectors and associated
                                  equipment"}

@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-PATTERN-RECOGN-LETT   = "Pattern Recognition Letters"}

@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-B-PLUS-C      = "Physica. B + C; B: Physics of condensed
                                  matter. C: Atomic, molecular and plasma
                                  physics; optics"}

@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-PROC-VLDB-ENDOWMENT   = "Proceedings of the VLDB Endowment"}

@String{j-PROBAB-SURV           = "Probability 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-QUAL-QUANT            = "Quality \& Quantity"}

@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-RESONANCE             = "Resonance"}

@String{j-REV-ECON-STAT         = "Review of Economics and Statistics"}

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

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@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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
}

@Book{Pareto:1896:CEP,
  author =       "Vilfredo Pareto",
  title =        "Cours d'{\'e}conomie politique profess{\'e} a
                 l'universit{\'e} de {Lausanne}. (French) [{Course} on
                 political economy given at the {University of
                 Lausanne}]",
  publisher =    "F. Rouge",
  address =      "Lausanne, Switzerland",
  pages =        "????",
  year =         "1896--1897",
  LCCN =         "HB173 .P22",
  bibdate =      "Wed Nov 16 08:41:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "Two volumes issued in successive years. The Italian
                 economist and mathematician, Vilfredo Federico (born in
                 Paris, France, and initially named Wilfried Fritz)
                 Pareto (15 July 1848--19 August 1923), introduced the
                 80--20 rule in economics (80\% of the wealth is owned
                 by 20\% of the people, which was true at the time in
                 Italy, and found to be similar in other countries). He
                 developed the Pareto distribution, in which a random
                 variable $X$ has the property that the probability that
                 it is greater than some number $x$ is given by $ {\rm
                 Pr}(X > x) = (x_m / x)^\alpha $ for $ x > x_m $, and $
                 {\rm Pr}(X > x) = 1 $ otherwise. The positive value $
                 x_m $ is a cutoff, and as $ \alpha \to \infty $, the
                 Pareto distribution approaches a Dirac delta function,
                 $ \delta (x - x_m) $. When this models the distribution
                 of wealth, the exponent $ \alpha $ is called the {\em
                 Pareto index}.",
}

@Article{Doolittle:1910:SNF,
  author =       "C. L. Doolittle",
  title =        "{Simon Newcomb, F.R.S., LL.D., D.C.L.}",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "49",
  number =       "197",
  pages =        "iii--xviii",
  month =        oct # "\slash " # dec,
  year =         "1910",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Sat Aug 24 19:37:51 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/procamerphilsoc1900.bib",
  URL =          "https://www.jstor.org/stable/984092",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. Amer. Philos. Soc.",
  fjournal =     "Proceedings of the American Philosophical Society",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "This obituary does not mention Newcomb's short paper
                 on the leading-digit phenomenon now known as Benford's
                 Law, but it does give an overview of Newcomb's humble
                 origins, education, life, and scientific influence.",
}

@Book{Poincare:1912:CPL,
  author =       "H. Poincar{\'e}",
  title =        "Calcul des Probabilit{\'e}s: Le{\c{c}}ons
                 profess{\'e}es pendant le deuxi{\`e} me semestre
                 1893--1894. ({French}) [{Calculation} of Probabilities:
                 Lectures from the second semester 1893--1894]",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  pages =        "ii + 274",
  year =         "1912",
  LCCN =         "QA273 .P75",
  bibdate =      "Mon Nov 14 10:08:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1854--1912",
  language =     "French",
  remark =       "See pp. 313--320.",
}

@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 =    "https://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{Stamp:1914:NIP,
  author =       "J. C. Stamp",
  title =        "A New Illustration of {Pareto}'s Law",
  journal =      j-J-R-STAT-SOC,
  volume =       "77",
  number =       "2",
  pages =        "200--204",
  month =        jan,
  year =         "1914",
  DOI =          "https://doi.org/10.2307/2339802",
  ISSN =         "0952-8385",
  ISSN-L =       "0952-8385",
  bibdate =      "Sat Jan 24 11:18:04 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i315805;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1910.bib",
  URL =          "http://www.jstor.org/stable/2339802",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
}

@Article{Weyl:1915:GZM,
  author =       "Hermann Weyl",
  title =        "{{\"U}ber die Gleichverteilung von Zahlen mod. Eins}.
                 ({German}) [{On} the uniform distribution of numbers
                 mod. one]",
  journal =      j-MATH-ANN,
  volume =       "77",
  number =       "3",
  pages =        "313--352",
  month =        "????",
  year =         "1915",
  CODEN =        "MAANA3",
  DOI =          "https://doi.org/10.1007/BF01475864",
  ISSN =         "0025-5831 (print), 1432-1807 (electronic)",
  ISSN-L =       "0025-5831",
  bibdate =      "Sun Nov 13 10:54:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Ann.",
  fjournal =     "Mathematische Annalen",
  journal-URL =  "http://link.springer.com/journal/208",
  language =     "German",
  xxyear =       "1916",
}

@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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  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 =    "https://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.",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Yule:1925:MTE,
  author =       "G. Udny Yule",
  title =        "A Mathematical Theory of Evolution, Based on the
                 Conclusions of {Dr. J. C. Willis, F.R.S.}",
  journal =      j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI,
  volume =       "213",
  number =       "??",
  pages =        "21--87",
  day =          "14",
  month =        may,
  year =         "1925",
  CODEN =        "PTRBAE",
  DOI =          "https://doi.org/10.1098/rstb.1925.0002",
  ISSN =         "0962-8436 (print), 1471-2970 (electronic)",
  ISSN-L =       "0962-8436",
  bibdate =      "Tue Nov 15 10:45:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rstb.royalsocietypublishing.org/content/213/402-410/21",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical transactions of the Royal Society of
                 London Series B, Biological sciences",
}

@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",
  day =          "19",
  month =        jun,
  year =         "1926",
  CODEN =        "JWASA3",
  ISSN =         "0043-0439",
  ISSN-L =       "0043-0439",
  bibdate =      "Thu Nov 24 14:36:11 2011",
  bibsource =    "https://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}.",
  URL =          "http://www.jstor.org/stable/24529203",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Washington Academy of Sciences",
  journal-URL =  "http://www.jstor.org/journal/jwashacadscie",
  keywords =     "Lotka's Law",
}

@Article{Yule:1927:RS,
  author =       "G. Udny Yule",
  title =        "On Reading a Scale",
  journal =      j-J-R-STAT-SOC,
  volume =       "90",
  number =       "3",
  pages =        "570--587",
  month =        "????",
  year =         "1927",
  ISSN =         "0952-8385",
  ISSN-L =       "0952-8385",
  bibdate =      "Wed Nov 23 12:29:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See related later work \cite{Preece:1981:DFD}.",
  URL =          "http://www.jstor.org/stable/2341205",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
  remark =       "This paper reports on human bias in the recording of
                 last digits in measurements, or from roundings, or from
                 later scale conversions.",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
}

@Article{Sun:1928:EFD,
  author =       "C. P. Sun",
  title =        "On the Examination of Final Digits by Experiments in
                 Artificial Sampling",
  journal =      j-BIOMETRIKA,
  volume =       "20A",
  number =       "1/2",
  pages =        "64--68",
  month =        jul,
  year =         "1928",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2331941",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  bibdate =      "Sat Jun 21 13:38:07 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315380;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1920.bib",
  URL =          "http://www.jstor.org/stable/2331941",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://www.jstor.org/journals/00063444.html",
}

@Article{Zipf:1929:RFD,
  author =       "George Kingsley Zipf",
  title =        "Relative frequency as a determinant of phonetic
                 change",
  journal =      "Harvard Studies in Classical Philology",
  volume =       "40",
  number =       "??",
  pages =        "1--95",
  month =        "????",
  year =         "1929",
  CODEN =        "????",
  ISSN =         "0073-0688",
  ISSN-L =       "0073-0688",
  bibdate =      "Fri Nov 25 09:02:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/journals/00730688.html;
                 http://www.jstor.org/stable/310585",
  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 =    "https://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''.",
}

@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 =    "https://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.",
}

@Book{Zipf:1932:SSP,
  author =       "George Kingsley Zipf",
  title =        "Selected studies of the principle of relative
                 frequency in language",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "51",
  year =         "1932",
  LCCN =         "P123 .Z5",
  bibdate =      "Wed Nov 16 09:03:46 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This book is the origin of {\em Zipf's Law}, but the
                 phenomenon was apparently first reported two decades
                 earlier in \cite{Auerbach:1913:GBG} for city
                 populations, in \cite{Estoup:1916:GSM} for word
                 frequencies, and in \cite{Lotka:1926:FDS} for
                 researcher publication counts.",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  subject =      "Plautus, Titus Maccius; language and languages;
                 semantics; comparative linguistics; Chinese language;
                 phonology; Latin language; glossaries, vocabularies,
                 etc; dialects; China; Beijing",
}

@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 =    "https://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,
}

@Book{Zipf:1935:PBL,
  author =       "George Kingsley Zipf",
  title =        "The psycho-biology of language: an introduction to
                 dynamic philology",
  publisher =    pub-HOUGHTON-MIFFLIN,
  address =      pub-HOUGHTON-MIFFLIN:adr,
  pages =        "ix + 336",
  year =         "1935",
  LCCN =         "P105 .Z5",
  bibdate =      "Wed Nov 16 09:07:09 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  subject =      "language and languages; semantics; comparative
                 linguistics",
}

@Article{Keyser:1936:VFD,
  author =       "C. J. Keyser",
  title =        "{Vilfredo Federico Damaso Pareto}. {Mathematician},
                 economist, sociologist",
  journal =      j-SCRIPTA-MATH,
  volume =       "4",
  number =       "??",
  pages =        "5--23",
  month =        "????",
  year =         "1936",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "62.0027.01",
  ZBmath =       "2525107",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "See pages 420ff.",
}

@Article{Bresciani-Turroni:1937:PL,
  author =       "C. Bresciani-Turroni",
  title =        "On {Pareto}'s Law",
  journal =      j-J-R-STAT-SOC,
  volume =       "100",
  number =       "3",
  pages =        "421--432",
  month =        "????",
  year =         "1937",
  DOI =          "https://doi.org/10.2307/2980528",
  ISSN =         "0952-8385",
  ISSN-L =       "0952-8385",
  bibdate =      "Sat Jan 24 11:18:08 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349533;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
  URL =          "http://www.jstor.org/stable/2980528",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
}

@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 (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  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{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 (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Wed Nov 23 14:27:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 https://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",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  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??",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.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",
}

@Unpublished{Stigler:1945:DLD,
  author =       "George J. Stigler",
  title =        "The distribution of leading digits in statistical
                 tables",
  year =         "1945",
  bibdate =      "Sat Nov 12 16:07:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unpublished, but written about 1945--1946, and
                 presented in an 1975 address at Haskell Hall,
                 University of Chicago. Stigler's distribution is more
                 complex than that of Newcomb and Benford. Stigler has $
                 F_d = (d \ln (d) - (d + 1) \ln (d + 1) + (1 + (10 / 9)
                 \ln (10))) / 9 $, which gives leading-digit frequencies
                 of 0.2413, 0.1832, 0.1455, 0.1174, 0.0950, 0.0764,
                 0.0605, 0.0465, and 0.0342. See \cite{Lee:2010:SAR} for
                 a comparison of the Benford and Stigler distributions,
                 and their relations to Zipf and Pareto distributions.
                 For derivations of Stigler's distribution, see
                 \cite{Logan:1978:FDP,Raimi:1985:FDP}.",
  URL =          "http://www.nobelprize.org/nobel_prizes/economics/laureates/1982/",
  acknowledgement = ack-nhfb,
  remark =       "Stigler won the 1982 Sveriges Riksbank Prize in
                 Economic Sciences in Memory of Alfred Nobel (often
                 called the Nobel Prize in Economics, although that
                 field was not among the original ones funded by Nobel's
                 will).",
}

@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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
}

@Book{Zipf:1949:HBP,
  author =       "George Kingsley Zipf",
  title =        "Human behaviour and the principle of least effort",
  publisher =    "Hafner Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "xi + 573",
  year =         "1949",
  LCCN =         "H91 .Z5 1949a",
  bibdate =      "Tue Nov 15 09:35:14 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  remark =       "Reprinted 1965.",
  subject =      "Human ecology",
}

@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 =          "https://doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO%3B2-7",
  ISSN =         "0021-9762 (print), 1097-4679 (electronic)",
  ISSN-L =       "0021-9762",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Psychology",
}

@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 =    "https://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)",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica",
}

@Article{Tsuji:1952:UDN,
  author =       "M. Tsuji",
  title =        "On the uniform distribution of numbers $ \bmod 1 $",
  journal =      j-J-MATH-SOC-JPN,
  volume =       "4",
  number =       "3--4",
  pages =        "313--322",
  month =        "????",
  year =         "1952",
  CODEN =        "NISUBC",
  DOI =          "https://doi.org/10.2969/jmsj/00430313",
  ISSN =         "0025-5645",
  ISSN-L =       "0025-5645",
  bibdate =      "Sun Feb 17 06:33:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.jmsj/1261415780",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the {Mathematical Society of Japan}",
}

@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,
  bookpages =    "xii + 532",
  pages =        "486--502",
  year =         "1953",
  LCCN =         "Q350 .S92 1952",
  bibdate =      "Wed Nov 16 09:37:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://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,
  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.",
}

@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 =    "https://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{Simon:1955:CSD,
  author =       "Herbert A. Simon",
  title =        "On a Class of Skew Distribution Functions",
  journal =      j-BIOMETRIKA,
  volume =       "42",
  number =       "3/4",
  pages =        "425--440",
  month =        dec,
  year =         "1955",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2333389",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62.0X",
  MRnumber =     "0073085 (17,380e)",
  MRreviewer =   "H. A. David",
  bibdate =      "Sat Jun 21 14:32:48 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315425;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib",
  URL =          "http://www.jstor.org/stable/2333389",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
  keywords =     "distribution of income; distribution of species among
                 genera; distributions of city populations;
                 distributions of document word frequencies;
                 distributions of scientific publication counts; Zipf's
                 Law",
  remark =       "This work is an extension of Yule's work
                 \cite{Yule:1925:MTE}. See discussion
                 \cite{Mandelbrot:1959:NCS} and comments
                 \cite{Mitzenmacher:2003:BHG}.",
}

@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 =    "https://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",
}

@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 =    "https://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)",
}

@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 =    "https://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{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 =    "https://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{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 =    "https://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",
}

@Book{Zeller:1958:TLG,
  author =       "Karl Zeller",
  title =        "{Theorie der Limitierungsverfahren}. (German)
                 [{Theory} of limiting processes]",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "242",
  year =         "1958",
  LCCN =         "QA295 .Z4",
  bibdate =      "Wed Nov 16 06:43:43 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "{Ergebnisse der Mathematik und ihrer Grenzgebiete}",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "series; convergence",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00199958",
}

@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 =    "https://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",
  journal-URL =  "http://www.jstor.org/journal/inteeconrevi",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Jber. Deutsch. Math.--Verein",
  language =     "German",
}

@Article{Pinkham:1961:DFS,
  author =       "Roger S. Pinkham",
  title =        "On the Distribution of First Significant Digits",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "4",
  pages =        "1223--1230",
  month =        dec,
  year =         "1961",
  CODEN =        "AASTAD",
  ISSN =         "0003-4851",
  ISSN-L =       "0003-4851",
  bibdate =      "Sat Sep 17 10:19:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2237922",
  abstract =     "It has been noticed by astute observers that well used
                 tables of logarithms are invariably dirtier at the
                 front than at the back. Upon reflection one is led to
                 inquire whether there are more physical constants with
                 low order first significant digits than high. Actual
                 counts by Benford [2] show that not only is this the
                 case but that it seems to be an empirical truth that
                 whenever one has a large body of physical data,
                 Farmer's Almanac, Census Reports, Chemical Rubber
                 Handbook, etc., the proportion of these data with first
                 significant digit $n$ or less is approximately $
                 \log_{10}(n + 1) $. Any reader formerly unaware of this
                 ``peculiarity'' will find an actual sampling experiment
                 wondrously tantalizing. Thus, for example,
                 approximately $ 0.7 $ of the physical constants in the
                 Chemical Rubber Handbook begin with $4$ or less ($
                 \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
                 with the widespread intuitive evaluation $ 4 / 9 $
                 ths.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 1223: ``\ldots{} the proportion of these data
                 with first significant digit $n$ or less is
                 approximately $ \log_{10}(n + 1) $.''\par

                 \ldots{} ``The only distribution for first significant
                 digits which is invariant under scale change of the
                 underlying distribution is $ \log_{10}(n + 1) $.
                 Contrary to suspicion this is a non-trivial
                 mathematical result, for the variable $n$ is
                 discrete.''.\par

                 From p. 1230: ``The foregoing results bear on questions
                 of round-off in computing machines. Since $ d(u v) = u
                 d v + v d u $, the error resulting from multiplying two
                 rounded numbers will be governed primarily by the first
                 significant digits of the two numbers being multiplied.
                 Now the distribution of first significant digits,
                 favoring as it does low order digits, tends to produce
                 less error than would be the case if first significant
                 digits were uniform as has sometimes been
                 assumed.''\par

                 Cited in \cite{Sterbenz:1974:FPC}.",
}

@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 =        "xvii + 411",
  year =         "1962",
  LCCN =         "QA297 .H28",
  MRclass =      "65.00",
  MRnumber =     "0137279",
  MRreviewer =   "G. E. Forsythe",
  bibdate =      "Mon Aug 6 07:24:38 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International Series in Pure and Applied Mathematics",
  acknowledgement = ack-nhfb,
  HDnumber =     "51",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis; Electronic digital computers;
                 random numbers",
  tableofcontents = "1. The difference calculus \\
                 2. Roundoff noise \\
                 3. The summation calculus \\
                 4. Evaluation of infinite series \\
                 5. Finite difference equations \\
                 6. The finite Fourier series \\
                 7--9. Polynomial approximation introduction \\
                 10. A uniform method for finding formulas \\
                 11. On finding the error term of a formula \\
                 12. Formulas for definite integrals \\
                 13. Indefinite integrals \\
                 14. Introduction to differential equations \\
                 15. A general theory of predictor-corrector methods \\
                 16. Special methods of integrating ordinary
                 differential equations \\
                 17--18. Least squares theory and practice \\
                 19. Chebyshev polynomials \\
                 20. Rational functions \\
                 21--22. Periodic functions --- Fourier series \\
                 23. Nonperiodic functions --- the Fourier integral \\
                 24. Linear filters --- smoothing and differentiating
                 \\
                 25. Integrals and differential equations \\
                 26. Exponential approximation \\
                 27. Singularities \\
                 28. On finding zeros \\
                 29. Simultaneous linear algebraic equations \\
                 30. Inversion of matrices and eigenvalues \\
                 31. Some examples of the simulation of situations and
                 processes \\
                 32. Random numbers and Monte Carlo methods \\
                 $N+1$: The art of computing for scientists and
                 engineers",
}

@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 =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Weaver:1963:LLT,
  author =       "Warren Weaver",
  title =        "{Lady Luck}: The Theory of Probability",
  publisher =    "Doubleday Anchor Series",
  address =      "New York, NY, USA",
  pages =        "392",
  year =         "1963",
  LCCN =         "QA273 .W4",
  bibdate =      "Mon Nov 14 09:54:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Benford's Law is discussed on pp. 270--277.",
  acknowledgement = ack-nhfb,
  author-dates = "Warren, Weaver (1894--1978)",
  remark =       "Reprinted in \cite{Weaver:1982:LLT}.",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Compositio Mathematica",
}

@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 =    "https://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.",
}

@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 =          "https://doi.org/10.1109/PGEC.1965.264258",
  ISSN =         "0367-7508",
  ISSN-L =       "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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/",
}

@Book{Zipf:1965:PBL,
  author =       "George Kingsley Zipf",
  title =        "The psycho-biology of language: an introduction to
                 dynamic philology",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "xv + 336",
  year =         "1965",
  LCCN =         "P105 .Z5 1965",
  bibdate =      "Wed Nov 16 09:07:09 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  remark =       "Reprint of \cite{Zipf:1935:PBL}.",
  subject =      "language; philology; semantics; psycholinguistics;
                 comparative linguistics",
}

@Article{Ball:1966:BRB,
  author =       "R. J. Ball",
  title =        "Book Review: {{\booktitle{Random Processes and the
                 Growth of Firms: A Study of the Pareto Law}}, by Josef
                 Steindl}",
  journal =      j-J-R-STAT-SOC-SER-A-GENERAL,
  volume =       "129",
  number =       "4",
  pages =        "600--601",
  month =        "????",
  year =         "1966",
  CODEN =        "JSSAEF",
  DOI =          "https://doi.org/10.2307/2982275",
  ISSN =         "0035-9238",
  ISSN-L =       "0035-9238",
  bibdate =      "Sat Jan 24 11:18:12 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349635;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1960.bib",
  URL =          "http://www.jstor.org/stable/2982275",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series A
                 (General)",
  journal-URL =  "http://www.jstor.org/journals/00359238.html",
}

@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 =    "https://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.",
}

@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 =          "https://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 =    "https://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 =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{Petersen:1966:RMT,
  author =       "Gordon Marshall Petersen",
  title =        "Regular Matrix Transformations",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "viii + 142",
  year =         "1966",
  LCCN =         "QA263 .P415 1966",
  bibdate =      "Mon Nov 14 10:18:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Groos:1967:BCB,
  author =       "Ole V. Groos",
  title =        "Brief Communications: {Bradford's Law} and the
                 {Keenan--Atherton} data",
  journal =      j-AM-DOC,
  volume =       "18",
  number =       "1",
  pages =        "46--46",
  month =        jan,
  year =         "1967",
  CODEN =        "AMDOA7",
  DOI =          "https://doi.org/10.1002/asi.5090180108",
  ISSN =         "0096-946X (print), 1936-6108 (electronic)",
  ISSN-L =       "0096-946X",
  bibdate =      "Fri Sep 11 06:21:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amdoc.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Documentation",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643/",
  onlinedate =   "23 Apr 2007",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =    "https://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",
}

@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 =    "https://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{Shenton:1968:PDM,
  author =       "L. R. Shenton",
  title =        "Periodicity and Density of Modified {Fibonacci}
                 Sequences",
  journal =      j-FIB-QUART,
  volume =       "6",
  number =       "2",
  pages =        "109--116",
  month =        apr,
  year =         "1968",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:02 MDT 2011",
  bibsource =    "http://www.fq.math.ca/6-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/6-2/shenton.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{Wilk:1968:PPM,
  author =       "M. B. Wilk and R. Gnanadesikan",
  title =        "Probability Plotting Methods for the Analysis of
                 Data",
  journal =      j-BIOMETRIKA,
  volume =       "55",
  number =       "1",
  pages =        "1--17",
  month =        mar,
  year =         "1968",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2334448",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  bibdate =      "Sat Jun 21 14:33:29 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315458;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
  URL =          "http://www.jstor.org/stable/2334448",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://www.jstor.org/journals/00063444.html",
  keywords =     "empirical cumulative distribution function (ECDF);
                 percent ($p$--$p$) plots; quantile ($q$--$q$) plots",
  remark =       "This article does not mention Benford's Law, but MJN
                 \cite{Nigrini:2012:BLA} lists this reference for
                 analysis of data.",
}

@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 =    "https://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{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 (print), 1730-6329 (electronic)",
  ISSN-L =       "0016-2736",
  bibdate =      "Sat Nov 12 16:19:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fundamenta mathematicae",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprinted in \cite{Fairthorne:2005:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Unpublished{Hafner:1969:CSR,
  author =       "Everett M. Hafner",
  title =        "Circular slide roulette",
  year =         "1969",
  bibdate =      "Mon Nov 14 10:00:25 2011",
  bibsource =    "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Polska Akademia Nauk. Instytut Matematyczny.
                 Zastosowania Matematyki",
}

@Article{Holewijn:1969:UDS,
  author =       "Dr. P. J. Holewijn",
  title =        "On the uniform distribution of sequences of random
                 variables",
  journal =      j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB,
  volume =       "14",
  number =       "2",
  pages =        "89--92",
  month =        "????",
  year =         "1969",
  CODEN =        "ZWVGAA",
  DOI =          "https://doi.org/10.1007/BF00537514",
  ISSN =         "0044-3719",
  ISSN-L =       "0044-3719",
  bibdate =      "Sat Apr 26 19:23:29 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00537514",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und
                 verwandte Gebiete",
  journal-URL =  "http://link.springer.com/journal/440",
}

@Book{Knuth:1969:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical 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",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "44 \#3531",
  MRreviewer =   "M. Muller",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is discussed on pp. 219--229.",
  tableofcontents = "3: Random Numbers \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 9 \\
                 3.2.1. The Linear Congruential Method / 9 \\
                 3.2.1.1. Choice of modulus / 11 \\
                 3.2.1.2. Choice of multiplier / 15 \\
                 3.2.1.3. Potency / 21 \\
                 3.2.2. Other Methods / 25 \\
                 3.3. Statistical Tests / 34 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 35 \\
                 3.3.2. Empirical Tests / 54 \\
                 *3.3.3. Theoretical Tests / 69 \\
                 3.3.4. The Spectral Test / 82 \\
                 3.4. Other Types of Random Quantities / 100 \\
                 3.4.1. Numerical Distributions / 101 \\
                 3.4.2. Random Sampling and Shuffling / 121 \\
                 *3.5. What is a Random Sequence? / 127 \\
                 3.6. Summary / 155 \\
                 4: Arithmetic \\
                 4.1. Positional Number Systems / 162 \\
                 4.2. Floating-Point Arithmetic / 180 \\
                 4.2.1. Single-Precision Calculations / 180 \\
                 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
                 *4.2.3. Double-Precision Calculations / 210 \\
                 4.2.4. Statistical Distribution / 218 \\
                 4.3. Multiple-Precision Arithmetic / 229 \\
                 4.3.1. The Classical Algorithms / 229 \\
                 *4.3.2. Modular Arithmetic / 248 \\
                 *4.3.3. How Fast Can We Multiply? / 258 \\
                 4.4. Radix Conversion / 280 \\
                 4.5. Rational Arithmetic / 290 \\
                 4.5.1. Fractions / 290 \\
                 4.5.2. The Greatest Common Divisor / 293 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 316 \\
                 4.5.4. Factoring into Primes / 339 \\
                 4.6. Polynomial Arithmetic / 360 \\
                 4.6.1. Division of Polynomials / 363 \\
                 *4.6.2. Factorization of Polynomials / 381 \\
                 4.6.3. Evaluation of Powers / 398 \\
                 4.6.4. Evaluation of Polynomials / 422 \\
                 *4.7. Manipulation of Power Series / 444 \\
                 Answers to Exercises / 452 \\
                 Appendix A: MIX / 565 \\
                 1. Description of MIX / 565 \\
                 2. The MIX Assembly Language / 584 \\
                 Appendix B: Tables of Numerical Quantities / 596 \\
                 1. Fundamental Constants (decimal) / 596 \\
                 2. Fundamental Constants (octal) / 597 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 598 \\
                 Appendix C: Index to Notations / 600 \\
                 Index and Glossary / 605",
  xxyear =       "{\noopsort{1968c}}1969",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Raimi:1969:DFS,
  author =       "R. A. Raimi",
  title =        "On the Distribution of First Significant Figures",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "76",
  number =       "4",
  pages =        "342--348",
  month =        apr,
  year =         "1969",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2316424",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:39:22 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Raimi:1969:PDF,
  author =       "R. Raimi",
  title =        "The peculiar distribution of first significant
                 digits",
  journal =      j-SCI-AMER,
  volume =       "221",
  number =       "6",
  pages =        "109--120",
  month =        dec,
  year =         "1969",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican1269-109",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Sat Nov 12 16:39:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@PhdThesis{Wong:1969:GDS,
  author =       "James Teng Wong",
  title =        "On the Generalization of the Distribution of the
                 Significant Digits Under Computation",
  type =         "{Ph.D.} thesis",
  school =       "Department of Mathematics, Oregon State University",
  address =      "Corvallis, OR, USA",
  pages =        "52",
  year =         "1969",
  bibdate =      "Fri Nov 25 15:41:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/docview/302476508?accountid=14677",
  acknowledgement = ack-nhfb,
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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;
                 https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Orlov:1970:GZM,
  author =       "Ju. K. Orlov",
  title =        "A generalization of the {Zipf--Mandelbrot} law",
  journal =      "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
  volume =       "57",
  pages =        "37--40",
  year =         "1970",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "94.50",
  MRnumber =     "0274234 (42 \#9109)",
  MRreviewer =   "T. Nemetz",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sakharth. SSR Mech. Akad. Moambe",
}

@Article{Taguchi:1970:ZLC,
  author =       "Tokio Taguchi",
  title =        "On {Zipf}'s law. {A} characterization of distributions
                 in linguistics and demography",
  journal =      j-PROC-INST-STATIST-MATH,
  volume =       "17",
  pages =        "83--90",
  year =         "1970",
  CODEN =        "????",
  ISSN =         "0912-6112",
  ISSN-L =       "0912-6112",
  bibdate =      "Sat Nov 12 10:39:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0238.68026",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. Inst. Statist. Math.",
  classmath =    "68Q45 (Formal languages)",
  fjournal =     "Proceedings of the Institute of Statistical
                 Mathematics",
  language =     "Japanese",
}

@Book{Zeller:1970:TLG,
  author =       "Karl Zeller and Wolfgang Beekmann",
  title =        "{Theorie der Limitierungsverfahren}. (German)
                 [{Theory} of limiting processes]",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xii + 314",
  year =         "1970",
  LCCN =         "QA295 .Z4 1970",
  bibdate =      "Wed Nov 16 06:43:43 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Ergebnisse der Mathematik und ihrer Grenzgebiete",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "series; convergence",
}

@Article{Thorp:1971:PCD,
  author =       "E. Thorp and R. Whitley",
  title =        "{Poincar{\'e}}'s conjecture and the distribution of
                 digits in logarithm tables",
  journal =      j-COMPOS-MATH,
  volume =       "21",
  number =       "??",
  pages =        "233--250",
  month =        "????",
  year =         "1971",
  CODEN =        "CMPMAF",
  ISSN =         "0010-437X (print), 1570-5846 (electronic)",
  ISSN-L =       "0010-437X",
  bibdate =      "Sat Nov 12 16:36:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comp. Math.",
  fjournal =     "Compositio Mathematica",
}

@Article{Wlodarski:1971:FLN,
  author =       "J. Wlodarski",
  title =        "{Fibonacci} and {Lucas} Numbers Tend to Obey
                 {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "9",
  number =       "1",
  pages =        "87--88",
  month =        feb,
  year =         "1971",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/9-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Krevitt:1972:BCC,
  author =       "Beth Krevitt and Belver C. Griffith",
  title =        "Brief Communications: 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",
  month =        may,
  year =         "1972",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630230310",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:44 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Varian:1972:LEB,
  author =       "Hal R. Varian",
  title =        "Letter to the {Editor}: {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "26",
  number =       "3",
  pages =        "65--66",
  month =        jun,
  year =         "1972",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Mar 30 11:34:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
  abstract =     "Around 1938 the physicist Frank Benford observed a
                 rather strange fact: tables of logarithms in libraries
                 tend to be dirtier at the beginning than at the end.
                 This indicated to Benford that people had more occasion
                 to calculate with numbers beginning with 1 or 2 than
                 with 8 or 9.\par

                 Benford also found that the frequency of the digit $p$
                 being the first digit of a decimal number was very
                 closely approximated by $ \log (p + 1) - \log p $
                 [i.e., $ \log (1 + 1 / p) $ ]. This has become known as
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Vlachy:1972:VFS,
  author =       "Jan Vlach{\'y}",
  title =        "Variable Factors in Scientific Communities
                 (Observations on {Lotka's Law})",
  journal =      "Teorie a Metoda",
  volume =       "4",
  number =       "??",
  pages =        "91--120",
  month =        "????",
  year =         "1972",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 25 07:53:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  xxvolume =     "6",
}

@Article{Whitney:1972:MNI,
  author =       "R. E. Whitney",
  title =        "Mathematical Notes: Initial Digits for the Sequence of
                 Primes",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "79",
  number =       "2",
  pages =        "150--152",
  month =        feb,
  year =         "1972",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2316536",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:38 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Wilkinson:1972:ABL,
  author =       "Elizabeth A. Wilkinson",
  title =        "The Ambiguity of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "28",
  number =       "2",
  pages =        "122--130",
  month =        "????",
  year =         "1972",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026534",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:20:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://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{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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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/",
}

@Article{Loynes:1973:SRP,
  author =       "R. M. Loynes",
  title =        "Some results in the probabilistic theory of asymptotic
                 uniform distribution modulo 1",
  journal =      j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB,
  volume =       "26",
  number =       "1",
  pages =        "33--41",
  month =        "????",
  year =         "1973",
  CODEN =        "ZWVGAA",
  DOI =          "https://doi.org/10.1007/BF00533958",
  ISSN =         "0044-3719",
  ISSN-L =       "0044-3719",
  bibdate =      "Sat Apr 26 19:24:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00533958",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und
                 verwandte Gebiete",
  journal-URL =  "http://link.springer.com/journal/440",
}

@Article{Murphy:1973:BCL,
  author =       "Larry J. Murphy",
  title =        "Brief Communications: ``{Lotka's Law} in the
                 humanities?''",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "24",
  number =       "6",
  pages =        "461--462",
  month =        nov,
  year =         "1973",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630240607",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:48 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Petruszewycz:1973:LLE,
  author =       "M. Petruszewycz",
  title =        "{L'histoire} de la loi d'{Estoup--Zipf}: documents.
                 ({French}) [{The} history of the {Estoup--Zipf} law]",
  journal =      "Math. Sci. Humaines",
  volume =       "??",
  number =       "44",
  pages =        "41--56",
  year =         "1973",
  CODEN =        "????",
  ISSN =         "0025-5815",
  ISSN-L =       "0025-5815",
  MRclass =      "92A25",
  MRnumber =     "0354071 (50 \#6553)",
  MRreviewer =   "J. S. Joel",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centre de Math{\'e}matique Sociale. \'Ecole Pratique
                 des Hautes \'Etudes. Math{\'e}matiques et Sciences
                 Humaines",
  language =     "French",
}

@Article{Sarkar:1973:OSD,
  author =       "B. P. Sarkar",
  title =        "An observation on the significant digits of the
                 binomial coefficients and factorials",
  journal =      j-SANKHYA-B,
  volume =       "35",
  number =       "??",
  pages =        "363--364",
  month =        "????",
  year =         "1973",
  CODEN =        "SANBBV",
  ISSN =         "0581-5738",
  ISSN-L =       "0581-5738",
  bibdate =      "Sat Nov 12 16:29:39 2011",
  bibsource =    "https://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{Schatte:1973:VMG,
  author =       "Peter Schatte",
  title =        "{Zur Verteilung der Mantisse in der
                 Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
                 ({German}) [Distribution of the mantissa in the
                 floating-point representation of a random variable]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "53",
  number =       "??",
  pages =        "553--565",
  month =        "????",
  year =         "1973",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Mon Nov 14 16:35:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}

@Article{Sentance:1973:FAB,
  author =       "W. A. Sentance",
  title =        "A Further Analysis of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "490--494",
  month =        dec,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@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 =          "https://doi.org/10.1037/h0035850",
  ISSN =         "0096-3445 (print), 1939-2222 (electronic)",
  ISSN-L =       "0096-3445",
  bibdate =      "Fri Feb 15 06:32:17 2013",
  bibsource =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "https://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/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://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",
}

@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 =    "https://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)",
}

@Article{Schorr:1974:LLL,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and Library Science",
  journal =      "RQ",
  volume =       "14",
  number =       "1",
  pages =        "32--33",
  month =        "Fall",
  year =         "1974",
  CODEN =        "????",
  ISSN =         "0033-7072",
  ISSN-L =       "0033-7072",
  bibdate =      "Fri Nov 25 08:12:46 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "RQ",
  fjournal =     "Reference Quarterly",
}

@Unpublished{Singmaster:1974:RSB,
  author =       "D. Singmaster",
  title =        "Recurrent sequences and {Benford}'s law",
  year =         "1974",
  bibdate =      "Sat Nov 12 16:25:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Preprint submitted to Fibonacci Quarterly in 1974, but
                 never published there.",
  acknowledgement = ack-nhfb,
}

@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 316",
  year =         "1974",
  ISBN =         "0-13-322495-3",
  ISBN-13 =      "978-0-13-322495-5",
  LCCN =         "QA76.8.I12 S771 1974",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "50 1556",
  bibdate =      "Sat May 29 08:01:36 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Prentice-Hall Series in Automatic Computation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Compiling (Electronic computers); Computation by
                 computer systems --- Floating point representation;
                 Floating-point arithmetic; IBM 360 (Computer) ---
                 Programming",
  remark =       "From p. 116: ``There is general agreement that the
                 mantissas of floating-point numbers are not uniformly
                 distributed. [See Hamming (1962)
                 [\cite{Hamming:1962:NMS}], Pinkham (1961)
                 [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
                 Instead, it is customary to assume that they are
                 distributed logarithmically, that is, that the
                 probability density function is

                  $$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
                 \leq m \leq 1. $$

                 This assumption is based on the following observations:
                 First, this distribution reproduces itself under
                 multiplication, but a uniform distribution does not.
                 [See Hamming (1962) [\cite{Hamming:1962:NMS}] and
                 Exercise 20.] A second justification is based on the
                 fact that many of the numbers that arise in computation
                 represent measurable quantities such as lengths,
                 forces, etc., and it is reasonable to believe that the
                 distribution of the mantissas of such quantities is
                 independent of the units in which they are measured.
                 Pinkham (1961) shows that this leads to the conclusion
                 that the distribution of mantissas must be
                 logarithmic.''",
  reviewer =     "F. J. Murray",
  tableofcontents = "Preface / ix \\
                 1. Floating-Point Number Systems / 1 \\
                 1.1 Fixed-Point Calculation / 1 \\
                 1.2 Floating-Decimal Representation of Numbers / 4 \\
                 1.3 Floating-Decimal Arithmetic / 6 \\
                 1.4 Floating-Point Number Systems / 9 \\
                 1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
                 1.6 Laws of Algebra / 14 \\
                 1.7 Inequalities in FP(r,p, c) / 21 \\
                 1.8 FP(r, p, clq) / 22 \\
                 1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
                 1.10 Division / 33 \\
                 Exercises / 35 \\
                 2. Floating-Point Overflow and Underflow / 39 \\
                 2.1 Bounds for Exponents / 39 \\
                 2.2 $\Omega$-Zero Fixup / 41 \\
                 2.3 Interrupt / 44 \\
                 2.4 Messages and Tests / 46 \\
                 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
                 2.6 Example / 50 \\
                 2.7 Counting Mode / 57 \\
                 2.8 Gradual Underflow / 59 \\
                 2.9 Imprecise Interrupt / 61 \\
                 2.10 Changing the Treatment of Spill / 62 \\
                 2.11 Virtual Overflow and Underflow / 64 \\
                 2.12 Division by Zero and Indeterminant Forms / 66 \\
                 Exercises / 67 \\
                 3. Error Analysis / 71 \\
                 3.1 Significant Digits / 71 \\
                 3.2 Relative Error / 73 \\
                 3.3 Relative Error in FP(r,p, clq) / 75 \\
                 3.4 Approximate Laws of Algebra / 80 \\
                 3.5 Propagation of Rounding Error / 87 \\
                 3.6 X**N / 92 \\
                 3.7 Condition / 98 \\
                 3.8 Error Analysis of a Program / 103 \\
                 3.9 Backward Error Analysis / 105 \\
                 3.10 Examples / 107 \\
                 3.11 Changing the Problem / 109 \\
                 3.12 Statistical Error Analysis / 113 \\
                 Exercises / 117 \\
                 4. Example / 123 \\
                 4.1 Quadrature / 123 \\
                 4.2 Power Series / 130 \\
                 4.3 Exact Sums and Differences in FP(r, p, clq) / 137
                 \\
                 4.4 Dismantling Floating-Point Numbers / 143 \\
                 Exercises / 146 \\
                 5. Double-Precision Calculation / 154 \\
                 5.1 Programs Using Double-Precision Arithmetic / 155
                 \\
                 5.2 Implicit Typing of Names / 162 \\
                 5.3 Routines to Perform Double-Precision Arithmetic /
                 163 \\
                 5.4 Double-Precision Multiplication / 165 \\
                 5.5 Double-Precision Addition and Subtraction / 168 \\
                 5.6 Double-Precision Division / 171 \\
                 5.7 Writing Double-Precision Programs Without Language
                 Support / 178 \\
                 5.8 Uses of Double-Precision / 180 \\
                 5.9 Higher-Precision Arithmetic / 185 \\
                 Exercises / 186 \\
                 6. Rounding / 189 \\
                 6.1 General Considerations / 189 \\
                 6.2 Uses of Rounding / 191 \\
                 6.3 Implementation of Rounding / 192 \\
                 6.4 Bias Removal / 194 \\
                 6.5 Other ``Rounding'' Procedures / 197 \\
                 Exercises / 198 \\
                 7. Automatic Analysis of Error / 201 \\
                 7.1 Introduction / 201 \\
                 7.2 Significance Arithmetic / 202 \\
                 7.3 Noisy Mode / 205 \\
                 7.4 Interval Arithmetic / 207 \\
                 7.5 Rerunning the Program in Higher-Precision / 213 \\
                 Exercises / 222 \\
                 8. Radix Conversion / 224 \\
                 8.1 Equivalent Number of Digits / 224 \\
                 8.2 Properties of Conversion Transformations / 228 \\
                 8.3 Conversion Techniques / 232 \\
                 Exercises / 238 \\
                 9/ Carefully Written Programs / 240 \\
                 9.1 Introduction / 240 \\
                 9.2 Average Problem / 240 \\
                 9.3 Quadratic Equation / 246 \\
                 Exercises / 252 \\
                 10. Checking and Testing / 255 \\
                 10.1 Range Checking / 255 \\
                 10.2 Mathematical Checks / 256 \\
                 10.3 Testing / 259 \\
                 Exercises / 261 \\
                 11. Language Features for Floating-Point Computation /
                 263 \\
                 11.1 Introduction / 263 \\
                 11.2 Predictability, Controllability, Observability /
                 264 \\
                 11.3 Ease of Programming / 265 \\
                 11.4 Machine Independence / 267 \\
                 Exercises / 269 \\
                 12. Floating-Point Hardware / 271 \\
                 12.1 Choice of Radix / 271 \\
                 12.2 The Representation of Floating-Point Numbers / 273
                 \\
                 12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
                 12.4 Unnormalized Numbers and Unnormalized Arithmetic /
                 278 \\
                 Exercises / 282 \\
                 13. Complex Numbers / 285 \\
                 13.1 Programs Using Complex Numbers / 285 \\
                 13.2 Relative Error / 286 \\
                 13.3 Complex Arithmetic / 287 \\
                 Exercises / 297 \\
                 Bibliography / 301 \\
                 Glossary of Symbols / 309 \\
                 Index / 311",
}

@Article{Tsao:1974:DSD,
  author =       "Nai Kuan Tsao",
  title =        "On the Distributions of Significant Digits and
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05",
  MRnumber =     "49 6595",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Mon Jan 22 07:26:38 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Generalized logarithmic law is derived for the
                 distribution of the first $t$ significant digits of a
                 random digital integer. This result is then used to
                 determine the distribution of the roundoff errors in
                 floating-point operations, which is a mixture of
                 uniform and reciprocal distributions.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "921",
  corpsource =   "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  journalabr =   "Commun ACM",
  keywords =     "Benford's Law; digital arithmetic; digital integer;
                 distributions; error analysis; floating point
                 operations; Law of Anomalous Numbers; logarithmic law;
                 mathematical techniques; mean value; random;
                 reciprocal; roundoff errors; significant digits;
                 uniform distribution; variance; Zipf's Law",
  oldlabel =     "Tsao74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}

@Article{Voos:1974:BCL,
  author =       "Henry Voos",
  title =        "Brief Communications: {Lotka} and information
                 science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "25",
  number =       "4",
  pages =        "270--272",
  month =        jul,
  year =         "1974",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630250410",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:50 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Voos:1974:LIS,
  author =       "Henry Voos",
  title =        "{Lotka} and Information Science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "25",
  number =       "4",
  pages =        "270--272",
  month =        jul # "\slash " # aug,
  year =         "1974",
  CODEN =        "AISJB6",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:14:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  keywords =     "Lotka's Law",
}

@Article{Yavuz:1974:ZLE,
  author =       "Davras Yavuz",
  title =        "{Zipf}'s law and entropy",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "20",
  number =       "5",
  pages =        "650--650",
  year =         "1974",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/TIT.1974.1055269",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Sat Nov 12 10:43:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0295.94048",
  acknowledgement = ack-nhfb,
  classmath =    "94A15 (General topics of information theory)",
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0322.68068",
  acknowledgement = ack-nhfb,
  classmath =    "68P20 (Information storage and retrieval) 68N01
                 (General)",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =       "1",
  pages =        "138--138",
  month =        "????",
  year =         "1975",
  CODEN =        "SMBCVA",
  ISSN =         "0146-3942",
  ISSN-L =       "0146-3942",
  bibdate =      "Sat Nov 12 16:26:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Abstract no. 75t-47.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin --- Institute of Mathematical Statistics",
  keywords =     "Benford's Law",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://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",
}

@Article{Partridge:1975:DDW,
  author =       "D. Partridge",
  title =        "A dynamic database which automatically removes
                 unwanted generalisation for the efficient analysis of
                 language features that exhibit a disparate frequency
                 distribution",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "1",
  pages =        "43--48",
  month =        feb,
  year =         "1975",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/43.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/44.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/45.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/46.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/47.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/48.tif",
  abstract =     "A self-organising database was developed as part of a
                 general language analysis system. The periodic,
                 automatic reorganisation of the database was aimed at
                 increasing the efficiency of analysis of a language in
                 which the constituent features exhibit a Zipfian type
                 rank-frequency relationship. Such a distribution means
                 that only a small number of features account for a
                 large proportion of the information, while a large
                 number of possible features are seldom encountered and
                 thus seldom accessed within the database. The mechanism
                 described aims at reconciling two conflicting
                 procedures: condensation by generalisation of language
                 features to minimise the total size of the database,
                 and the particularisation of the few commonly occurring
                 features to minimise the average analysis time. Results
                 are presented for the application of this mechanism to
                 the analysis of batches of FORTRAN programs that
                 constituted part of the `normal' workload for computers
                 within five different environments.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6120 (File organisation); C7820 (Humanities
                 computing)",
  classification = "723",
  corpsource =   "Univ. Nairobi, Kenya",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "analysis; data bases; data processing; disparate
                 frequency distribution; dynamic database; file
                 organisation; language; language translation and
                 linguistics; self organising; unwanted generalisation",
  treatment =    "P Practical",
}

@Article{Pope:1975:BLP,
  author =       "Andrew Pope",
  title =        "{Bradford's Law} and the periodical literature of
                 information science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "4",
  pages =        "207--213",
  month =        jul,
  year =         "1975",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630260403",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:54 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Schorr:1975:BCL,
  author =       "Alan Edward Schorr",
  title =        "Brief Communications: {Lotka's Law} and {Map
                 Librarianship}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "3",
  pages =        "189--190",
  month =        may,
  year =         "1975",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630260308",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:53 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Schorr:1975:LLH,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and the History of Legal Medicine",
  journal =      "Research in Librarianship",
  volume =       "30",
  number =       "??",
  pages =        "205--209",
  month =        sep,
  year =         "1975",
  CODEN =        "????",
  ISSN =         "0034-5245",
  ISSN-L =       "0034-5245",
  bibdate =      "Fri Nov 25 08:17:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Res. Librarianship",
}

@Article{Schorr:1975:LLM,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and Map Librarianship",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "3",
  pages =        "189--190",
  month =        may # "\slash " # jun,
  year =         "1975",
  CODEN =        "AISJB6",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:11:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Webb:1975:DFD,
  author =       "William Webb",
  title =        "Distribution of the First Digits of {Fibonacci}
                 Numbers",
  journal =      j-FIB-QUART,
  volume =       "13",
  number =       "4",
  pages =        "334--336",
  month =        dec,
  year =         "1975",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:03 MDT 2011",
  bibsource =    "http://www.fq.math.ca/13-4.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/13-4/webb.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
  keywords =     "Benford's Law",
}

@Article{Woodroofe:1975:ZL,
  author =       "Michael Woodroofe and Bruce Hill",
  title =        "On {Zipf}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "12",
  number =       "3",
  pages =        "425--434",
  month =        sep,
  year =         "1975",
  CODEN =        "JPRBAM",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "62E20 (62P10)",
  MRnumber =     "0440764 (55 \#13634)",
  MRreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3212857",
  ZMnumber =     "Zbl 0343.60012",
  abstract =     "A Zipf's law is a probability distribution on the
                 positive integers which decays algebraically. Such laws
                 describe (approximately) a large class of phenomena. We
                 formulate a model for such phenomena and, in terms of
                 our model, give necessary and sufficient conditions for
                 a Zipf's law to hold.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "classical occupancy problem; laws of large numbers:
                 weak convergence; regularly varying functions",
}

@Article{Worthen:1975:ABL,
  author =       "Dennis B. Worthen",
  title =        "The Application of {Bradford's Law} to Monographs",
  journal =      j-J-DOC,
  volume =       "31",
  number =       "1",
  pages =        "19--25",
  month =        "????",
  year =         "1975",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026590",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:18:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Allison:1976:LLP,
  author =       "Paul D. Allison and Derek de Solla Price and Belver C.
                 Griffith and Michael J. Moravcsik and John A. Stewart",
  title =        "{Lotka's Law}: a Problem in Its Interpretation and
                 Application",
  journal =      j-SOC-STUD-SCI,
  volume =       "6",
  number =       "2",
  pages =        "269--276",
  day =          "1",
  month =        may,
  year =         "1976",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631277600600205",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:29 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631277600600205",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
  keywords =     "Lotka's Law of scientific authorship for the relative
                 contributions of the most prolific authors",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
}

@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 =    "https://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{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 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  bibdate =      "Thu Feb 15 16:29:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory (Series A)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://doi.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;
                 https://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{Haspers:1976:YFB,
  author =       "Jan H. Haspers",
  title =        "The yield formula and {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "27",
  number =       "5",
  pages =        "281--287",
  month =        sep,
  year =         "1976",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630270503",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:57 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Hubert:1976:NIB,
  author =       "John J. Hubert",
  title =        "On the {Naranan} interpretation of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "27",
  number =       "5",
  pages =        "339--341",
  month =        sep,
  year =         "1976",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630270510",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:57 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Orlov:1976:CBP,
  author =       "Ju. K. Orlov",
  title =        "The connection between the {Pareto} distribution and
                 the generalized {Zipf--Mandelbrot} law",
  journal =      "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
  volume =       "83",
  number =       "1",
  pages =        "57--60",
  year =         "1976",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "90A15",
  MRnumber =     "0434355 (55 \#7321)",
  MRreviewer =   "S. Krcevinac",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sakharth. SSR Mech. Akad. Moambe",
}

@Article{Raimi:1976:FDP,
  author =       "Ralph A. Raimi",
  title =        "The first digit problem",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "83",
  number =       "7",
  pages =        "521--538",
  month =        aug # "\slash " # sep,
  year =         "1976",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2319349",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Sat Nov 12 15:49:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2319349",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "This article surveys the literature up to 1976,
                 reports defects in several earlier mathematical
                 `explanations' of Benford's Law, and gives a 52-entry
                 bibliography of prior work. All of those entries are
                 incorporated in this bibliography. It criticizes parts
                 of \cite{Goudsmit:1944:SFN} as `dead wrong' (and the
                 author reiterates that view in \cite{Raimi:1985:FDP}).
                 See also later work \cite{Logan:1978:FDP}. On page 529,
                 Raimi writes ``If the first digits of all the tables in
                 the universe obey some fixed distribution law,
                 Stigler's or Benford's or some other, that law must
                 surely be independent of the system of units chosen,
                 since God is not known to favor either the metric
                 system or the English system. In other words, a
                 universal first digit law, if it exists, must be
                 scale-invariant.''",
  remark-2 =     "This is so far the second earliest reference that I
                 have found to \cite{Newcomb:1881:NFU}; the earliest is
                 \cite{Boring:1920:LNL}, which has only brief mention of
                 the question of digit frequencies. Raimi comments on p.
                 522: ``This assertion, whatever it may mean, will be
                 called Benford's Law because it has been thought by
                 many writers to have originated with the General
                 Electric Company physicist Frank Benford [2]. Certainly
                 Benford popularized the problem, and he may well have
                 been unaware that the polymathic Simon Newcomb,
                 primarily an astronomer but also sometime editor of The
                 American Journal of Mathematics, had also formulated
                 the same law 57 years earlier [1]. There is ample
                 precedent for naming laws and theorems for persons
                 other than their discoverers, else half of analysis
                 would be named after Euler. Besides, even Newcomb
                 implied that the observation giving rise to the Benford
                 law was an old one in his day. One would hate to change
                 the name of the law now only to find later that another
                 change was called for.''",
}

@Article{Rouault:1976:PAE,
  author =       "Alain Rouault",
  title =        "Propri{\'e}t{\'e}s asymptotiques d'un
                 {$n$}-{\'e}chantillon d'une variable al{\'e}atoire
                 d{\'e}nombrable connues sous le nom de lois de {Zipf}.
                 ({French}) [Asymptotic properties of an $n$-sample of a
                 denumerable random variable known under the name of
                 {Zipf}'s law]",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-AB,
  volume =       "283",
  number =       "6",
  pages =        "Aiv, A379--A380",
  year =         "1976",
  CODEN =        "CHASAP",
  ISSN =         "0151-0509",
  ISSN-L =       "0151-0509",
  MRclass =      "62E20",
  MRnumber =     "0423644 (54 \#11619)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Hebdomadaires des S{\'e}ances de
                 l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
  language =     "French",
}

@Article{Rouault:1976:SML,
  author =       "Alain Rouault",
  title =        "Sources markoviennes et lois de {Zipf}. ({French})
                 [{Markovian} source and {Zipf} laws]",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-AB,
  volume =       "283",
  number =       "10",
  pages =        "Aiii, A789--A790",
  year =         "1976",
  CODEN =        "CHASAP",
  ISSN =         "0151-0509",
  ISSN-L =       "0151-0509",
  MRclass =      "62E20",
  MRnumber =     "0423645 (54 \#11620)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Hebdomadaires des S{\'e}ances de
                 l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
  language =     "French",
}

@Article{Vlachy:1976:TFL,
  author =       "Jan Vlach{\'y}",
  title =        "Time Factor in {Lotka's Law}",
  journal =      "Probleme de Informare si Documentare",
  volume =       "10",
  number =       "2",
  pages =        "44--87",
  month =        "????",
  year =         "1976",
  CODEN =        "PIDCA6",
  ISSN =         "0032-924X",
  ISSN-L =       "0032-924X",
  bibdate =      "Fri Nov 25 07:56:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Prob. inf. \& doc.",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@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;
                 https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  keywords =     "Lotka's Law",
}

@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 =          "https://doi.org/10.1214/aop/1176995891",
  ISSN =         "0091-1798 (print), 2168-894X (electronic)",
  ISSN-L =       "0091-1798",
  bibdate =      "Sun Apr 20 10:44:17 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
                 https://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{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 (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 22 08:50:02 2013",
  bibsource =    "https://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",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  keywords =     "Benford's Law; biased coin flips; biased dice throws;
                 roulette wheels",
}

@Article{Hubert:1977:LEL,
  author =       "John J. Hubert",
  title =        "Letters to the {Editor}: {Lotka's Law} in the
                 humanities",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "1",
  pages =        "66--66",
  month =        jan,
  year =         "1977",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630280115",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Krisciunas:1977:LEL,
  author =       "Kevin Krisciunas",
  title =        "Letters to the {Editor}: {Lotka's Law} --- year by
                 year",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "1",
  pages =        "65--66",
  month =        jan,
  year =         "1977",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630280114",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Kubovy:1977:RAA,
  author =       "M. Kubovy",
  title =        "Response Availability and the Apparent Spontaneity of
                 Numerical Choices",
  journal =      "Journal of Experimental Psychology: Human Performance
                 and Performance",
  volume =       "3",
  number =       "2",
  pages =        "359--364",
  month =        may,
  year =         "1977",
  DOI =          "https://doi.org/10.1037/0096-1523.3.2.359",
  ISSN =         "0096-1523 (print), 1939-1277 (electronic)",
  ISSN-L =       "0096-1523",
  bibdate =      "Sat Sep 10 12:51:40 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://psycnet.apa.org/index.cfm?fa=search.displayrecord&uid=1977-30946-001",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Ylvisaker:1977:TR,
  author =       "Donald Ylvisaker",
  title =        "Test Resistance",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "72",
  number =       "359",
  pages =        "551--556",
  month =        sep,
  year =         "1977",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:48 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314242;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2286216",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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/",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@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 =    "https://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{Drott:1978:EEB,
  author =       "M. Carl Drott and Belver C. Griffith",
  title =        "An empirical examination of {Bradford's Law} and the
                 scattering of scientific literature",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "5",
  pages =        "238--246",
  month =        sep,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290506",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:02 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@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 =          "https://doi.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/;
                 https://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",
}

@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 =    "https://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{Hubert:1978:BCR,
  author =       "John J. Hubert",
  title =        "Brief Communications: A relationship between two forms
                 of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "3",
  pages =        "159--161",
  month =        may,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290311",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:01 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "23 Mar 2007",
}

@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 (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 30 11:20:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.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",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  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{Praunlich:1978:BDN,
  author =       "Peter Praunlich and Michael Kroll",
  title =        "{Bradford}'s distribution: a new formulation",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "2",
  pages =        "51--55",
  month =        mar,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290203",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:01 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Rouault:1978:LZS,
  author =       "Alain Rouault",
  title =        "Lois de {Zipf} et sources markoviennes. ({French})
                 [{Zipf}'s law and {Markovian} sources]",
  journal =      "Ann. Inst. H. Poincar{\'e} Sect. B (N.S.)",
  volume =       "14",
  number =       "2",
  pages =        "169--188",
  year =         "1978",
  CODEN =        "AHPBAR",
  ISSN =         "0020-2347",
  ISSN-L =       "0020-2347",
  MRclass =      "62E99 (60J20 62P99)",
  MRnumber =     "507732 (80c:62026a)",
  MRreviewer =   "Bruce M. Hill",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales de l'Institut Henri Poincar{\'e}. Section B.
                 Calcul des Probabilit{\'e}s et Statistique. Nouvelle
                 S{\'e}rie",
  language =     "French",
}

@Article{Samson:1978:STU,
  author =       "W. B. Samson and R. H. Davis",
  title =        "Search Times Using Hash Tables for Records with
                 Non-Unique Keys",
  journal =      j-COMP-J,
  volume =       "21",
  number =       "3",
  pages =        "210--214",
  month =        aug,
  year =         "1978",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/210.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/211.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/212.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/213.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/214.tif",
  abstract =     "Recent research in hash coding has concentrated on
                 unique keys, or uniform distributions of keys. This
                 paper is intended to clarify the effect of non-unique
                 keys with various distributions on search times in the
                 hash table thus enabling recommendations to be made to
                 those who must deal with hash tables of this type. It
                 is found that extreme rank-order frequency distribution
                 of keys, such as the Zipf distribution, result in much
                 higher access times than more uniform distributions,
                 but it is possible to reduce these to some extent by
                 loading records with common keys on to the hash table
                 first.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6120 (File organisation); C6130 (Data handling
                 techniques)",
  classification = "723",
  corpsource =   "Dept. of Math. and Computer Studies, Dundee Coll. of
                 Technol., Dundee, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  journalabr =   "Comput J",
  keywords =     "common keys; compiler symbol; computer programming;
                 data handling; data processing --- Data Structures;
                 direct access files; distribution; extreme; file
                 organisation; hash tables; higher access times; non
                 unique keys; overflow method; rank order frequency
                 distribution of keys; records; search times;
                 simulation; tables; uniform distributions; Zipf",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brookes:1979:LEB,
  author =       "B. C. Brookes",
  title =        "Letters to the {Editor}: The {Bradford Law}: a new
                 calculus for the social sciences?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "4",
  pages =        "233--234",
  month =        jul,
  year =         "1979",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630300412",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:05 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@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 =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://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.''",
}

@Article{Marulli:1979:BCB,
  author =       "Luciana Marulli and Michael E. D. Koenig",
  title =        "Brief Communications: {Bradford} distribution of data
                 elements",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "2",
  pages =        "107--108",
  month =        mar,
  year =         "1979",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630300209",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:04 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@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 =          "https://doi.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/;
                 https://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{Radhakrishnan:1979:LLC,
  author =       "T. Radhakrishnan and R. Kernizan",
  title =        "{Lotka's Law} and Computer Science Literature",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "1",
  pages =        "51--54",
  month =        jan,
  year =         "1979",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630300109",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 07:45:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "6 September 2007",
  remark =       "This paper analyzes publication statistics from
                 Communications of the Association for Computing
                 Machinery (CACM) and in the Journal of the ACM
                 (JACM).",
}

@Article{Vlachy:1979:FDS,
  author =       "Jan Vlach{\'y}",
  title =        "Frequency Distribution of Scientific Performance: a
                 Bibliography of {Lotka's Law} and Related Phenomena",
  journal =      j-SCIENTOMETRICS,
  volume =       "1",
  number =       "1",
  pages =        "107--130",
  month =        sep,
  year =         "1979",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02016844",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Fri Nov 25 07:59:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02016844;
                 http://www.springerlink.com/content/0138-9130/",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
  xxjournal =    "Scientometrics, Bibliography Section",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://jis.sagepub.com/",
  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 =          "https://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 =    "https://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",
  journal-URL =  "http://jis.sagepub.com/",
  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 =          "https://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 =    "https://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",
  journal-URL =  "http://jis.sagepub.com/",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@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 =    "https://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",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
}

@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 =          "https://doi.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/;
                 https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "https://doi.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/;
                 https://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{Asai:1981:GFB,
  author =       "Isao Asai",
  title =        "A general formulation of {Bradford}'s distribution:
                 the graph-oriented approach",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "32",
  number =       "2",
  pages =        "113--119",
  month =        mar,
  year =         "1981",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630320206",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:10 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://jis.sagepub.com/",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@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 =    "https://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",
}

@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",
  year =         "1981",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610918108812195",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 30 06:32:15 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law",
  onlinedate =   "27 Jun 2007",
}

@Article{Morse:1981:IEB,
  author =       "Philip M. Morse",
  title =        "Implications of the exact {Bradford} distribution",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "32",
  number =       "1",
  pages =        "43--50",
  month =        jan,
  year =         "1981",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630320106",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:10 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Pavlov:1981:DFF,
  author =       "A. I. Pavlov",
  title =        "On the distribution of fractions and {F. Benford}'s
                 law",
  journal =      j-IZV-AKAD-NAUK-SSSR-MAT,
  volume =       "45",
  number =       "4",
  pages =        "760--774, 927",
  year =         "1981",
  CODEN =        "IZAMAT",
  ISSN =         "0373-2436",
  ISSN-L =       "0373-2436",
  MRclass =      "10K10",
  MRnumber =     "631437 (83m:10093)",
  MRreviewer =   "Michael Keane",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia
                 (Moscow)",
  xxtitle =      "On the distribution mod one and {Benford}'s law",
}

@Article{Peters:1981:EFB,
  author =       "James V. Peters",
  title =        "An Equivalent Form of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "1",
  pages =        "74--76",
  month =        feb,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "60C05 (10K10 60-01)",
  MRnumber =     "606117 (82k:60024)",
  MRreviewer =   "L. E. Clarke",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/19-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-1/peters.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{Peters:1981:SCC,
  author =       "James V. Peters",
  title =        "Short Communications: a combinatoric proof of
                 {Benford}'s law",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "23",
  number =       "1",
  pages =        "122--123",
  year =         "1981",
  CODEN =        "AEMABN",
  DOI =          "https://doi.org/10.1007/BF02188018",
  ISSN =         "0001-9054 (print), 1420-8903 (electronic)",
  ISSN-L =       "0001-9054",
  MRclass =      "Contributed Item",
  MRnumber =     "1553878",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/BF02188018",
  acknowledgement = ack-nhfb,
  fjournal =     "Aequationes Mathematicae",
  journal-URL =  "http://link.springer.com/journal/10",
}

@Article{Potter:1981:LLR,
  author =       "William Gray Potter",
  title =        "{Lotka's Law} revisited",
  journal =      j-LIBR-TRENDS,
  volume =       "31",
  number =       "2",
  pages =        "21--39",
  month =        "Summer",
  year =         "1981",
  CODEN =        "LIBTA3",
  ISSN =         "0024-2594 (print), 1559-0682 (electronic)",
  ISSN-L =       "0024-2594",
  bibdate =      "Thu Nov 24 14:41:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.9842",
  acknowledgement = ack-nhfb,
  fjournal =     "Library Trends",
}

@Article{Preece:1981:DFD,
  author =       "D. A. Preece",
  title =        "Distributions of Final Digits in Data",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "30",
  number =       "1",
  pages =        "31--60",
  month =        mar,
  year =         "1981",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Wed Nov 23 12:19:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2987702",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
  remark =       "This paper extends previous work \cite{Yule:1927:RS}
                 on human bias in the recording of last digits in
                 measurements, or from roundings, or from later scale
                 conversions, and how such bias can be detected.",
}

@Article{Schatte:1981:RVL,
  author =       "Peter Schatte",
  title =        "On random variables with logarithmic mantissa
                 distribution relative to several bases",
  journal =      j-ELEK-INFO-KYBER,
  volume =       "17",
  number =       "??",
  pages =        "293--295",
  month =        "????",
  year =         "1981",
  CODEN =        "EIVKAX",
  ISSN =         "0013-5712",
  ISSN-L =       "0013-5712",
  bibdate =      "Sat Nov 12 15:53:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elektronische Informationsverarbeitung und Kybernetik
                 (EIK)",
}

@Article{Washington:1981:BLF,
  author =       "Lawrence C. Washington",
  title =        "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "2",
  pages =        "175--177",
  month =        apr,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "10A30 (10A35)",
  MRnumber =     "614056 (82f:10009)",
  MRreviewer =   "S. P. Mohanty",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/19-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-2/washington.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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Fedorowicz:1982:ZMA,
  author =       "Jane Fedorowicz",
  title =        "A {Zipfian} Model of an Automatic Bibliographic
                 System: An Application to {MEDLINE}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "33",
  number =       "4",
  pages =        "223--232",
  month =        jul,
  year =         "1982",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630330406",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:14 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "6 Sep 2007",
}

@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 =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://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{MacRoberts:1982:REL,
  author =       "Michael H. MacRoberts and Barbara R. MacRoberts",
  title =        "A Re-evaluation of {Lotka}'s {Law of Scientific
                 Productivity}",
  journal =      j-SOC-STUD-SCI,
  volume =       "12",
  number =       "3",
  pages =        "443--450",
  day =          "1",
  month =        aug,
  year =         "1982",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631282012003005",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:38 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631282012003005",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
  keywords =     "Lotka's Law of scientific authorship for the relative
                 contributions of the most prolific authors",
}

@Article{Pavlov:1982:DFP,
  author =       "A. I. Pavlov",
  title =        "On the Distribution of Fractional Parts and {Benford's
                 Law}",
  journal =      j-MATH-USSR-IZV,
  volume =       "19",
  number =       "1",
  pages =        "65--77",
  month =        "????",
  year =         "1982",
  CODEN =        "MUSIAE",
  DOI =          "https://doi.org/10.1070/IM1982v019n01ABEH001411",
  ISSN =         "0025-5726 (print), 2169-5075 (electronic)",
  ISSN-L =       "0025-5726",
  bibdate =      "Sun Nov 13 10:46:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://stacks.iop.org/0025-5726/19/i=1/a=A05",
  abstract =     "This article investigates the distribution of the
                 first digits (from the left) in the $q$-nary expansions
                 of numerical sequences and functions ($q$ an integer $
                 \geq 2 $ )",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of the {USSR} --- Izvestiya",
  journal-URL =  "http://iopscience.iop.org/0025-5726",
}

@PhdThesis{Perline:1982:EVM,
  author =       "Richard K. Perline",
  title =        "An extreme value model of weakly harmonic
                 ({Pareto--Zipf} type) laws",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Behavioral Sciences, The University of
                 Chicago",
  address =      "Chicago, IL, USA",
  pages =        "129",
  month =        dec,
  year =         "1982",
  MRnumber =     "2611828",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/docview/251796701",
  acknowledgement = ack-nhfb,
  remark =       "Available from ProQuest LLC, Ann Arbor, MI, USA.",
}

@Article{Regazzini:1982:BFL,
  author =       "Eugenio Regazzini",
  title =        "The {Benford--Furlan} law as a statistical law",
  journal =      j-STATISTICA-BOLOGNA,
  volume =       "42",
  number =       "3",
  pages =        "351--370",
  year =         "1982",
  CODEN =        "STATDJ",
  ISSN =         "0390-590X (print), 1973-2201 (electronic)",
  ISSN-L =       "0390-590X",
  MRclass =      "62E99 (10K05 62A15)",
  MRnumber =     "695467 (84h:62032)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistica (Bologna)",
}

@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The distribution of leading significant digits",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "407--412",
  month =        oct,
  year =         "1982",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/2.4.407",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G99 (60E05)",
  MRnumber =     "84f:65038",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  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; Zipf's Law",
}

@Book{Weaver:1982:LLT,
  author =       "Warren Weaver",
  title =        "{Lady Luck}: the theory of probability",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "392",
  year =         "1982",
  ISBN =         "0-486-24342-7",
  ISBN-13 =      "978-0-486-24342-9",
  LCCN =         "QA273 .W4 1982",
  bibdate =      "Mon Nov 14 11:35:17 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover031/82007396.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1978",
  remark =       "Reprint of \cite{Weaver:1963:LLT}.",
  subject =      "Probabilities",
}

@Article{White:1982:FSS,
  author =       "Warren H. White",
  title =        "On the form of steady-state solutions to the
                 coagulation equations",
  journal =      j-J-COLLOID-INTERFACE-SCI,
  volume =       "87",
  number =       "1",
  pages =        "204--208",
  month =        may,
  year =         "1982",
  CODEN =        "JCISA5",
  DOI =          "https://doi.org/10.1016/0021-9797(82)90382-4",
  ISSN =         "0021-9797 (print), 1095-7103 (electronic)",
  ISSN-L =       "0021-9797",
  bibdate =      "Thu Feb 28 10:46:13 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021979782903824",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Colloid and Interface Science",
  keywords =     "power law; scale invariance; Zipf's law",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://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{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 =          "https://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 =    "https://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",
}

@Article{Orlov:1983:SSZ,
  author =       "Yu. K. Orlov and R. Ya. Chitashvili",
  title =        "The statistical significance of {Zipf}'s
                 distribution",
  journal =      "Soobshch. Akad. Nauk Gruzin. SSR",
  volume =       "109",
  number =       "3",
  pages =        "505--508",
  year =         "1983",
  CODEN =        "????",
  ISSN =         "0132-1447",
  ISSN-L =       "0132-1447",
  MRclass =      "62E99 (62P99)",
  MRnumber =     "723296",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR",
}

@Article{Schatte:1983:AUD,
  author =       "Peter Schatte",
  title =        "On the asymptotic uniform distribution of sums reduced
                 $ \bmod 1 $",
  journal =      j-MATH-NACHR,
  volume =       "115",
  number =       "1",
  pages =        "257--281",
  month =        "????",
  year =         "1983",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19841150121",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sat Feb 16 19:12:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Schatte:1983:SUD,
  author =       "Peter Schatte",
  title =        "On {$ H_\infty $}-summability and the uniform
                 distribution of sequences",
  journal =      j-MATH-NACHR,
  volume =       "113",
  number =       "1",
  pages =        "237--243",
  month =        "????",
  year =         "1983",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19831130122",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sat Feb 16 19:13:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19831130122/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Whittaker:1983:SID,
  author =       "James V. Whittaker",
  title =        "On Scale-Invariant Distributions",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "43",
  number =       "2",
  pages =        "257--267",
  month =        apr,
  year =         "1983",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "60E05 (10K10 62E10)",
  MRnumber =     "84h:60035",
  MRreviewer =   "K. C. Chanda",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of British Columbia, Dep of Mathematics,
                 Vancouver, BC, Can",
  classification = "922",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabr =   "SIAM J Appl Math",
  keywords =     "probability",
}

@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 =    "https://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",
}

@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 =    "https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@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 =          "https://doi.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/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
}

@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;
                 https://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{Friedberg:1984:DFD,
  author =       "Stephen H. Friedberg",
  title =        "The Distribution of First Digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "15",
  number =       "2",
  pages =        "120--125",
  month =        mar,
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1984.11972760",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:49:53 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.jstor.org/stable/2686516;
                 http://www.tandfonline.com/doi/abs/10.1080/00494925.1984.11972760",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  keywords =     "Benford's Law",
  onlinedate =   "30 Jan 2018",
}

@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",
  bibdate =      "Wed Aug 12 10:09:50 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0557.60011",
  acknowledgement = ack-nhfb,
  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{Karmeshu:1984:RBL,
  author =       "Karmeshu and N. C. Lind and V. Cano",
  title =        "Rationales for {Bradford's Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "6",
  number =       "4",
  pages =        "233--241",
  month =        jul,
  year =         "1984",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02279358",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:02:53 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02279358",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
  journal-URL =  "http://ptp.oxfordjournals.org/content/by/year",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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/",
}

@Article{Nagasaka:1984:BL,
  author =       "Kenji Nagasaka",
  title =        "On {Benford}'s law",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "36",
  number =       "1",
  pages =        "337--352",
  month =        "????",
  year =         "1984",
  CODEN =        "AISXAD",
  DOI =          "https://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 Jan 31 18:19:56 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02481974",
  acknowledgement = ack-nhfb,
  ajournal =     "Ann. Inst. Statist. Math.",
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
  journal-URL =  "http://link.springer.com/journal/10463",
}

@Article{Schatte:1984:AUD,
  author =       "Peter Schatte",
  title =        "On the asymptotic uniform distribution of sums reduced
                 $ \bmod 1 $",
  journal =      j-MATH-NACHR,
  volume =       "115",
  number =       "1",
  pages =        "275--281",
  month =        "????",
  year =         "1984",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19841150121",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sat Nov 12 15:54:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Turner:1984:FRD,
  author =       "Peter R. Turner",
  title =        "Further revelations on l.s.d",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "4",
  number =       "2",
  pages =        "225--231",
  month =        apr,
  year =         "1984",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/4.2.225",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G10 (11K99)",
  MRnumber =     "85m:65039",
  MRreviewer =   "Calvin T. Long",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  abstract =     "In a recent paper the author showed that the
                 distribution of leading significant digits, l.s.d.,
                 resulting from successive multiplications is
                 logarithmic. In this paper these results are extended
                 by establishing, still without any assumptions of
                 invariance to scaling, that this distribution remains
                 invariant under all further arithmetic operations ---
                 both multiplicative and additive. The fact that 30\% of
                 decimal numbers have l.s.d. 1 persists.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "l. s. d. (leading significant digits)",
}

@Article{Yuan:1984:LOC,
  author =       "Y. Yuan",
  title =        "On the least {$Q$}-order of convergence of variable
                 metric algorithms",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "4",
  number =       "2",
  pages =        "233--239",
  month =        apr,
  year =         "1984",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65K05",
  MRnumber =     "85h:65133",
  MRreviewer =   "A. I. \c Schiop",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
}

@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 =    "https://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",
  journal-URL =  "http://jis.sagepub.com/",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
  keywords =     "Bradford's Law",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "Benford's Law",
}

@Article{Pao:1985:LLT,
  author =       "Miranda Lee Pao",
  title =        "{Lotka}'s law: a testing procedure",
  journal =      j-INFO-PROC-MAN,
  volume =       "21",
  number =       "4",
  pages =        "305--320",
  month =        "????",
  year =         "1985",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/0306-4573(85)90055-X",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Fri Nov 25 08:41:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
}

@Article{Raimi:1985:FDP,
  author =       "Ralph A. Raimi",
  title =        "The First Digit Phenomenon Again",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "129",
  number =       "2",
  pages =        "211--219",
  month =        jun,
  year =         "1985",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Sat Nov 12 16:56:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains strong criticism of a derivation
                 of Benford's Law \cite{Logan:1978:FDP}.",
  URL =          "http://www.jstor.org/stable/986989",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "This paper contains mathematical derivations of both
                 Stigler's Law and Benford's Law. Raimi comments on p.
                 217: ``the Benford law itself as a conclusion to be
                 derived is by no means as firm as Kepler's planetary
                 curves. Indeed, it has been pointed out by Diaconis and
                 Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
                 statistical analysis of Benford's announced data gives
                 a high probability to the conjecture that he did a bit
                 of rounding-off here and there, always in the direction
                 of his law. The license that a physicist often takes on
                 the path from his hypotheses to verified, observable,
                 and repeatable conclusion is not justified here.''.",
}

@Article{Tichy:1985:UDD,
  author =       "Robert F. Tichy",
  title =        "Uniform distribution and diophantine inequalities",
  journal =      j-MONAT-MATH,
  volume =       "99",
  number =       "2",
  pages =        "147--152",
  month =        jun,
  year =         "1985",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01304194",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  bibdate =      "Sun Feb 17 06:26:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01304194",
  ZMnumber =     "0538.10039",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
  keywords =     "diophantine inequalities; discrepancy; Uniformly
                 distributed sequences",
  ZMclass =      "11K06 (General theory of distribution modulo 1); 11D75
                 (Diophantine inequalities)",
}

@Article{Tuldava:1985:FST,
  author =       "Yu. A. Tuldava",
  title =        "The frequency structure of a text and {Zipf}'s law",
  journal =      "Tartu Riikl. {\"U}l. Toimetised",
  volume =       "??",
  number =       "711",
  pages =        "93--116",
  year =         "1985",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "92A25 (94A15)",
  MRnumber =     "836129 (87c:92063)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://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{Uppuluri:1985:DFD,
  author =       "V. R. R. Uppuluri and S. A. Patil",
  title =        "The distribution of the first $j$ digits of beta
                 related random variables",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "14",
  number =       "2",
  pages =        "467--472",
  year =         "1985",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610918508812450",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 30 06:32:23 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law",
}

@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 =          "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Chen:1986:RRB,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "Research: 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",
  month =        sep,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Egghe:1986:RDB,
  author =       "L. Egghe",
  title =        "Research: The dual of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "4",
  pages =        "246--255",
  month =        jul,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198607)37:4<246::AID-ASI10>3.0.CO%3B2-D",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@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 =    "https://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",
}

@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 =    "https://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",
}

@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 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Sat Feb 16 17:57:52 2013",
  bibsource =    "https://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{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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ajp.aapt.org/",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
  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}.",
}

@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 =    "https://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{MacRoberts:1986:QMC,
  author =       "Michael H. MacRoberts and Barbara R. MacRoberts",
  title =        "Quantitative Measures of Communication in Science: a
                 Study of the Formal Level",
  journal =      j-SOC-STUD-SCI,
  volume =       "16",
  number =       "1",
  pages =        "151--172",
  day =          "1",
  month =        feb,
  year =         "1986",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631286016001008",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:44 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "See \cite{Stigler:1987:PMF} and reply
                 \cite{MacRoberts:1987:MFU}.",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631286016001008",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@Article{Pao:1986:EEL,
  author =       "Miranda Lee Pao",
  title =        "An empirical examination of {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "1",
  pages =        "26--33",
  month =        jan,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630370105",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:25 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "24 May 2007",
}

@Article{Pao:1986:REE,
  author =       "Miranda Lee Pao",
  title =        "Research: An empirical examination of {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "1",
  pages =        "26--33",
  month =        jan,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198601)37:1<26::AID-ASI4>3.0.CO%3B2-Z",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:25 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Patil:1986:DFD,
  author =       "S. A. Patil and V. R. R. Uppuluri",
  title =        "The Distribution of First $j$ Digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "17",
  number =       "3",
  pages =        "240--243",
  month =        may,
  year =         "1986",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1986.11972963",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:20 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.jstor.org/stable/2686982;
                 http://www.tandfonline.com/doi/abs/10.1080/07468342.1986.11972963",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  keywords =     "Benford's Law",
  onlinedate =   "30 Jan 2018",
}

@Article{Pontigo:1986:QAB,
  author =       "J. Pontigo and F. W. Lancaster",
  title =        "Qualitative aspects of the {Bradford} distribution",
  journal =      j-SCIENTOMETRICS,
  volume =       "9",
  number =       "1--2",
  pages =        "59--70",
  month =        jan,
  year =         "1986",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02016608",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:02:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02016608",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Schatte:1986:ALD,
  author =       "Peter Schatte",
  title =        "On the asymptotic logarithmic distribution of the
                 floating-point mantissas of sums",
  journal =      j-MATH-NACHR,
  volume =       "127",
  number =       "1",
  pages =        "7--20",
  month =        "????",
  year =         "1986",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19861270102",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sun Feb 17 06:04:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19861270102/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Tichy:1986:GZU,
  author =       "Robert F. Tichy",
  title =        "{Gleichverteilung und zahlentheoretische Ungleichungen
                 II}. ({German}) [{Uniform} distribution and
                 number-theoretic inequalities {II}]",
  journal =      "Anzeiger der {\"O}sterreichischen Akademie der
                 Wissenschaften. Mathematisch-Naturwissenschaftliche
                 Klasse",
  volume =       "122(1985)",
  number =       "??",
  pages =        "95--99",
  month =        "????",
  year =         "1986",
  CODEN =        "OSAWA8",
  DOI =          "????",
  ISSN =         "0065-535X",
  ISSN-L =       "0065-535X",
  bibdate =      "Sun Feb 17 06:24:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
  ajournal =     "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
  classmath =    "11K06 (General theory of distribution modulo 1); 11J25
                 (Diophantine inequalities)",
  keywords =     "diophantine inequalities; discrepancy; H infinity;
                 logarithmic mean; summation method; uniform
                 distribution",
  language =     "German",
  xxnote =       "Despite repeated searches, I have not found this
                 journal online, not even from links at the Austrian
                 Academy of Sciences, \path=http://www.oeaw.ac.at=.",
}

@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 =          "https://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 =    "https://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",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "index approach; Mandelbrot-Zipf law; Zipf's law",
}

@Article{Chen:1987:BLI,
  author =       "Ye-Sho Chen and F. F. Leimkuhler",
  title =        "{Bradford's Law}: An index approach",
  journal =      j-SCIENTOMETRICS,
  volume =       "11",
  number =       "3--4",
  pages =        "183--198",
  month =        mar,
  year =         "1987",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02016591",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:03 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02016591",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@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/;
                 https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html;
                 http://www.tandfonline.com/loi/utch20",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{MacRoberts:1987:MFU,
  author =       "Michael H. MacRoberts and Barbara R. MacRoberts",
  title =        "Measurement in the Face of Universal Uncertainty: a
                 Reply to {Stigler}",
  journal =      j-SOC-STUD-SCI,
  volume =       "17",
  number =       "2",
  pages =        "334--336",
  day =          "1",
  month =        may,
  year =         "1987",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631287017002008",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:46 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "See \cite{MacRoberts:1986:QMC}.",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002008",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tsukuba Journal of Mathematics",
}

@Article{Nicholls:1987:BCE,
  author =       "Paul Travis Nicholls",
  title =        "Brief Communications: Estimation of {Zipf}
                 parameters",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "38",
  number =       "6",
  pages =        "443--445",
  month =        nov,
  year =         "1987",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:31 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "24 May 2007",
}

@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 =          "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Sanders:1987:PPUa,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Consumer Marketing",
  volume =       "4",
  number =       "1",
  pages =        "47--50",
  month =        "????",
  year =         "1987",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/eb008188",
  ISSN =         "0736-3761",
  ISSN-L =       "0736-3761",
  bibdate =      "Fri Nov 25 06:56:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sanders:1987:PPUb,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Services Marketing",
  volume =       "1",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1987",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/eb024706",
  ISSN =         "0887-6045",
  ISSN-L =       "0887-6045",
  bibdate =      "Fri Nov 25 06:56:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1987:ABM,
  author =       "Peter Schatte",
  title =        "On the asymptotic behaviour of the mantissa
                 distribution of sums",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "23",
  number =       "??",
  pages =        "353--360",
  month =        "????",
  year =         "1987",
  CODEN =        "JICYE5",
  ISSN =         "0863-0593",
  ISSN-L =       "0863-0593",
  bibdate =      "Sat Nov 12 15:58:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Inform. Process. Cybern. EIK",
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
}

@Article{Schatte:1987:SEU,
  author =       "Peter Schatte",
  title =        "Some estimates of the {$ \mathcal {H}_\infty
                 $}-uniform distribution",
  journal =      j-MONAT-MATH,
  volume =       "103",
  number =       "3",
  pages =        "233--249",
  month =        sep,
  year =         "1987",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01364342",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  bibdate =      "Sat Nov 12 15:57:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01364342",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
}

@Article{Stigler:1987:PMF,
  author =       "Stephen M. Stigler",
  title =        "Precise Measurement in the Face of Error: a Comment on
                 {MacRoberts} and {MacRoberts}",
  journal =      j-SOC-STUD-SCI,
  volume =       "17",
  number =       "2",
  pages =        "332--334",
  day =          "1",
  month =        may,
  year =         "1987",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631287017002007",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:46 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "See \cite{MacRoberts:1986:QMC} and reply
                 \cite{MacRoberts:1987:MFU}.",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002007",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@Article{Tague:1987:MVZ,
  author =       "Jean Tague and Paul Nicholls",
  title =        "The maximal value of a {Zipf} size variable: Sampling
                 properties and relationship to other parameters",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "155--170",
  day =          "7",
  month =        jun,
  year =         "1987",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/0306-4573(87)90001-X",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/030645738790001X",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "Zipf's Law",
}

@Article{Tichy:1987:GS,
  author =       "Robert F. Tichy",
  title =        "{Gleichverteilung zum Summierungsverfahren {$ H_\infty
                 $}}. ({German}) [{Uniform} distribution to the {$
                 H_\infty $} summation method]",
  journal =      j-MATH-NACHR,
  volume =       "131",
  number =       "??",
  pages =        "119--125",
  month =        "????",
  year =         "1987",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19871310112",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Mon Feb 18 06:44:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  ZMnumber =     "0626.10044",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  keywords =     "$H_\infty$-discrepancy; difference sequences; real
                 sequences; uniform distribution",
  language =     "German",
  ZMclass =      "11K06 (General theory of distribution modulo 1); 40J05
                 (Summability in abstract structures)",
  ZMreviewer =   "D. Leitmann",
}

@Article{Turner:1987:DDI,
  author =       "Peter R. Turner",
  title =        "The Distribution of l.s.d. and Its Implications for
                 Computer Design",
  journal =      j-MATH-GAZ,
  volume =       "71",
  number =       "455",
  pages =        "26--31",
  month =        mar,
  year =         "1987",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3616283",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue Oct 30 23:36:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "[l.s.d. = least significant digits]. The topic is
                 variously known as Benford's Law, the Law of Anomalous
                 Numbers, and Zipf's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@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 =    "https://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{Carslaw:1988:AIN,
  author =       "C. A. Carslaw",
  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 Sep 10 11:00:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/248109",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  journal-URL =  "https://www.jstor.org/journal/accountingreview",
  keywords =     "Benford's Law; New Zealand firms; second-digit
                 frequency",
  remark-1 =     "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.",
  remark-2 =     "According to \cite{Kossovsky:2015:BLT}, this may be
                 the first published serious use of Benford's Law for
                 fraud detection in accounting, although the possibility
                 had been mentioned 16 years earlier
                 \cite{Varian:1972:LEB}, and that earlier paper is not
                 cited in this 1988 paper.",
}

@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 =          "https://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 =    "https://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",
}

@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 =          "https://doi.org/10.1007/BFb0078471",
  MRclass =      "11K06 (60E99)",
  MRnumber =     "935987 (89d:11059)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Math.",
  acknowledgement = ack-nhfb,
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Prather:1988:CET,
  author =       "R. E. Prather",
  title =        "Comparison and Extension of Theories of {Zipf} and
                 {Halstead}",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "3",
  pages =        "248--252",
  month =        jun,
  year =         "1988",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  affiliation =  "Trinity Univ, San Antonio, TX, USA",
  affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
  classcodes =   "C6110B (Software engineering techniques)",
  classification = "723",
  corpsource =   "Comput. and Inf. Sci., Trinity Univ., San Antonio, TX,
                 USA",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "behavioural psychology; computer programming; computer
                 software; empirical law; Halstead metrics; Halstead's
                 hypothesis; length estimates; Measurements;
                 probabilistic hypothesis; process; programming;
                 software engineering; software metrication; software
                 science; Zipf metrics; Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sanders:1988:PPU,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Business \& Industrial Marketing",
  volume =       "3",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/eb006057",
  ISSN =         "0885-8624",
  ISSN-L =       "0885-8624",
  bibdate =      "Fri Nov 25 07:04:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1988:ASC,
  author =       "Peter Schatte",
  title =        "On the Almost Sure Convergence of Floating-Point
                 Mantissas and {Benford's Law}",
  journal =      j-MATH-NACHR,
  volume =       "135",
  number =       "1",
  pages =        "79--83",
  month =        "????",
  year =         "1988",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19881350108",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  MRclass =      "60F15 (11K31)",
  MRnumber =     "944219 (89g:60114)",
  MRreviewer =   "S. A. Book",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  onlinedate =   "12 Nov 2006",
  reviewer =     "S. A. Book",
}

@Article{Schatte:1988:LIL,
  author =       "Peter Schatte",
  title =        "On a law of the iterated logarithm for sums {$ \bmod 1
                 $} with application to {Benford}'s law",
  journal =      j-PROBAB-THEORY-RELAT-FIELDS,
  volume =       "77",
  number =       "2",
  pages =        "167--178",
  month =        feb,
  year =         "1988",
  CODEN =        "PTRFEU",
  DOI =          "https://doi.org/10.1007/BF00334035",
  ISSN =         "0178-8051 (print), 1432-2064 (electronic)",
  ISSN-L =       "0178-8051",
  MRclass =      "60F15 (11K31)",
  MRnumber =     "927235 (89b:60081)",
  MRreviewer =   "L. Kuipers",
  bibdate =      "Sun Apr 27 11:18:06 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/probab-theory-relat-fields.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00334035",
  acknowledgement = ack-nhfb,
  fjournal =     "Probability Theory and Related Fields",
  journal-URL =  "http://link.springer.com/journal/440",
}

@Article{Schatte:1988:MDC,
  author =       "Peter Schatte",
  title =        "On Mantissa Distribution in Computing and {Benford's
                 Law}",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "24",
  number =       "9",
  pages =        "443--455",
  month =        "????",
  year =         "1988",
  CODEN =        "JICYE5",
  ISSN =         "0863-0593",
  ISSN-L =       "0863-0593",
  MRclass =      "60E05 (11K06 11K31 65G99)",
  MRnumber =     "984516 (90g:60016)",
  MRreviewer =   "F. Schweiger",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/eik/eik24.html#Schatte88",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  dblp-key =     "journals/eik/Schatte88",
  dblp-mdate =   "2020-03-06",
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Schatte:1988:UDC,
  author =       "Peter Schatte",
  title =        "On the uniform distribution of certain sequences and
                 {Benford}'s law",
  journal =      j-MATH-NACHR,
  volume =       "136",
  number =       "1",
  pages =        "271--273",
  year =         "1988",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19881360119",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  MRclass =      "11K06 (11K31)",
  MRnumber =     "952478 (89j:11075)",
  MRreviewer =   "O. P. Stackelberg",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  onlinedate =   "11 Nov 2006",
}

@Article{Tichy:1988:SRC,
  author =       "Robert F. Tichy",
  title =        "{Statistische Resultate {\"u}ber computergerechte
                 Darstellungen von Zahlen}. ({German}) [Statistical
                 results on computer-oriented representations of
                 numbers]",
  journal =      "Anzeiger der {\"O}sterreichischen Akademie der
                 Wissenschaften. Mathematisch-Naturwissenschaftliche
                 Klasse",
  volume =       "1987",
  number =       "??",
  pages =        "1--8",
  month =        "????",
  year =         "1988",
  CODEN =        "OSAWA8",
  DOI =          "????",
  ISSN =         "0065-535X",
  ISSN-L =       "0065-535X",
  bibdate =      "Mon Feb 18 06:45:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  ZMnumber =     "0625.10041",
  acknowledgement = ack-nhfb,
  ajournal =     "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
  language =     "German",
  xxnote =       "Despite repeated searches, I have not found this
                 journal online, not even from links at the Austrian
                 Academy of Sciences, \path=http://www.oeaw.ac.at=.",
  ZMclass =      "11K16 (Normal numbers, etc.); 11J71 (Distribution
                 modulo one); 11K38 (Irregularities of distribution)",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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/;
                 https://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{Nicholls:1989:RBM,
  author =       "Paul Travis Nicholls",
  title =        "Research: Bibliometric modeling processes and the
                 empirical validity of {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "40",
  number =       "6",
  pages =        "379--385",
  month =        nov,
  year =         "1989",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198911)40:6<379::AID-ASI1>3.0.CO%3B2-Q",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:37 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "27 May 2007",
}

@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 =          "https://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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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,
  volume =       "82",
  number =       "2",
  pages =        "254--274",
  year =         "1989",
  CODEN =        "PTPKAV",
  ISSN =         "0033-068X (print), 1347-4081 (electronic)",
  ISSN-L =       "0033-068X",
  MRclass =      "58F13 (92K20)",
  MRnumber =     "1023357 (91d:58165)",
  MRreviewer =   "Nima Geffen",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
  journal-URL =  "http://ptp.oxfordjournals.org/content/by/year",
}

@Article{Schatte:1989:MUD,
  author =       "Peter Schatte",
  title =        "On measures of uniformly distributed sequences and
                 {Benford}'s law",
  journal =      j-MONAT-MATH,
  volume =       "107",
  number =       "3",
  pages =        "245--256",
  year =         "1989",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01300347",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  MRclass =      "11K36 (60F99)",
  MRnumber =     "1008683 (90k:11097)",
  MRreviewer =   "Kazuo Goto",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
}

@Article{Shanbhag:1989:BRBa,
  author =       "D. N. Shanbhag",
  title =        "Book Review: {{\booktitle{Pareto Distributions}}, by
                 B. C. Arnold}",
  journal =      j-J-R-STAT-SOC-SER-A-STAT-SOC,
  volume =       "152",
  number =       "2",
  pages =        "253--254",
  month =        "????",
  year =         "1989",
  CODEN =        "JSSAEF",
  DOI =          "https://doi.org/10.2307/2982920",
  ISSN =         "0964-1998 (print), 1467-985X (electronic)",
  ISSN-L =       "0964-1998",
  bibdate =      "Sat Jan 24 15:13:38 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349642;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1980.bib",
  URL =          "http://www.jstor.org/stable/2982920",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series A
                 (Statistics in Society)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-985X;
                 http://www.jstor.org/journals/09641998.html",
}

@Article{Shieh:1989:BZE,
  author =       "Yeung-Nan Shieh",
  title =        "The {Beckmann--Zipf} effect and plant location under
                 uniform pricing",
  journal =      j-ECONOM-LETT,
  volume =       "30",
  number =       "1",
  pages =        "89--92",
  day =          "1",
  month =        jan,
  year =         "1989",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/0165-1765(89)90162-6",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "90A12 (90B05)",
  MRnumber =     "1010312",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0165176589901626",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Thomas:1989:UPR,
  author =       "Jacob K. Thomas",
  title =        "Unusual patterns in reported earnings",
  journal =      j-ACCOUNT-REV,
  volume =       "59",
  number =       "4",
  pages =        "773--787",
  month =        oct,
  year =         "1989",
  CODEN =        "ACRVAS",
  ISSN =         "0001-4826 (print), 1558-7967 (electronic)",
  ISSN-L =       "0001-4826",
  bibdate =      "Fri Feb 15 06:49:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/247861",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  keywords =     "Benford's Law; distribution of first digits;
                 distribution of second digits",
}

@Article{Xekalaki:1989:APY,
  author =       "E. Xekalaki and J. Panaretos",
  title =        "On the Association of the {Pareto} and the {Yule}
                 Distribution",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "33",
  number =       "1",
  pages =        "191--195",
  month =        "????",
  year =         "1989",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/1133028",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Tue Apr 1 10:40:04 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/33/1;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and its Applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  onlinedate =   "January 1989",
}

@Article{Egghe:1990:RAT,
  author =       "L. Egghe",
  title =        "Research: Applications of the theory of {Bradford}'s
                 {Law} to the calculation of {Leimkuhler's Law} and to
                 the completion of bibliographies",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "41",
  number =       "7",
  pages =        "469--492",
  month =        oct,
  year =         "1990",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199010)41:7<469::AID-ASI1>3.0.CO%3B2-P",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:41 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Egghe:1990:RND,
  author =       "L. Egghe",
  title =        "Research: A note on different {Bradford} multipliers",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "41",
  number =       "3",
  pages =        "204--209",
  month =        apr,
  year =         "1990",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199004)41:3<204::AID-ASI7>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:39 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@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 =          "https://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 =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Colloq. Math. Soc. J{\'a}nos Bolyai",
  acknowledgement = ack-nhfb,
}

@Article{Peritz:1990:BDB,
  author =       "Bluma C. Peritz",
  title =        "A {Bradford} distribution for bibliometrics",
  journal =      j-SCIENTOMETRICS,
  volume =       "18",
  number =       "5--6",
  pages =        "323--329",
  month =        may,
  year =         "1990",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02020148",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:16 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02020148",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Schatte:1990:BLC,
  author =       "Peter Schatte",
  title =        "On {Benford}'s law for continued fractions",
  journal =      j-MATH-NACHR,
  volume =       "148",
  pages =        "137--144",
  year =         "1990",
  CODEN =        "MTMNAQ",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  MRclass =      "11K50 (11K06)",
  MRnumber =     "1127337 (92m:11077)",
  MRreviewer =   "Harald Niederreiter",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Book{Szekely:1990:PKN,
  author =       "G{\'a}bor J. Sz{\'e}kely",
  title =        "{Paradoxa: klassische und neue {\"U}berraschungen aus
                 Wahrscheinlichkeitsrechnung und mathematischer
                 Statistik}. (German) [{Paradoxes}: traditional and new
                 surprises in probability and mathematical statistics]",
  publisher =    "Deutsch",
  address =      "Thun, Switzerland",
  pages =        "239",
  year =         "1990",
  ISBN =         "3-87144-850-8",
  ISBN-13 =      "978-3-87144-850-8",
  LCCN =         "????",
  bibdate =      "Thu Nov 17 19:26:05 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  note =         "Translation by Ulrike Leitner from the Hungarian
                 original.",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht003363686.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0743.60004",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{VandenBroeck:1990:LFB,
  author =       "C. {Van den Broeck} and R. Kawai",
  title =        "Learning in feedforward {Boolean} networks",
  journal =      j-PHYS-REV-A,
  volume =       "42",
  number =       "??",
  pages =        "6210--??",
  day =          "15",
  month =        nov,
  year =         "1990",
  CODEN =        "PLRAAN",
  DOI =          "https://doi.org/10.1103/PhysRevA.42.6210",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  ISSN-L =       "1050-2947",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevA.42.6210",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  journal-URL =  "http://pra.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Yeh:1990:ODT,
  author =       "Hsiaw-Chan Yeh",
  title =        "One discrete time series model for fat-tailed integer
                 random variables: {Zipf} process",
  journal =      "Bulletin of the Institute of Mathematics. Academia
                 Sinica",
  volume =       "18",
  number =       "1",
  pages =        "19--33",
  year =         "1990",
  CODEN =        "BIMSDG",
  ISSN =         "0304-9825",
  ISSN-L =       "0304-9825",
  MRclass =      "60J10 (62M10)",
  MRnumber =     "1072827 (91i:60175)",
  MRreviewer =   "Ed McKenzie",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Math. Acad. Sinica",
  fjournal =     "Bulletin of the Institute of Mathematics. Academia
                 Sinica",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
}

@Article{Burrell:1991:BDG,
  author =       "Q. L. Burrell",
  title =        "The {Bradford} distribution and the {Gini} index",
  journal =      j-SCIENTOMETRICS,
  volume =       "21",
  number =       "2",
  pages =        "181--194",
  month =        jun,
  year =         "1991",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02017568",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:22 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02017568",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@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 =          "https://doi.org/10.1080/00207729108910791",
  ISSN =         "0020-7721 (print), 1464-5319 (electronic)",
  ISSN-L =       "0020-7721",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "https://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",
}

@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 =    "https://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{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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Schatte:1991:NBL,
  author =       "P. Schatte and K. Nagasaka",
  title =        "A note on {Benford}'s law for second order linear
                 recurrences with periodical coefficients",
  journal =      j-Z-ANAL-ANWEND,
  volume =       "10",
  number =       "2",
  pages =        "251--254",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "0232-2064 (print), 1661-4534 (electronic)",
  ISSN-L =       "0232-2064",
  MRclass =      "11K31",
  MRnumber =     "1155374 (93b:11101)",
  MRreviewer =   "F. Schweiger",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}

@Article{Schatte:1991:ULI,
  author =       "P. Schatte",
  title =        "On a uniform law of the iterated logarithm for sums
                 mod {$1$} and {Benford}'s law",
  journal =      "Litovsk. Mat. Sb.",
  volume =       "31",
  number =       "1",
  pages =        "205--217",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/BF00972327",
  ISSN =         "0132-2818",
  ISSN-L =       "0132-2818",
  MRclass =      "60F15 (11K99)",
  MRnumber =     "1161363 (93g:60067)",
  MRreviewer =   "O. P. Stackelberg",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lietuvos TSR Moksl\polhk u Akademija. Lietuvos TSR
                 Auk\v stosios Mokyklos. Lietuvos Matematikos Rinkinys.
                 Akademiya Nauk Litovsko{\u\i} SSR. Vysshie Uchebnye
                 Zavedeniya Litovsko{\u\i} SSR. Litovski\u\i\
                 Matematicheski{\u\i} Sbornik",
  xxnote =       "Check pages: reprinted in two version of this
                 journal??",
}

@Book{Schroeder:1991:FCP,
  author =       "Manfred Schroeder",
  title =        "Fractals, Chaos, Power Laws",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  pages =        "xviii + 429",
  year =         "1991",
  ISBN =         "0-671-74217-5, 0-7167-2136-8, 0-7167-2357-3",
  ISBN-13 =      "978-0-671-74217-1, 978-0-7167-2136-9,
                 978-0-7167-2357-8",
  LCCN =         "QD921 .S3 1990",
  bibdate =      "Wed Dec 15 10:41:35 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/shannon-claude-elwood.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "Reveals the extraordinary dimensions of new
                 mathematical insights about the nature of physical
                 reality; explores the powerful applications of these
                 symmetry concepts in physics, chemistry, music, and the
                 visual arts. Includes such areas as deterministic chaos
                 and strange attractors, iterated mappings, nonlinear
                 dynamics, Cayley trees, cellular automata, random
                 fractals and related topics.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Introduction \\
                 Similarity and dissimilarity \\
                 Self-similarity --- discrete, continuous, strict, and
                 otherwise \\
                 Power laws: endless sources of self-similarity \\
                 Noises: white, pink, brown, and black \\
                 Brownian motion, gambling losses, and intergalactic
                 voids: random fractals par excellence \\
                 Cantor sets: self-similarity and arithmetic dust \\
                 Fractals in higher dimensions and a digital sundial \\
                 Multifractals: intimately intertwined fractals \\
                 Some practical fractals and their measurement \\
                 Iteration, strange mappings, and a billion digits for
                 $\pi$ \\
                 A self-similar sequence, the logistic parabola, and
                 symbolic dynamics \\
                 A forbidden symmetry, Fibonacci's rabbits, and a new
                 state of matter \\
                 Periodic and quasiperiodic structures in space --- the
                 route to spatial chaos \\
                 Percolation: from forest fires to epidemics \\
                 Phase transitions and renormalization \\
                 Cellular automata",
  tableofcontents = "Preface / xiii \\
                 1: Introduction / 1 \\
                 Einstein, Pythagoras, and Simple Similarity / 3 \\
                 A Self-Similar Array of Self-Preserving Queens / 4 \\
                 A Self-Similar Snowflake / 7 \\
                 A New Dimension for Fractals / 9 \\
                 A Self-Similar Tiling and a ``Non-Euclidean'' Paradox /
                 13 \\
                 At the Gates of Cantor's Paradise / 15 \\
                 The Sierpinski Gasket / 17 \\
                 Sir Pinski's Game and Deterministic Chaos / 20 \\
                 Three Bodies Cause Chaos / 25 \\
                 Strange Attractors, Their Basins, and a Chaos Game 2 /
                 7 \\
                 Percolating Random Fractals / 30 \\
                 Power Laws: from Alvarez to Zipf / 33 \\
                 Newton's Iteration and How to Abolish Two-Nation
                 Boundaries / 38 \\
                 Could Minkowski Hear the Shape of a Drum? / 40 \\
                 Discrete Self-Similarity: Creases and Center Folds / 45
                 \\
                 Golden and Silver Means and Hyperbolic Chaos / 49 \\
                 Winning at Fibonacci Nim / 53 \\
                 Self-Similar Sequences from Square Lattices / 55 \\
                 John Horton Conway's ``Death Bet'' / 57 \\
                 2: Similarity and Dissimilarity / 61 \\
                 More Than One Scale / 61 \\
                 To Scale or Not to Scale: A Bit of Biology and
                 Astrophysics / 63 \\
                 Similarity in Physics: Some Astounding Consequences /
                 66 \\
                 Similarity in Concert Halls, Microwaves, and
                 Hydrodynamics / 68 \\
                 Scaling in Psychology / 70 \\
                 Acousticians, Alchemy, and Concert Halls / 72 \\
                 Preference and Dissimilarity: Concert Halls Revisited /
                 74 \\
                 3: Self-Similarity --- Discrete, Continuous, Strict,
                 and Otherwise / 81 \\
                 The Logarithmic Spiral, Cutting Knives, and Wideband
                 Antennas / 89 \\
                 Some Simple Cases of Self-Similarity / 93 \\
                 Weierstrass Functions and a Musical Paradox / 96 \\
                 More Self-Similarity in Music: The Tempered Scales of
                 Bach / 99 \\
                 The Excellent Relations between the Primes 3, 5, and 7
                 / 102 \\
                 4: Power Laws: Endless Sources of Self-Similarity / 103
                 \\
                 The Sizes of Cities and Meteorites / 103 \\
                 A Fifth Force of Attraction / 105 \\
                 Free of Natural Scales / 107 \\
                 Bach Composing on All Scales / 107 \\
                 Birkhoff's Aesthetic Theory / 109 \\
                 Heisenberg's Hyperbolic Uncertainty Principle / 112 \\
                 Fractional Exponents / 115 \\
                 The Peculiar Distribution of the First Digit / 116 \\
                 The Diameter Exponents of Trees, Rivers, Arteries, and
                 Lungs / 117 \\
                 5: Noises: White, Pink, Brown, and Black / 121 \\
                 Pink Noise / 122 \\
                 Self-Similar Trends on the Stock Market / 126 \\
                 Black Noises and Nile Floods / 129 \\
                 Warning: World Warming / 131 \\
                 Fractional Integration: A Modem Tool / 131 \\
                 Brownian Mountains / 133 \\
                 Radon Transform and Computer Tomography / 134 \\
                 Fresh and Tired Mountains / 135 \\
                 6: Brownian Motion, Gambling Losses, and Intergalactic
                 Voids: Random Fractals Par Excellence / 139 \\
                 The Brownian Beast Tamed / 140 \\
                 Brownian Motion as a Fractal / 141 \\
                 How Many Molecules? / 143 \\
                 The Spectrum of Brownian Motion / 144 \\
                 The Gambler's Ruin, Random Walks, and Information
                 Theory / 145 \\
                 Counterintuition Runs Rampant in Random Runs / 146 \\
                 More Food for Fair Thought / 147 \\
                 The St. Petersburg Paradox / 148 \\
                 Shannon's Outguessing Machine / 149 \\
                 The Classical Mechanics of Roulette and Shannon's
                 Channel Capacity / 150 \\
                 The Clustering of Poverty and Galaxies / 152 \\
                 Levy Flights through the Universe / 155 \\
                 Paradoxes from Probabilistic Power Laws / 155 \\
                 Invariant Distributions: Gauss, Cauchy, and Beyond /
                 157 \\
                 7: Cantor Sets: Self-Similarity and Arithmetic Dust /
                 161 \\
                 A Comer of Cantor's Paradise / 161 \\
                 Cantor Sets as Invariant Sets / 165 \\
                 Symbolic Dynamics and Deterministic Chaos / 166 \\
                 Devil's Staircases and a Pinball Machine / 167 \\
                 Mode Locking in Swings and Clocks / 171 \\
                 The Frustrated Manhattan Pedestrian / 172 \\
                 Arnold Tongues 17 / 4 \\
                 8: Fractals in Higher Dimensions and a Digital Sundial
                 / 177 \\
                 Cartesian Products of Cantor Sets / 177 \\
                 A Leaky Gasket, Soft Sponges, and Swiss Cheeses / 178
                 \\
                 A Cantor-Set Sundial / 181 \\
                 Fat Fractals / 183 \\
                 9: Multifractals: Intimately Intertwined Fractals / 187
                 \\
                 The Distributions of People and Ore / 187 \\
                 Self-Affine Fractals without Holes / 190 \\
                 The Multifractal Spectrum: Turbulence and
                 Diffusion-Limited Aggregation / 193 \\
                 Viscous Fingering / 199 \\
                 Multifractals on Fractals / 200 \\
                 Fractal Dimensions from Generalized Entropies / 203 \\
                 The Relation between the Multifractal Spectrum
                 $f(\alpha)$ and the Mass Exponents $(q)$ / 205 \\
                 Strange Attractors as Multifractals / 206 \\
                 A Greedy Algorithm for Unfavorable Odds / 207 \\
                 10: Some Practical Fractals and Their Measurement / 211
                 \\
                 Dimensions from Box Counting / 213 \\
                 The Mass Dimension / 215 \\
                 The Correlation Dimension / 220 \\
                 Infinitely Many Dimensions / 220 \\
                 The Determination of Fractal Dimensions from Time
                 Series / 223 \\
                 Abstract Concrete / 224 \\
                 Fractal Interfaces Enforce Fractional Frequency
                 Exponents / 225 \\
                 The Fractal Dimensions of Fracture Surfaces / 230 \\
                 The Fractal Shapes of Clouds and Rain Areas / 231 \\
                 Cluster Agglomeration / 232 \\
                 Diffraction from Fractals / 233 \\
                 11: Iteration, Strange Mappings, and a Billion Digits
                 for Pi / 237 \\
                 Looking for Zeros and Encountering Chaos / 239 \\
                 The Strange Sets of Julia / 243 \\
                 A Multifractal Julia Set / 245 \\
                 The Beauty of Broken Linear Relationships / 249 \\
                 The Baker's Transformation and Digital Musical Chairs /
                 251 \\
                 Arnol'd's Cat Map / 253 \\
                 A Billion Digits for $\pi$ / 257 \\
                 Bushes and Flowers from Iterations / 259 \\
                 12: A Self-Similar Sequence, the Logistic Parabola, and
                 Symbolic Dynamics / 263 \\
                 Self-Similarity from the Integers / 264 \\
                 The Logistic Parabola and Period Doubling / 268 \\
                 Self-Similarity in the Logistic Parabola / 272 \\
                 The Scaling of the Growth Parameter / 274 \\
                 Self-Similar Symbolic Dynamics / 277 \\
                 Periodic Windows Embedded in Chaos / 279 \\
                 The Parenting of New Orbits / 282 \\
                 The Calculation of the Growth Parameters for Different
                 Orbits / 286 \\
                 Tangent Bifurcations, Intermittency, and I/f Noise /
                 289 \\
                 A Case of Complete Chaos / 291 \\
                 The Mandelbrot Set / 295 \\
                 The Julia Sets of the Complex Quadratic Map / 297 \\
                 13: A Forbidden Symmetry, Fibonacci's Rabbits, and a
                 New State of Matter / 301 \\
                 The Forbidden Fivefold Symmetry / 301 \\
                 Long-Range Order from Neighborly Interactions / 304 \\
                 Generation of the Rabbit Sequence from the Fibonacci
                 Number System / 307 \\
                 The Self-Similar Spectrum of the Rabbit Sequence / 308
                 \\
                 Self-Similarity in the Rabbit Sequence / 310 \\
                 A One-Dimensional Quasiperiodic Lattice / 310 \\
                 Self-Similarity from Projections / 311 \\
                 More Forbidden Symmetries / 315 \\
                 14: Periodic and Quasiperiodic Structures in Space ---
                 The route to Spatial Chaos / 319 \\
                 Periodicity and Quasiperiodicity in Space / 320 \\
                 The Devil's Staircase for Ising Spins / 321 \\
                 Quasiperiodic Spatial Distributions / 322 \\
                 Beatty Sequence Spins / 325 \\
                 The Scaling Laws for Quasiperiodic Spins / 329 \\
                 Self-Similar Winding Numbers / 330 \\
                 Circle Maps and Arnold Tongues / 331 \\
                 Mediants, Farey Sequences, and the Farey Tree / 334 \\
                 The Golden-Mean Route to Chaos / 340 \\
                 15: Percolation: From Forest Fires to Epidemics / 345
                 \\
                 Critical Conflagration on a Square Lattice / 346 \\
                 Universality / 350 \\
                 The Critical Density / 353 \\
                 The Fractal Perimeters of Percolation / 353 \\
                 Finite-Size Scaling / 354 \\
                 16: Phase Transitions and Renormalization / 357 \\
                 A First-Order Markov Process / 357 \\
                 Self-Similar and Non-Self-Similar Markov Processes /
                 358 \\
                 The Scaling of Markov Output's / 360 \\
                 Renormalization and Hierarchical Lattices / 362 \\
                 The Percolation Threshold of the Bethe Lattice / 363
                 \\
                 A Simple Renormalization / 367 \\
                 17: Cellular Automata / 371 \\
                 The Game of Life / 373 \\
                 Cellular Growth and Decay / 375 \\
                 Biological Pattern Formation / 382 \\
                 Self-Similarity from a Cellular Automaton / 383 \\
                 A Catalytic Converter as a Cellular Automaton / 386 \\
                 Pascal's Triangle Modulo $N$ / 387 \\
                 Bak's Self-Organized Critical Sandpiles / 389 \\
                 Appendix / 391 \\
                 References / 395 \\
                 Author Index / 411 \\
                 Subject Index / 417",
}

@Article{Trubnikov:1991:SDZ,
  author =       "B. A. Trubnikov and I. A. Rumynski{\u\i}",
  title =        "A simple derivation of the {Zipf--Krylov} law for
                 words and the possibility of its ``evolution''
                 interpretation",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "321",
  number =       "2",
  pages =        "270--275",
  year =         "1991",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  ISSN-L =       "0002-3264",
  MRclass =      "00A69 (92K20)",
  MRnumber =     "1153554",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii Nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
}

@Article{Basu:1992:RHD,
  author =       "Aparna Basu",
  title =        "Research: Hierarchical distributions and {Bradford's
                 Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "7",
  pages =        "494--500",
  month =        aug,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<494::AID-ASI4>3.0.CO%3B2-F",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:51 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dehaene:1992:CLR,
  author =       "Stanislas Dehaene and Jacques Mehler",
  title =        "Cross-linguistic regularities in the frequency of
                 number words",
  journal =      j-COGNITION,
  volume =       "43",
  number =       "1",
  pages =        "1--29",
  year =         "1992",
  CODEN =        "CGTNAU",
  DOI =          "https://doi.org/10.1016/0010-0277(92)90030-L",
  ISSN =         "0010-0277 (print), 1873-7838 (electronic)",
  ISSN-L =       "0010-0277",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001002779290030L",
  abstract =     "We examine the frequency of numerals and ordinals in
                 seven different languages and/or cultures. Many
                 cross-cultural and cross-linguistic patterns are
                 identified. The most striking is a decrease of
                 frequency with numerical magnitude, with local
                 increases for reference numerals such as 10, 12, 15,
                 20, 50 or 100. Four explanations are considered for
                 this effect: sampling artifacts, notational
                 regularities, environmental biases and psychological
                 limitations on number representations. The
                 psychological explanation, which appeals to a
                 Fechnerian encoding of numerical magnitudes and to the
                 existence of numerical points of reference, accounts
                 for most of the data. Our finding also has practical
                 importance since it reveals the frequent confound of
                 two experimental variables: numerical magnitude and
                 numeral frequency.",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognition",
  keywords =     "Benford's Law",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Journal of Okayama University",
}

@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 =          "https://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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete Mathematics",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/annapplprobab.bib;
                 https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}

@Article{Longfellow:1992:LER,
  author =       "Charles A. {Longfellow, Jr.}",
  title =        "Letters to the {Editor}: Regarding {``Lotka's Law and
                 the Kolmogorov--Smirnov Test: An Error in
                 Calculation''}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "7",
  pages =        "518--518",
  month =        aug,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<518::AID-ASI7>3.0.CO%3B2-#",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:51 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  note =         "See \cite{Loughner:1992:BCL}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Loughner:1992:BCL,
  author =       "William Loughner",
  title =        "Brief Communications: {Lotka's Law} and the
                 {Kolmogorov--Smirnov} test: an error in calculation",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "2",
  pages =        "149--150",
  month =        mar,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199203)43:2<149::AID-ASI4>3.0.CO%3B2-Y",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  note =         "See comment \cite{Longfellow:1992:LER}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@PhdThesis{Nigrini:1992:DIE,
  author =       "Mark John Nigrini",
  title =        "The detection of income tax evasion through an
                 analysis of digital distributions",
  type =         "{Ph.D.} Dissertation",
  school =       "Department of Accounting\slash Business Law,
                 University of Cincinnati",
  address =      "Cincinnati, OH, USA",
  pages =        "xvi + 309",
  day =          "28",
  month =        aug,
  year =         "1992",
  bibdate =      "Sat Nov 12 15:47:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/docview/304052348",
  acknowledgement = ack-nhfb,
  advisor =      "Wallace R. Wood",
  remark =       "There are more than 230 mentions of Frank Benford, and
                 8 of Simon Newcomb, but no mention of Pareto or Zipf.",
}

@Article{Rousseau:1992:RBR,
  author =       "Ronald Rousseau",
  title =        "Research: Breakdown of the robustness property of
                 {Lotka's Law}: the case of adjusted counts for
                 multiauthorship attribution",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "10",
  pages =        "645--647",
  month =        dec,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199212)43:10<645::AID-ASI1>3.0.CO%3B2-X",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:48 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Sanders:1992:PPU,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: its Use and Abuse",
  journal =      j-J-PROD-BRAND-MANAG,
  volume =       "1",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/10610429210036762",
  ISSN =         "1061-0421",
  ISSN-L =       "1061-0421",
  bibdate =      "Fri Nov 25 06:50:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Product \& Brand Management",
  keywords =     "80/20 rule",
}

@Article{Too:1992:UDM,
  author =       "Yeu-Hua Too",
  title =        "On the uniform distribution modulo one of some
                 log-like sequences",
  journal =      "Proceedings of the Japan Academy, Series A.
                 Mathematical Sciences",
  volume =       "68",
  number =       "9",
  pages =        "269--272",
  month =        "????",
  year =         "1992",
  DOI =          "https://doi.org/10.3792/pjaa.68.269",
  ISSN =         "0021-4280",
  ISSN-L =       "0021-4280",
  bibdate =      "Mon Feb 18 06:55:06 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195511634",
  acknowledgement = ack-nhfb,
}

@Article{Trachtenberg:1992:WFR,
  author =       "M. Trachtenberg",
  title =        "Why failure rates observe {Zipf}'s law in operational
                 software",
  journal =      j-IEEE-TRANS-RELIAB,
  volume =       "41",
  number =       "3",
  pages =        "386--389",
  year =         "1992",
  CODEN =        "IEERAJ",
  DOI =          "https://doi.org/10.1109/24.159803",
  ISSN =         "0018-9529 (print), 1558-1721 (electronic)",
  ISSN-L =       "0018-9529",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0825.68222",
  acknowledgement = ack-nhfb,
  classmath =    "68M15 (Reliability and testing of computer systems)
                 68N01 (General)",
  fjournal =     "IEEE Transactions on Reliability",
}

@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 =          "https://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 =    "https://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{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",
  DOI =          "https://doi.org/10.1088/0143-0807/14/2/003",
  ISSN =         "0143-0807 (print), 1361-6404 (electronic)",
  ISSN-L =       "0143-0807",
  bibdate =      "Mon Nov 14 17:32:53 2011",
  bibsource =    "https://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",
  journal-URL =  "http://iopscience.iop.org/0143-0807/",
}

@Article{Christian:1993:NES,
  author =       "C. W. Christian and S. Gupta",
  title =        "New Evidence on ``Secondary Evasion''",
  journal =      "Journal of the {American Taxation Association}",
  volume =       "15",
  number =       "??",
  pages =        "72--93",
  month =        "????",
  year =         "1993",
  ISSN =         "0198-9073 (print), 1558-8017 (electronic)",
  ISSN-L =       "0198-9073",
  bibdate =      "Thu Oct 13 06:50:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Amer. Tax. Assoc.",
  fjournal =     "Journal of the {American Taxation Association}",
  journal-URL =  "http://aaajournals.org/loi/atax",
  remark =       "No journal issues online before 1999.",
}

@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 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  MRclass =      "11K36",
  MRnumber =     "1268513 (95j:11072)",
  MRreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Mathematical Society Gazette",
  journal-URL =  "http://www.austms.org.au/gazette",
}

@Article{Nigrini:1993:CBL,
  author =       "Mark Nigrini",
  title =        "Can {Benford's Law} be used in Forensic Accounting?",
  journal =      "The Balance Sheet",
  volume =       "??",
  number =       "??",
  pages =        "7--8",
  month =        jun,
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 21 22:03:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Oluic-Vukovic:1993:LEW,
  author =       "Vesna Olui{\'c}-Vukovi{\'c}",
  title =        "Letters to the {Editor}: Why has {Bradford's Law} been
                 an elusive phenomenon so far?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "44",
  number =       "3",
  pages =        "182--183",
  month =        apr,
  year =         "1993",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199304)44:3<182::AID-ASI9>3.0.CO%3B2-S",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:54 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@TechReport{Stewart:1993:LAN,
  author =       "Ian Stewart",
  title =        "The law of anomalous numbers",
  type =         "Working paper",
  institution =  "Mathematics Institute, University of Warwick",
  address =      "Warwick, UK",
  year =         "1993",
  bibdate =      "Fri Mar 22 09:15:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Published in Spektrum der Wissenschaft (April 1994)",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@TechReport{Sundheim:1993:FNT,
  author =       "R. Sundheim and B. Busta",
  title =        "{Fibonacci} numbers tend to obey {Benford's Law}: an
                 extension of {Wlodarski} and {Sentance}",
  type =         "Working Paper",
  institution =  "St. Cloud State University",
  address =      "St. Cloud, MN, USA",
  month =        "????",
  year =         "1993",
  bibdate =      "Mon Feb 18 06:37:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sury:1993:FPD,
  author =       "B. Sury",
  title =        "Fractional parts of $ \log p $ and a digit function",
  journal =      j-EXPO-MATH,
  volume =       "11",
  number =       "4",
  pages =        "381--384",
  month =        "????",
  year =         "1993",
  DOI =          "????",
  ISSN =         "0723-0869 (print), 1878-0792 (electronic)",
  ISSN-L =       "0723-0869",
  bibdate =      "Mon Feb 18 06:39:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  ZMnumber =     "0787.11003",
  acknowledgement = ack-nhfb,
  ajournal =     "Expo. Math.",
  fjournal =     "Expositiones Mathematicae",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07230869",
  keywords =     "decimal expansion; sum of digits",
  ZMclass =      "11A63 (Radix representation; digital problems)",
  ZMreviewer =   "G. Larcher (Salzburg)",
}

@Article{Wolf:1993:PHJ,
  author =       "Joel L. Wolf and Philip S. Yu and John Turek and
                 Daniel M. Dias",
  title =        "A parallel hash join algorithm for managing data
                 skew",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "4",
  number =       "12",
  pages =        "1355--1371",
  month =        dec,
  year =         "1993",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.250117",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Apr 11 15:20:39 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM T. J. Watson Research Cent",
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "721.1; 722.4; 723.1; 723.2; 723.3; 921.4; C4240P
                 (Parallel programming and algorithm theory); C4250
                 (Database theory); C6160D (Relational DBMS)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Algorithms; combinatorial; Combinatorial mathematics;
                 Combinatorial optimization; Complex queries; complex
                 queries; Computational complexity; Data handling; Data
                 skew; data skew; database theory; hash; Hash joins;
                 hashing; heuristic optimization; hierarchical; join
                 column; joins; load balancing; Load balancing;
                 optimization; parallel algorithms; parallel hash join
                 algorithm; Parallel processing systems; Program
                 processors; Query languages; query processing;
                 Relational database systems; relational databases;
                 resource allocation; scheduling; Zipf-like
                 distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Wolf:1993:PSM,
  author =       "Joel L. Wolf and Daniel M. Dias and Philip S. Yu",
  title =        "Parallel sort merge join algorithm for managing data
                 skew",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "4",
  number =       "1",
  pages =        "70--86",
  month =        jan,
  year =         "1993",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.205654",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Apr 11 15:20:39 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM",
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "723.1; 723.3; 921.5; C4240P (Parallel programming
                 and algorithm theory); C4250 (Database theory); C6130
                 (Data handling techniques); C6160B (Distributed DBMS);
                 C6160D (Relational DBMS)",
  corpsource =   "IBM T. J. Watson Res. Center. Yorktown Heights, NY,
                 USA",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Algorithms; Computer systems programming; Data skew;
                 data skew management; distributed databases; Divide and
                 conquer approach; divide-and-conquer; join phases; load
                 balancing; merging; multiple processors;
                 Multiprocessing programs; Optimization; parallel;
                 Parallel algorithms; parallel algorithms; Parallel sort
                 merge join algorithm; parallelizable optimization
                 algorithm; phase; Query processing; relational algebra;
                 Relational database systems; relational databases;
                 scheduling; Scheduling; sort merge join algorithm; sort
                 phase; sorting; Sorting; transfer phase; Zipf-like
                 distribution",
  treatment =    "T Theoretical or Mathematical",
}

@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 =    "https://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{Basu:1994:LEE,
  author =       "Aparna Basu",
  title =        "Letters to the {Editor}: The elusive phenomenon of
                 {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "45",
  number =       "1",
  pages =        "59--60",
  month =        jan,
  year =         "1994",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199401)45:1<59::AID-ASI8>3.0.CO%3B2-F",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Bookstein:1994:TMD,
  author =       "A. Bookstein",
  title =        "Towards a multi-disciplinary {Bradford Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "30",
  number =       "1",
  pages =        "353--361",
  month =        may,
  year =         "1994",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02017233",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Thu Sep 3 07:35:17 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02017233",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Egghe:1994:RSF,
  author =       "L. Egghe",
  title =        "Research: Special features of the author--publication
                 relationship and a new explanation of {Lotka's Law}
                 based on convolution theory",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "45",
  number =       "6",
  pages =        "422--427",
  month =        jul,
  year =         "1994",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199407)45:6<422::AID-ASI8>3.0.CO%3B2-C",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:01 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@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 =    "https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comment \cite{Voss:1996:CLF} and reply
                 \cite{Mantegna:1996:MAR}.",
  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{Nigrini:1994:UDF,
  author =       "Mark J. Nigrini",
  title =        "Using digital frequencies to detect fraud",
  journal =      "The White Paper",
  volume =       "??",
  number =       "2",
  pages =        "3--6",
  month =        apr # "\slash " # may,
  year =         "1994",
  bibdate =      "Sat Feb 16 18:53:08 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "The White Paper is the precursor to Fraud Magazine; I
                 cannot find it in the Library of Congress catalog.",
}

@Article{Pedrotti:1994:ALU,
  author =       "A. Pedrotti",
  title =        "Analysis of a list-update strategy",
  journal =      j-INFO-PROC-LETT,
  volume =       "52",
  number =       "3",
  pages =        "115--121",
  day =          "11",
  month =        nov,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Scuola Normale Superiore",
  affiliationaddress = "Pisa, Italy",
  classification = "721.1; 723.2; 921.6; 922.1; 922.2; C4240C
                 (Computational complexity); C6130 (Data handling
                 techniques)",
  corpsource =   "Scuola Normale Superiore, Pisa, Italy",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "Algorithms; analysis of algorithms; average-case
                 complexity; BIT; competitive algorithms; Computational
                 complexity; computational complexity; convergence;
                 Convergence of numerical methods; Data handling;
                 Function evaluation; Heuristic methods; list
                 processing; list update; Markov chains; Move to front
                 algorithm; move-to-front; Probability; Random number
                 generation; searching; Theorem proving; transpose;
                 Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sheppard:1994:TNA,
  author =       "Lee A. Sheppard",
  title =        "{Tax Notes} audits the {Clintons}",
  journal =      "Tax Notes Today",
  volume =       "??",
  number =       "??",
  pages =        "18--23",
  day =          "4",
  month =        apr,
  year =         "1994",
  bibdate =      "Fri Mar 22 09:13:48 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.bankler.com/docs/Tax_Notes_Audits_the_Clintons.pdf",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Tritch:1994:MAC,
  author =       "Teresa Tritch and Mary L. Sprouse",
  title =        "{Money} audits the {Clintons}",
  journal =      "Money Magazine",
  volume =       "??",
  number =       "??",
  pages =        "84--98",
  day =          "1",
  month =        apr,
  year =         "1994",
  bibdate =      "Fri Mar 22 09:16:28 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://money.cnn.com/magazines/moneymag/moneymag_archive/1994/04/01/88775/index.htm",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wall Street Journal",
}

@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 =    "https://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{Chen:1995:LED,
  author =       "Ye-Sho Chen",
  title =        "Letters to the {Editor}: On the dynamic behavior of
                 {Bradford's Law} --- response",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "10",
  pages =        "799--800",
  month =        dec,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<799::AID-ASI19>3.0.CO%3B2-P",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:04 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Chen:1995:RDB,
  author =       "Ye-Sho Chen and P. Pete Chong and Morgan Y. Tong",
  title =        "Research: Dynamic behavior of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "5",
  pages =        "370--383",
  month =        jun,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<370::AID-ASI7>3.0.CO%3B2-J",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:06 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@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 =          "https://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 =    "https://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{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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@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 (print), 2168-8745 (electronic)",
  ISSN-L =       "0883-4237",
  MRclass =      "60E99 (60A10 62E99)",
  MRnumber =     "1421567 (98a:60021)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 10:09:36 2011",
  bibsource =    "https://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",
  journal-URL =  "http://projecteuclid.org/all/euclid.ss",
}

@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 =          "https://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 =    "https://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{Koenig:1995:BCL,
  author =       "Michael Koenig and Toni Harrell",
  title =        "Brief Communications: {Lotka's Law}, {Price}'s urn,
                 and electronic publishing",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "5",
  pages =        "386--388",
  month =        jun,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<386::AID-ASI9>3.0.CO%3B2-V",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:06 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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{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",
  DOI =          "https://doi.org/10.1080/08989629508573866",
  ISSN =         "0898-9621 (print), 1545-5815 (electronic)",
  ISSN-L =       "0898-9621",
  bibdate =      "Sat Dec 10 11:56:38 2011",
  bibsource =    "https://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",
  journal-URL =  "http://www.tandfonline.com/toc/gacr20",
  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{Oluic-Vukovic:1995:LED,
  author =       "Vesna Olui{\'c}-Vukovi{\'c}",
  title =        "Letters to the {Editor}: On the dynamic behavior of
                 {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "10",
  pages =        "798--799",
  month =        dec,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<798::AID-ASI18>3.0.CO%3B2-T",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:04 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Stanley:1995:ZPS,
  author =       "Michael H. R. Stanley and Sergey V. Buldyrev and
                 Shlomo Havlin and Rosario N. Mantegna and Michael A.
                 Salinger and H. Eugene Stanley",
  title =        "{Zipf} plots and the size distribution of firms",
  journal =      j-ECONOM-LETT,
  volume =       "49",
  number =       "4",
  pages =        "453--457",
  day =          "15",
  month =        oct,
  year =         "1995",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/0165-1765(95)00696-D",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/016517659500696D",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Wagner-Dobler:1995:DLL,
  author =       "Roland Wagner-D{\"o}bler and Jan Berg",
  title =        "The Dependence of {Lotka's Law} on the Selection of
                 Time Periods in the Development of Scientific Areas and
                 Authors",
  journal =      j-J-DOC,
  volume =       "51",
  number =       "1",
  pages =        "28--43",
  month =        "????",
  year =         "1995",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026941",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:29:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Zornig:1995:URZ,
  author =       "Peter Z{\"o}rnig and Gabriel Altmann",
  title =        "Unified representation of {Zipf} distributions",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "461--473",
  day =          "1",
  month =        apr,
  year =         "1995",
  CODEN =        "CSDADW",
  DOI =          "https://doi.org/10.1016/0167-9473(94)00009-8",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  MRclass =      "62E10 (62F10)",
  MRnumber =     "1333065 (96f:62029)",
  MRreviewer =   "Friedrich Liese",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0167947394000098",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
  keywords =     "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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Bonhoeffer:1996:NSH,
  author =       "Sebastian Bonhoeffer and Andreas V. M. Herz and
                 Maarten C. Boerlijst and Sean Nee and Martin A. Nowak
                 and Robert M. May",
  title =        "No Signs of Hidden Language in Noncoding {DNA}",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "11",
  pages =        "1977--1977",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1977",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sat Sep 10 17:27:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1977",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@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 =          "https://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 =    "https://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)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03032647",
  keywords =     "Zipf's Law",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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{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 =    "https://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{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 =          "https://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 =    "https://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",
}

@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 =    "https://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,
}

@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 =       "11",
  pages =        "1976--??",
  day =          "11",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://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 =    "https://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",
}

@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 =          "https://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 =    "https://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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Mantegna:1996:MAR,
  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 =        "{Mantegna} {\em et al.} Reply",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  pages =        "1979--1981",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1979",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sat Sep 10 17:28:12 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mantegna:1994:LFN,Voss:1996:CLF}",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1979",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  issue =        "11",
  journal-URL =  "http://prl.aps.org/browse",
}

@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 =          "https://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 =    "https://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",
}

@InProceedings{Nigrini:1996:DAR,
  author =       "Mark J. Nigrini",
  editor =       "M. Ettredge",
  booktitle =    "{Proceedings of the 1996 Deloitte \& Touche I
                 University of Kansas Symposium on Auditing Problems}",
  title =        "Digital Analysis and the Reduction of Auditor
                 Litigation Risk",
  publisher =    "University of Kansas",
  address =      "Lawrence, KS, USA",
  pages =        "69--81",
  year =         "1996",
  bibdate =      "Sat Sep 10 15:20:48 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Nigrini:1996:TCA,
  author =       "Mark J. Nigrini",
  title =        "A Taxpayer Compliance Application of {Benford's Law}",
  journal =      "Journal of the {American Taxation Association}",
  volume =       "18",
  number =       "1",
  pages =        "72--91",
  month =        "????",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "0198-9073 (print), 1558-8017 (electronic)",
  ISSN-L =       "0198-9073",
  bibdate =      "Mon Nov 14 16:30:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Amer. Tax. Assoc.",
  fjournal =     "Journal of the {American Taxation Association}",
  journal-URL =  "http://aaajournals.org/loi/atax",
  remark =       "No journal issues online before 1999.",
}

@Article{Perline:1996:ZLC,
  author =       "Richard Perline",
  title =        "{Zipf}'s law, the {Central Limit Theorem}, and the
                 random division of the unit interval",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "1",
  pages =        "220--223",
  day =          "1",
  month =        jul,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.220",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.220",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Mandelbrot's monkey-at-the-typewriter model of Zipf's
                 inverse power law; Zipf's Law",
}

@Article{Sole:1996:ESO,
  author =       "Ricard V. Sol{\'e} and Susanna C. Manrubia",
  title =        "Extinction and self-organized criticality in a model
                 of large-scale evolution",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "1",
  pages =        "R42--R45",
  month =        jul,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.R42",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:32:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.R42",
  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{Solomon:1996:SSE,
  author =       "Sorin Solomon and Moshe Levy",
  title =        "Spontaneous Scaling Emergence in Generic Stochastic
                 Systems",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "7",
  number =       "5",
  pages =        "745--752",
  month =        oct,
  year =         "1996",
  CODEN =        "IJMPEO",
  DOI =          "https://doi.org/10.1142/S0129183196000624",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  bibdate =      "Thu Feb 28 10:20:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.worldscientific.com/doi/abs/10.1142/S0129183196000624",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
}

@Article{Voss:1996:CLF,
  author =       "Richard F. Voss",
  title =        "Comment on {``Linguistic Features of Noncoding DNA
                 Sequences''}",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "11",
  pages =        "1978--1978",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1978",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mantegna:1994:LFN} and reply
                 \cite{Mantegna:1996:MAR}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1978",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Benford's Law",
}

@Article{Watanabe:1996:EZL,
  author =       "Makoto S. Watanabe",
  title =        "Erratum: {Zipf}'s law in percolation",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "??",
  pages =        "4483--4483",
  day =          "1",
  month =        oct,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.4483",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite {Watanabe:1996:ZLP}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.4483",
  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{Watanabe:1996:ZLP,
  author =       "Makoto S. Watanabe",
  title =        "{Zipf}'s law in percolation",
  journal =      j-PHYS-REV-E,
  volume =       "53",
  number =       "??",
  pages =        "4187--4190",
  day =          "1",
  month =        apr,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.53.4187",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See erratum \cite {Watanabe:1996:EZL}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.53.4187",
  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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf'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/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "https://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 =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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/;
                 https://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{Jeevanand:1997:BEB,
  author =       "E. S. Jeevanand",
  title =        "{Bayes} Estimation of {$ P(X_2 < X_1) $} for a
                 Bivariate {Pareto} Distribution",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "46",
  number =       "1",
  pages =        "93--99",
  month =        "????",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2988496",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Thu Jan 22 18:10:24 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349996;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-1990.bib",
  URL =          "http://www.jstor.org/stable/2988496",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
}

@Manual{Nigrini:1997:DAT,
  author =       "Mark J. Nigrini",
  title =        "Digital Analysis Tests and Statistics",
  organization = "The Nigrini Institute, Inc.",
  address =      "Allen, TX, USA",
  month =        "????",
  year =         "1997",
  bibdate =      "Sat Feb 16 18:55:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nigrini.com/data_software/Program_Details_2009.docx",
  acknowledgement = ack-nhfb,
}

@Article{Nigrini:1997:UBL,
  author =       "Mark J. Nigrini and L. J. Mittermaier",
  title =        "The Use of {Benford's Law} as an Aid in Analytical
                 Procedures",
  journal =      j-AUDITING,
  volume =       "16",
  number =       "2",
  pages =        "52--67",
  month =        "????",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0278-0380 (print), 1558-7991 (electronic)",
  ISSN-L =       "0278-0380",
  bibdate =      "Sun Nov 13 11:37:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaapubs.org/loi/ajpt",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
  remark =       "No journal issues online before 1999.",
}

@Article{Oluic-Vukovic:1997:BDC,
  author =       "Vesna Olui{\'c}-Vukovi{\'c}",
  title =        "{Bradford}'s distribution: {From} the classical
                 bibliometric ``law'' to the more general stochastic
                 models",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "48",
  number =       "9",
  pages =        "833--842",
  month =        sep,
  year =         "1997",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199709)48:9<833::AID-ASI7>3.0.CO%3B2-S",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:21 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Dec 1998",
}

@Book{Robertson:1997:FEM,
  author =       "Jack C. Robertson",
  title =        "Fraud Examination for Managers and Auditors",
  publisher =    "Viesca Books",
  address =      "Austin, TX, USA",
  edition =      "1997",
  pages =        "vii + 564",
  year =         "1997",
  ISBN =         "0-9656785-0-4",
  ISBN-13 =      "978-0-9656785-0-6",
  LCCN =         "HV8079.F7 R63 1997",
  bibdate =      "Thu Oct 13 09:04:19 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Fraud investigation",
}

@Article{Salsburg:1997:DPB,
  author =       "David Salsburg",
  title =        "Digit Preferences in the {Bible}",
  journal =      j-CHANCE,
  volume =       "10",
  number =       "4",
  pages =        "46--48",
  month =        "????",
  year =         "1997",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.1997.10542065",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Sat Feb 16 19:08:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://amstat.tandfonline.com/doi/full/10.1080/09332480.1997.10542065",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
}

@InCollection{Smith:1997:EBL,
  author =       "Steven W. Smith",
  booktitle =    "The Scientist and Engineer's Guide to Digital Signal
                 Processing",
  title =        "Explaining {Benford's Law}",
  chapter =      "34",
  publisher =    "California Technical Publishing",
  address =      "San Diego, CA, USA",
  bookpages =    "xiv + 626",
  pages =        "701--722",
  year =         "1997",
  ISBN =         "0-9660176-3-3",
  ISBN-13 =      "978-0-9660176-3-2",
  LCCN =         "TK5102.9 .S57 1997",
  bibdate =      "Sat Sep 10 16:54:35 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.dspguide.com/ch34.htm",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "Chapters appear to stop at 31 in 1997 edition
                 (according to Amazon book preview), so a later addition
                 should have a new ISBN (the 2002 edition from Newnes is
                 \booktitle{Digital Signal Processing: A Practical Guide
                 for Engineers and Scientists}, with ISBN
                 0-7506-7444-X). However, the Web site says it is the
                 same book. The Web edition has 34 chapters, and all are
                 freely downloadable.",
}

@Article{Tsonis:1997:ZLS,
  author =       "A. A. Tsonis and C. Schultz and P. A. Tsonis",
  title =        "{Zipf's Law} and the structure and evolution of
                 languages",
  journal =      j-COMPLEXITY,
  volume =       "2",
  number =       "5",
  pages =        "12--13",
  year =         "1997",
  CODEN =        "COMPFS",
  DOI =          "https://doi.org/10.1002/(SICI)1099-0526(199705/06)2:5<12::AID-CPLX3>3.0.CO%3B2-C",
  ISSN =         "1076-2787 (print), 1099-0526 (electronic)",
  ISSN-L =       "1076-2787",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Complexity",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0526",
}

@Article{Zanette:1997:RIU,
  author =       "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
  title =        "Role of Intermittency in Urban Development: A Model of
                 Large-Scale City Formation",
  journal =      j-PHYS-REV-LET,
  volume =       "79",
  number =       "3",
  pages =        "523--526",
  day =          "3",
  month =        jul,
  year =         "1997",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.79.523",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Feb 28 10:40:44 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.79.523",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@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 =          "https://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 =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  ZMnumber =     "0915.65003",
  abstract =     "This paper presents two properties of the random
                 number generator by {\em G. Marsaglia} and {\em 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",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  keywords =     "$b$-adic number; algorithm; continued fraction;
                 pseudo-random number generator",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@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 =    "https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chongde:1998:EMB,
  author =       "Wang Chongde and Wang Zhe",
  title =        "Evaluation of the models for {Bradford's Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "42",
  number =       "1",
  pages =        "89--95",
  month =        may,
  year =         "1998",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02465014",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:59 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02465014",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{DeCeuster:1998:HPB,
  author =       "Marc J. K. {De Ceuster} and Geert Dhaene and Tom
                 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 =          "https://doi.org/10.1016/S0927-5398(97)00024-8",
  ISSN =         "0927-5398 (print), 1879-1727 (electronic)",
  ISSN-L =       "0927-5398",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
  abstract =     "We consider the hypothesis of psychological barriers
                 at round numbers of a stock index. This hypothesis is
                 often examined by testing the uniformity of the
                 distribution of the trailing digits in the stock index,
                 a rejection being interpreted as evidencing the
                 existence of psychological barriers. By virtue of
                 Benford's Law, we show that the uniform distribution is
                 not the right benchmark against which to test. As an
                 alternative we propose a test based on the cyclical
                 permutations of the actual returns. Applying this test
                 to the Dow Jones 30 Industrial Average, the Financial
                 Times Stock Exchange 100 and the Nikkei Stock Average
                 225, we find no convincing evidence of psychological
                 barriers, contrary to previous findings.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Empirical Finance",
  keywords =     "Benford's Law; Psychological barriers",
}

@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 =    "https://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{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 =          "https://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 =    "https://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",
}

@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  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 =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.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,
  remark =       "Knuth comments on page 255: ``The fact that the
                 leading digits tend to be small makes the most obvious
                 techniques of ``average error'' estimation for floating
                 point calculations invalid. The relative error due to
                 rounding is usually a little more than expected.",
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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{Nigrini:1998:DIB,
  author =       "Mark J. Nigrini",
  title =        "{Dow} Illustrates {Benford's Law}",
  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 15:46:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/hnpnewyorktimes/docview/109901848/13C4AB0BB5661D397CE/1",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
}

@Article{NunesAmaral:1998:PLS,
  author =       "Lu{\'\i}s A. {Nunes Amaral} and Sergey V. Buldyrev and
                 Shlomo Havlin and Michael A. Salinger and H. Eugene
                 Stanley",
  title =        "Power Law Scaling for a System of Interacting Units
                 with Complex Internal Structure",
  journal =      j-PHYS-REV-LET,
  volume =       "80",
  number =       "7",
  pages =        "1385--1388",
  day =          "16",
  month =        feb,
  year =         "1998",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.80.1385",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Feb 28 11:09:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.80.1385",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Pietronero:1998:UDN,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "The Uneven Distribution of Numbers in Nature",
  journal =      "ArXiv e-prints",
  pages =        "9",
  day =          "27",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon Nov 21 06:58:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/cond-mat/9808305",
  abstract =     "Suppose you look at today's stock prices and bet on
                 the value of the first digit. One could guess that a
                 fair bet should correspond to the frequency of $ 1 / 9
                 = 11.11 \% $ for each digit from 1 to 9. This is by no
                 means the case, and one can easily observe a strong
                 prevalence of the small values over the large ones. The
                 first three integers 1, 2 and 3 alone have globally a
                 frequency of 60\% while the other six values 4, 5, 6,
                 7, 8 and 9 appear only in 40\% of the cases. This
                 situation is actually much more general than the stock
                 market and it occurs in a variety of number catalogs
                 related to natural phenomena. The first observation of
                 this property traces back to S. Newcomb in 1881 but a
                 more precise account was given by F. Benford in 1938.
                 In this note we illustrate these observations with the
                 enlightening specific example of the stock market. We
                 also identify the general mechanism for the origin of
                 this uneven distribution in the multiplicative nature
                 of fluctuations in economics and in many natural
                 phenomena. This provides a natural explanation for the
                 ubiquitous presence of the Benford's law in many
                 different phenomena with the common element that their
                 fluctuations refer to a fraction of their values. This
                 brings us close to the problem of the spontaneous
                 origin of scale invariant properties in various
                 phenomena which is a debated question at the frontier
                 of different fields.",
  acknowledgement = ack-nhfb,
}

@Article{Pocheau:1998:SRS,
  author =       "A. Pocheau",
  title =        "Scale ratios, statistical symmetries and
                 intermittency",
  journal =      j-EUROPHYS-LETT,
  volume =       "43",
  number =       "4",
  pages =        "410--415",
  month =        aug,
  year =         "1998",
  CODEN =        "EULEEJ",
  DOI =          "https://doi.org/10.1209/epl/i1998-00103-6",
  ISSN =         "0295-5075 (print), 1286-4854 (electronic)",
  ISSN-L =       "0295-5075",
  bibdate =      "Sat Feb 16 16:02:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Europhysics Letters",
  journal-URL =  "http://iopscience.iop.org/0295-5075",
}

@Article{Ramsden:1998:ZLB,
  author =       "J. J. Ramsden and J. Vohradsk{\'y}",
  title =        "{Zipf}-like behavior in procaryotic protein
                 expression",
  journal =      j-PHYS-REV-E,
  volume =       "58",
  number =       "??",
  pages =        "7777--??",
  day =          "1",
  month =        dec,
  year =         "1998",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.58.7777",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.58.7777",
  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{Rousset:1998:CPV,
  author =       "Olivier G. Rousset and Yilong Ma and Alan C. Evans",
  title =        "Correction for Partial Volume Effects in {PET}:
                 Principle and Validation",
  journal =      j-NUCL-MED,
  volume =       "39",
  number =       "5",
  pages =        "904--911",
  month =        may,
  year =         "1998",
  CODEN =        "JNMEAQ",
  ISSN =         "0161-5505 (print), 1535-5667 (electronic)",
  ISSN-L =       "0161-5505",
  bibdate =      "Sat Sep 10 16:10:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jnm.snmjournals.org/content/39/5/904.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Nuclear Medicine",
  journal-URL =  "http://jnm.snmjournals.org/content/by/year",
  keywords =     "Benford's Law",
}

@Article{Schatte:1998:BLV,
  author =       "P. Schatte",
  title =        "On {Benford's law} to variable base",
  journal =      j-STAT-PROB-LETT,
  volume =       "37",
  number =       "4",
  pages =        "391--397",
  day =          "30",
  month =        mar,
  year =         "1998",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/S0167-7152(97)00142-9",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60F05 (60E15)",
  MRnumber =     "1624423 (99e:60072)",
  MRreviewer =   "Theodore P. Hill",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715297001429",
  abstract =     "Benford's law is studied in dependence on the base $ b
                 > 1 $. It can hold to large bases $b$ only
                 approximately. The quality of approximation is
                 estimated in cases of products and sums of random
                 variables, respectively, and in case of some
                 deterministic sequences. Always the approximation by
                 Benford's law becomes worse as $ b \to \infty $, but as
                 a rule also as $ b \to 1 + 0 $",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; Discrepancy; First-digit problem;
                 Mantissa distribution; Products of random variables;
                 Sums of random variables",
}

@Article{Simon:1998:ADC,
  author =       "Jonathan Simon",
  title =        "An Analysis of the Distribution of Combinations Chosen
                 by {UK National Lottery} Players",
  journal =      j-J-RISK-UNCERT,
  volume =       "17",
  number =       "3",
  pages =        "243--277",
  year =         "1998",
  CODEN =        "JRUNEN",
  DOI =          "https://doi.org/10.1023/A:1007786901776",
  ISSN =         "0895-5646 (print), 1573-0476 (electronic)",
  ISSN-L =       "0895-5646",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Risk and Uncertainty",
  journal-URL =  "http://link.springer.com/journal/11166",
  keywords =     "Benford's Law",
}

@Article{Slijepcevic:1998:NID,
  author =       "Sini{\v{s}}a Slijep{\v{c}}evi{\'c}",
  title =        "A Note on Initial Digits of Recurrence Sequences",
  journal =      j-FIB-QUART,
  volume =       "36",
  number =       "4",
  pages =        "305--308",
  month =        aug,
  year =         "1998",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:02:49 MDT 2011",
  bibsource =    "http://www.fq.math.ca/36-4.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/36-4/slijepcevic.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{Troll:1998:ZLC,
  author =       "G. Troll and P. beim Graben",
  title =        "{Zipf}'s law is not a consequence of the {Central
                 Limit Theorem}",
  journal =      j-PHYS-REV-E,
  volume =       "57",
  number =       "3",
  pages =        "1347--1355",
  day =          "1",
  month =        feb,
  year =         "1998",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.57.1347",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.57.1347;
                 http://pre.aps.org/abstract/PRE/v57/i2/p1347_1",
  abstract =     "It has been observed that the rank statistics of
                 string frequencies of many symbolic systems (e.g., word
                 frequencies of natural languages) follows Zipf's law in
                 good approximation. We show that, contrary to claims in
                 the literature, Zipf's law cannot be realized by the
                 central limit theorem(s). The observation that a
                 log-normal distribution of string frequencies yields an
                 approximately Zipf-like rank statistics is actually
                 misleading. Indeed, Zipf's law for the rank statistics
                 is strictly equivalent to a power law distribution of
                 frequencies. There are two natural ways to perform the
                 infinite size limit for the vocabulary. The first one
                 is the method of choice in the literature; it makes the
                 upper word length bound tend to infinity and leads in
                 the case of a multistate Bernoulli process via a
                 central limit theorem to a log-normal frequency
                 distribution. An alternative and for text samples
                 actually better realizable way is to make the lower
                 frequency bound tend to zero. This limit procedure
                 leads to a power law distribution and hence to Zipf's
                 law --- at least for Bernoulli processes and to a very
                 good approximation for natural languages where it
                 passes the $ \chi^2 $ test. For the Bernoulli case we
                 will give a heuristic proof.",
  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",
}

@Book{Wirsching:1998:DSG,
  author =       "G{\"u}nther J. Wirsching",
  title =        "The dynamical system generated by the $ 3 n + 1 $
                 function",
  volume =       "1681",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vii + 158",
  year =         "1998",
  ISBN =         "3-540-63970-5 (softcover)",
  ISBN-13 =      "978-3-540-63970-1 (softcover)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  LCCN =         "QA3 .L28 no. 1681",
  bibdate =      "Mon Nov 21 08:00:54 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNM,
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/97051329-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/97051329-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Sequences (Mathematics); Combinatorial probabilities;
                 Convergence",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  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",
  MRnumber =     "K60xx",
  bibdate =      "Sat Feb 16 14:32:14 2013",
  bibsource =    "https://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",
  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 =     "Manuel {Perera Dom{\'\i}nguez} and Juan David
                 {Ayll{\'o}n Burguillo}",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Regional Science",
}

@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 =          "https://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 =    "https://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{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 =          "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Sep 10 06:09:31 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "17 Feb 1999",
}

@Article{Egghe:1999:RLZ,
  author =       "L. Egghe",
  title =        "Research: 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 =          "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "17 Feb 1999",
}

@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 =          "https://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 =    "https://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",
}

@Book{Gigerenzer:1999:SHM,
  author =       "Gerd Gigerenzer and Peter M. Todd",
  title =        "Simple heuristics that make us smart",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xv + 416",
  year =         "1999",
  ISBN =         "0-19-512156-2",
  ISBN-13 =      "978-0-19-512156-8",
  LCCN =         "BD260 .G54 1999",
  bibdate =      "Sat Sep 10 11:19:26 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Evolution and cognition",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0640/98051084-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0640/98051084-t.html;
                 http://www.loc.gov/catdir/enhancements/fy0726/98051084-b.html",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Heuristic",
  tableofcontents = "The ABC Research Group \\
                 I. The Research Agenda \\
                 1. Fast and Frugal Heuristics: The Adaptive Toolbox /
                 Gerd Gigerenzer and Peter M. Todd \\
                 II. Ignorance-Based Decision Making \\
                 2. The Recognition Heuristic: How Ignorance Makes Us
                 Smart / Daniel G. Goldstein and Gerd Gigerenzer \\
                 3. Can Ignorance Beat the Stock Market? / Bernhard
                 Borges et al. \\
                 III. One-Reason Decision Making \\
                 4. Betting on One Good Reason: The Take The Best
                 Heuristic / Gerd Gigerenzer and Daniel G. Goldstein \\
                 5. How Good Are Simple Heuristics? / Jean Czerlinski,
                 Gerd Gigerenzer, and Daniel G. Goldstein \\
                 6. Why Does One-Reason Decision Making Work? A Case
                 Study in Ecological Rationality / Laura Martignon and
                 Ulrich Hoffrage \\
                 7. When Do People Use Simple Heuristics, and How Can We
                 Tell? / J{\"o}rg Rieskamp and Ulrich Hoffrage \\
                 8. Bayesian Benchmarks for Fast and Frugal Heuristics /
                 Laura Martignon and Kathryn Blackmond Laskey \\
                 IV. Beyond Choice: Memory, Estimation, and
                 Categorization \\
                 9. Hindsight Bias: A Price Worth Paying for Fast and
                 Frugal Memory / Ulrich Hoffrage and Ralph Hertwig \\
                 10. Quick Estimation: Letting the Environment Do the
                 Work / Ralph Hertwig, Ulrich Hoffrage, and Laura
                 Martignon \\
                 11. Categorization by Elimination: Using Few Cues to
                 Choose / Patricia M. Berretty, Peter M. Todd, and Laura
                 Martignon \\
                 V. Social Intelligence \\
                 12. How Motion Reveals Intention: Categorizing Social
                 Interactions / Philip W. Blythe, Peter M. Todd, and
                 Geoffrey F. Miller \\
                 13. From Pride and Prejudice to Persuasion: Satisficing
                 in Mate Search / Peter M. Todd and Geoffrey F. Miller
                 \\
                 14. Parental Investment by Simple Decision Rules /
                 Jennifer Nerissa Davis and Peter M. Todd \\
                 VI. A Look Around, A Look Back, A Look Ahead \\
                 15. Demons versus Heuristics in Artificial
                 Intelligence, Behavioral Ecology, and Economics / Adam
                 S. Goodie et al. \\
                 16. What We Have Learned (So Far) / Peter M. Todd and
                 Gerd Gigerenzer \\
                 References \\
                 Name Index \\
                 Subject Index",
}

@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 =          "https://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 =    "https://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/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
  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 =    "https://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",
}

@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 =          "https://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 =    "https://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",
}

@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 =    "https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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 =          "https://doi.org/10.1142/S0218348X99000025",
  ISSN =         "0218-348X",
  ISSN-L =       "0218-348X",
  bibdate =      "Wed Feb 27 07:11:42 2013",
  bibsource =    "https://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",
  journal-URL =  "http://www.worldscientific.com/loi/fractals",
  keywords =     "Zipf's Law",
}

@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 =    "https://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{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 =          "https://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 =    "https://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",
}

@Book{Miller:1999:JFM,
  author =       "Irwin Miller and Marylees Miller",
  title =        "{John E. Freund}'s mathematical statistics",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Sixth",
  pages =        "xii + 624",
  year =         "1999",
  ISBN =         "0-13-123613-X",
  ISBN-13 =      "978-0-13-123613-4",
  LCCN =         "QA276 .M4726 1999",
  bibdate =      "Thu Oct 13 07:00:13 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1928--",
  remark =       "Revised edition of John E. Freund,
                 \booktitle{Mathematical statistics}, 5th edition,
                 1992.",
  subject =      "Mathematical statistics",
}

@Article{Nigrini:1999:AVD,
  author =       "Mark J. Nigrini",
  title =        "Adding value with digital analysis",
  journal =      "The Internal Auditor: Journal of the {Institute of
                 Internal Auditors}",
  volume =       "56",
  number =       "1",
  pages =        "21--23",
  month =        "????",
  year =         "1999",
  CODEN =        "ITAUAB",
  ISSN =         "0020-5745",
  ISSN-L =       "0020-5745",
  bibdate =      "Sat Feb 16 18:56:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nigrini:1999:IGY,
  author =       "Mark J. Nigrini",
  title =        "{I've} Got Your Number: How a Mathematical Phenomenon
                 Can Help {CPAs} Uncover Fraud and Other
                 Irregularities",
  journal =      j-J-ACCOUNTANCY,
  volume =       "187",
  number =       "2",
  pages =        "79--83",
  month =        may,
  year =         "1999",
  CODEN =        "JACYAD",
  ISSN =         "0021-8448 (print), 1945-0729 (electronic)",
  ISSN-L =       "0021-8448",
  bibdate =      "Mon Nov 14 16:31:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm;
                 http://www.journalofaccountancy.com/issues/1999/may/nigrini.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accountancy",
  journal-URL =  "http://www.journalofaccountancy.com/",
}

@Article{Nigrini:1999:PPF,
  author =       "Mark J. Nigrini",
  title =        "Peculiar patterns of first digits",
  journal =      j-IEEE-POT,
  volume =       "18",
  number =       "2",
  pages =        "24--27",
  month =        apr # "\slash " # may,
  year =         "1999",
  CODEN =        "IEPTDF",
  DOI =          "https://doi.org/10.1109/45.755849",
  ISSN =         "0278-6648 (print), 1558-1772 (electronic)",
  ISSN-L =       "0278-6648",
  bibdate =      "Mon Nov 21 22:18:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Despite seeing numbers all the time only occasionally
                 would one say that a list of numbers seems odd. For
                 this to occur, the numbers are typically highly rounded
                 or implausible (too much of a coincidence). However
                 digit pattern analysis, using a computer, can produce
                 valuable findings not revealed at a mere glance. The
                 most widely cited paper on digit frequencies was
                 published by Frank Benford in 1938. With powerful,
                 low-cost personal computers, Benford's law can help us
                 to efficiently test the integrity of data. The first
                 step is to assess whether Benford's law should apply to
                 the data. If the data is expected to conform, then
                 Benford's law becomes the expected distribution.
                 Conformity means that the actual distribution closely
                 approximates the expected distribution",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Potentials",
}

@Article{Okuyama:1999:ZLI,
  author =       "K. Okuyama and M. Takayasu and H. Takayasu",
  title =        "{Zipf}'s law in income distribution of companies",
  journal =      j-PHYSICA-A,
  volume =       "269",
  number =       "1",
  pages =        "125--131",
  day =          "1",
  month =        jul,
  year =         "1999",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(99)00086-2",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437199000862",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Growth rate of assets; Income distribution; Zipf's
                 Law",
}

@Article{Piqueira:1999:ZLO,
  author =       "J. R. C. Piqueira and L. H. A. Monteiro and T. M. C.
                 de Magalh{\~a}es and R. T. Ramos and R. B. Sassi and E.
                 G. Cruz",
  title =        "{Zipf's Law} Organizes a Psychiatric Ward",
  journal =      j-J-THEOR-BIOL,
  volume =       "198",
  number =       "3",
  pages =        "439--443",
  day =          "7",
  month =        jun,
  year =         "1999",
  CODEN =        "JTBIAP",
  DOI =          "https://doi.org/10.1006/jtbi.1999.0923",
  ISSN =         "0022-5193 (print), 1095-8541 (electronic)",
  ISSN-L =       "0022-5193",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022519399909232",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225193",
  keywords =     "Zipf's Law",
}

@Article{Stanley:1999:SUR,
  author =       "H. Eugene Stanley",
  title =        "Scaling, universality, and renormalization: Three
                 pillars of modern critical phenomena",
  journal =      j-REV-MOD-PHYS,
  volume =       "71",
  number =       "2",
  pages =        "S358--S366",
  month =        mar,
  year =         "1999",
  CODEN =        "RMPHAT",
  DOI =          "https://doi.org/10.1103/RevModPhys.71.S358",
  ISSN =         "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
  ISSN-L =       "0034-6861",
  bibdate =      "Wed May 23 10:16:18 MDT 2012",
  bibsource =    "http://rmp.aps.org/toc/RMP/v71/i2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/revmodphys1990.bib",
  URL =          "http://link.aps.org/doi/10.1103/RevModPhys.71.S358;
                 http://rmp.aps.org/abstract/RMP/v71/i2/pS358_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Reviews of Modern Physics",
  journal-URL =  "http://rmp.aps.org/browse",
}

@Article{Vandewalle:1999:ZAF,
  author =       "N. Vandewalle and M. Ausloos",
  title =        "The $n$-{Zipf} analysis of financial data series and
                 biased data series",
  journal =      j-PHYSICA-A,
  volume =       "268",
  number =       "1--2",
  pages =        "240--249",
  day =          "1",
  month =        jun,
  year =         "1999",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(99)00031-X",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037843719900031X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Vardi:1999:PCS,
  author =       "Ilan Vardi",
  title =        "Premiers chiffres significatifs et nombres
                 alg{\'e}briques. ({French}) [Significant leading digits
                 and algebraic numbers]",
  journal =      j-C-R-ACAD-SCI-I,
  volume =       "328",
  number =       "9",
  pages =        "749--754",
  month =        may,
  year =         "1999",
  CODEN =        "CASMEI",
  DOI =          "https://doi.org/10.1016/S0764-4442(99)80265-1",
  ISSN =         "0764-4442 (print), 1778-3577 (electronic)",
  ISSN-L =       "0764-4442",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0764444299802651",
  abstract =     "I show that there is a meromorphic continuation of $
                 \sigma \log_\beta n / a < \log_\beta a n^{-s} $ to the
                 whole plane if and only if $ \beta $ is a Pisot number,
                 $ \alpha \in Q(\beta) $, and either the second largest
                 conjugate of $ \beta $ is real or the conjugate of $
                 \alpha $ corresponding to the second largest conjugate
                 of $ \beta $ is positive.",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes rendus de l'Acad{\'e}mie des sciences.
                 S{\'e}rie I, Math{'e}matique",
  keywords =     "Benford's Law",
  language =     "French",
}

@Article{Walthoe:1999:LNO,
  author =       "Jon Walthoe and Robert Hunt and Mike Pearson",
  title =        "Looking out for number one",
  journal =      "Plus Magazine",
  volume =       "??",
  number =       "??",
  pages =        "1--9",
  month =        sep,
  year =         "1999",
  DOI =          "????",
  bibdate =      "Mon Feb 18 06:59:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Published by the University of Cambridge Millennium
                 Mathematics Project.",
  URL =          "http://plus.maths.org/issue9/features/benford/2pdf/index.html/op.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Banyard:2000:NAF,
  author =       "Peter Banyard",
  title =        "A New Aid for Fraud Detection",
  journal =      "Credit Management: journal of the {Institute of Credit
                 Management}",
  volume =       "??",
  number =       "??",
  address =      "Stamford College, UK",
  pages =        "32--33",
  month =        mar,
  year =         "2000",
  DOI =          "",
  ISSN =         "0265-2099",
  ISSN-L =       "0265-2099",
  bibdate =      "Thu Oct 13 08:34:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  abstract =     "A simple mathematical curiosity, discovered about a
                 century ago, may well prove a surefire way of sniffing
                 out swindlers. Benford's Law was just an observation
                 until the theory that proved it was discovered 3 years
                 ago. It seems unlikely, but about 30\% of numbers start
                 with the digit one. Another 18\% start with the digit 2
                 and only 4.6\% start with 9. It would be quite easy to
                 build a Benford fraud buster into any analysis of
                 figures, while it remains extremely difficult to
                 produce an artificial set of figures that will comply
                 with the law.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "I cannot find a Web site for this journal, or for its
                 archives, despite extensive searching.",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@InProceedings{Burns:2000:SSR,
  author =       "B. D. Burns",
  editor =       "Niels A. Taatgen and Hedderik van Rijn",
  booktitle =    "{Proceedings of the 31st Annual Conference of the
                 Cognitive Science Society 2009 (CogSci 2009):
                 Amsterdam, Netherlands, 29 July--1 August 2009}",
  title =        "Sensitivity to Statistical Regularities: People
                 (Largely) Follow {Benford's Law}",
  publisher =    "Cognitive Science Society",
  address =      "Austin, TX, USA",
  pages =        "2872--2877",
  year =         "2010",
  ISBN =         "1-61567-407-1",
  ISBN-13 =      "978-1-61567-407-7",
  LCCN =         "????",
  bibdate =      "Sat Sep 10 10:53:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Drake:2000:CAA,
  author =       "Philip D. Drake and Mark 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 =          "https://doi.org/10.1016/S0748-5751(00)00008-7",
  ISSN =         "0748-5751 (print), 1873-1996 (electronic)",
  ISSN-L =       "0748-5751",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://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",
  abstract =     "This case introduces students to Benford's Law and
                 Digital Analysis, which can be used as an analytical
                 procedure and fraud detection tool. Digital Analysis
                 (DA) is the analysis of digit and number patterns of a
                 data set. Actual digit frequencies in a data set are
                 compared to the expected frequencies according to
                 Benford's Law [Benford, F. (1938). The law of the
                 anomalous numbers, Proceedings of the American
                 Philosophical Society, 78, 551 572.]. Minor differences
                 suggest that the data have passed a reasonableness
                 test, while major differences signal possible financial
                 statement mis-statements. After describing Benford's
                 Law and the basic {DA} tests, the case requires
                 auditing students to download {DA} software and the
                 actual accounts payable file of a software company from
                 a designated Internet site. Students then, (1) analyse
                 the data using three {DA} tests as an analytical
                 procedure in an external audit context, and (2) graph
                 and a report the results and audit-related conclusions.
                 The teaching note includes the actual findings from the
                 audit of that data set and guidance on using the case
                 in an auditing course.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accounting Education",
  keywords =     "Benford's Law",
}

@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 =    "https://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{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;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://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",
}

@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 =          "https://doi.org/10.1145/337180.337629",
  bibdate =      "Sat Feb 16 18:28:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Lowe:2000:BLF,
  author =       "R. Lowe",
  title =        "{Benford's Law} and fraud detection",
  journal =      "Chartered Accountants Journal of New Zealand",
  volume =       "79",
  number =       "10",
  pages =        "32--36",
  month =        "????",
  year =         "2000",
  DOI =          "",
  ISSN =         "1172-9929",
  ISSN-L =       "1172-9929",
  bibdate =      "Thu Oct 13 08:55:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.nzica.com/journalarchive.aspx",
  remark =       "No archives online before 2012. Library of Congress
                 says that publication ceased in July 2005 at volume 84,
                 number 6.",
}

@Article{Lowe:2000:WBL,
  author =       "R. Lowe",
  title =        "When {Benford's Law} is broken",
  journal =      "Chartered Accountants Journal of New Zealand",
  volume =       "79",
  number =       "11",
  pages =        "24--27",
  month =        "????",
  year =         "2000",
  DOI =          "",
  ISSN =         "1172-9929",
  ISSN-L =       "1172-9929",
  bibdate =      "Thu Oct 13 08:55:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.nzica.com/journalarchive.aspx",
  remark =       "No archives online before 2012. Library of Congress
                 says that publication ceased in July 2005 at volume 84,
                 number 6.",
}

@TechReport{Nigrini:2000:CA,
  author =       "Mark J. Nigrini",
  title =        "Continuous Auditing",
  type =         "Preprint",
  institution =  "Ernst \& Young Center for Auditing Research and
                 Advanced Technology, University of Kansas",
  address =      "Lawrence, KS, USA",
  pages =        "23",
  day =          "30",
  month =        aug,
  year =         "2000",
  bibdate =      "Sat Feb 16 18:57:40 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://aaahq.org/audit/midyear/01midyear/papers/nigrini_continuous_audit.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Book{Nigrini:2000:DAT,
  author =       "Mark J. Nigrini",
  title =        "Digital analysis tests and statistics: using digit and
                 number patterns and Benford's law to detect errors,
                 biases, fraud, irregularities, and processing
                 inefficiencies",
  publisher =    "Nigrini Institute Inc.",
  address =      "Allen, TX, USA",
  pages =        "242",
  year =         "2000",
  LCCN =         "????",
  bibdate =      "Sat Jan 23 07:53:08 MST 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Nigrini:2000:DAU,
  author =       "Mark John Nigrini",
  title =        "Digital analysis using {Benford}'s law: tests and
                 statistics for auditors",
  publisher =    "Global Audit Publications",
  address =      "Vancouver, BC, Canada",
  edition =      "Second",
  pages =        "xvii + 278",
  year =         "2000",
  ISBN =         "189449709 (??invalid ISBN??)",
  ISBN-13 =      "189449709 (??invalid ISBN??)",
  LCCN =         "????",
  bibdate =      "Tue Nov 22 20:48:29 MST 2011",
  bibsource =    "amicus.nlc-bnc.ca:210/NL;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Data processing; Auditing;
                 Statistical methods; Analyse num{\'e}rique;
                 Informatique; V{\'e}rification comptable; M{\'e}thodes
                 statistiques",
}

@Article{Padmanabhan:2000:CAD,
  author =       "Venkata N. Padmanabhan and Lili Qiu",
  title =        "The content and access dynamics of a busy {Web} server
                 (poster session)",
  journal =      j-SIGMETRICS,
  volume =       "28",
  number =       "1",
  pages =        "122--123",
  month =        jun,
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/339331.339405",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Thu Jun 26 11:31:11 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "We study the MSNBC Web site, one of the busiest in the
                 Internet today. We analyze the dynamics of content
                 creation and modification as well as client accesses.
                 Our key findings are (a) files tend to change little
                 upon modification, (b) a small set of files get
                 modified repeatedly, (c) file popularity follows a
                 Zipf-like distribution with an $ \alpha $ much larger
                 than reported in previous, proxy-based studies, and (d)
                 there is significant temporal stability in file
                 popularity but not much stability in the domains from
                 which popular content is accessed. We discuss
                 implications of these findings.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
}

@Book{Sole:2000:SLH,
  author =       "Ricard Vicente Sol{\'e} and Brian Goodwin",
  title =        "Signs of Life: How Complexity Pervades Biology",
  publisher =    pub-BASIC-BOOKS,
  address =      pub-BASIC-BOOKS:adr,
  pages =        "xi + 322",
  year =         "2000",
  ISBN =         "0-465-01927-7, 0-465-01928-5 (paperback)",
  ISBN-13 =      "978-0-465-01927-4, 978-0-465-01928-1 (paperback)",
  LCCN =         "QH501 .S65 2000",
  bibdate =      "Thu Feb 28 09:59:50 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Mandelbrot; Zipf's law",
  tableofcontents = "Nonlinearity, chaos, and emergence \\
                 Order, complexity, disorder \\
                 Genetic networks, cell differentiation, and development
                 \\
                 Physiology on the edge of chaos \\
                 Brain dynamics \\
                 Ants, brains, and chaos \\
                 The Baroque of nature \\
                 Life on the edge of catastrophe \\
                 Evolution and extinction \\
                 Fractal cities and market crashes",
}

@Article{Soliman:2000:BPP,
  author =       "Ahmed A. Soliman",
  title =        "{Bayes} Prediction in a {Pareto} Lifetime Model with
                 Random Sample Size",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "49",
  number =       "1",
  pages =        "51--62",
  month =        "????",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2681255",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Thu Jan 22 18:10:23 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i326257;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-2000.bib",
  URL =          "http://www.jstor.org/stable/2681255",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
}

@Article{Stanley:2000:SIU,
  author =       "H. E. Stanley and L. A. N. Amaral and P. Gopikrishnan
                 and P. Ch. Ivanov and T. H. Keitt and V. Plerou",
  title =        "Scale invariance and universality: organizing
                 principles in complex systems",
  journal =      j-PHYSICA-A,
  volume =       "281",
  number =       "1--4",
  pages =        "60--68",
  day =          "15",
  month =        jun,
  year =         "2000",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00195-3",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 28 09:52:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437100001953",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Tapp:2000:UTD,
  author =       "D. J. Tapp and D. B. Burg",
  title =        "Using technology to detect fraud",
  journal =      "{Pennsylvania CPA} Journal",
  volume =       "71",
  number =       "4",
  pages =        "20--23",
  month =        "????",
  year =         "2000",
  ISSN =         "0746-1062",
  ISSN-L =       "0746-1062",
  bibdate =      "Thu Oct 13 09:05:22 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.picpa.org/keep-informed/pennsylvania-cpa-journal",
  keywords =     "Benford's Law",
  remark =       "No archives online before 2014.",
}

@Article{Tolle:2000:DDS,
  author =       "Charles R. Tolle and Joanne L. Budzien and Randall A.
                 Laviolette",
  title =        "Do dynamical systems follow {Benford}'s law?",
  journal =      j-CHAOS,
  volume =       "10",
  number =       "2",
  pages =        "331--336",
  month =        "????",
  year =         "2000",
  CODEN =        "CHAOEH",
  DOI =          "https://doi.org/10.1063/1.166498",
  ISSN =         "1054-1500",
  ISSN-L =       "1054-1500",
  bibdate =      "Mon Nov 14 17:35:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2000Chaos..10..331T;
                 http://link.aip.org/link/chaoeh/v10/i2/p331/s1;
                 http://link.aip.org/link/doi/10.1063/1.166498",
  abstract =     "Data compiled from a variety of sources follow
                 Benford's law, which gives a monotonically decreasing
                 distribution of the first digit (1 through 9). We
                 examine the frequency of the first digit of the
                 coordinates of the trajectories generated by some
                 common dynamical systems. One-dimensional cellular
                 automata fulfill the expectation that the frequency of
                 the first digit is uniform. The molecular dynamics of
                 fluids, on the other hand, provides trajectories that
                 follow Benford's law. Finally, three chaotic systems
                 are considered: Lorenz, H{\'e}non, and R{\"o}ssler. The
                 Lorenz system generates trajectories that follow
                 Benford's law. The H{\'e}non system generates
                 trajectories that resemble neither the uniform
                 distribution nor Benford's law. Finally, the
                 R{\"o}ssler system generates trajectories that follow
                 the uniform distribution for some parameters choices,
                 and Benford's law for others.",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos (Woodbury, NY)",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/chaos",
  xxpages =      "331--337",
}

@Article{Urzua:2000:SET,
  author =       "Carlos M. Urz{\'u}a",
  title =        "A simple and efficient test for {Zipf}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "66",
  number =       "3",
  pages =        "257--260",
  day =          "1",
  month =        mar,
  year =         "2000",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/S0165-1765(99)00215-3",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176599002153",
  ZMnumber =     "0951.91059",
  abstract =     "This paper presents a simple and locally optimal test
                 for Zipf's law. Its use is illustrated in the case of
                 the largest US metropolitan areas. An objection to the
                 general relevance of that law is also presented.",
  acknowledgement = ack-nhfb,
  classmath =    "91B82 (Statistical methods in economics) 91B74 (Models
                 of real-world systems)",
  fjournal =     "Economics Letters",
  keywords =     "rank-size law; Zipf's law",
}

@Article{Vogt:2000:BGS,
  author =       "W. Vogt",
  title =        "{Benford's Gesetz: Steuer- und Budgets{\"u}ndern auf
                 der Spur --- Zahlen l{\"u}gen nichts}. ({German})
                 [{Benford's Law}: tax and budget sinners lying on the
                 track --- Numbers do not lie]",
  journal =      "Schweizer Versicherung",
  volume =       "9",
  number =       "??",
  pages =        "27--29",
  month =        "????",
  year =         "2000",
  DOI =          "????",
  bibdate =      "Mon Feb 18 06:57:07 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.schweizerversicherung.ch/de/archiv_suche",
  language =     "German",
  remark =       "No ISSN assigned. Not found in journal archive on 18
                 February 2013.",
}

@Article{York:2000:ATB,
  author =       "D. York",
  title =        "Auditing Technique --- {Benford}'s law",
  journal =      j-ACCOUNTANCY,
  volume =       "126",
  number =       "1283",
  pages =        "126--??",
  month =        "????",
  year =         "2000",
  CODEN =        "ACTYAD",
  ISSN =         "0001-4664",
  ISSN-L =       "0001-4664",
  bibdate =      "Wed Nov 23 11:30:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountancy",
  journal-URL =  "https://www.cchdaily.co.uk/magazine",
  remark =       "No archives online before 2014",
}

@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 =          "https://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 =    "https://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{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 =          "https://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;
                 https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  xxjournal =    "Legal Times",
}

@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;
                 https://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",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@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 =    "https://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{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 =          "https://doi.org/10.3390/e3030191",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Thu Feb 28 10:55:45 2013",
  bibsource =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. Mat. Complut.",
  fjournal =     "Revista Matem{\'a}tica Complutense",
}

@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 =          "https://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 =    "https://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",
}

@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 =    "https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comments and extensions in \cite[Chapter
                 19]{Miller:2015:BLT}.",
  URL =          "http://link.springer.com/article/10.1023/A%3A1008363415314",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Imaging and Vision: JMIV",
}

@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 =          "https://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 =    "https://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",
}

@Article{Kretschmer:2001:RAI,
  author =       "Hildrun Kretschmer and Ronald Rousseau",
  title =        "Research: Author inflation leads to a breakdown of
                 {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "52",
  number =       "8",
  pages =        "610--614",
  month =        "????",
  year =         "2001",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.1118",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:41:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "27 Apr 2001",
}

@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 =          "https://doi.org/10.1007/PL00011657",
  ISSN =         "0219-1377",
  bibdate =      "Sat Nov 12 11:00:30 2011",
  bibsource =    "https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@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 =    "https://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{Nigrini:2001:DAU,
  author =       "Mark Nigrini",
  title =        "Digital Analysis Using {Benford's} Law: Tests and
                 Statistics for Auditors",
  journal =      j-EDPACS,
  volume =       "28",
  number =       "9",
  pages =        "1--2",
  month =        "????",
  year =         "2001",
  CODEN =        "EDPCDF",
  DOI =          "https://doi.org/10.1201/1079/43266.28.9.20010301/30389.4",
  ISSN =         "0736-6981 (print), 1936-1009 (electronic)",
  ISSN-L =       "0736-6981",
  bibdate =      "Sat Jan 07 09:08:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1201/1079/43266.28.9.20010301/30389.4",
  acknowledgement = ack-nhfb,
  fjournal =     "EDPACS",
  onlinedate =   "21 Dec 2006",
}

@Article{Pietronero:2001:EUD,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "Explaining the uneven distribution of numbers in
                 nature: the laws of {Benford} and {Zipf}",
  journal =      j-PHYSICA-A,
  volume =       "293",
  number =       "1--2",
  pages =        "297--304",
  day =          "1",
  month =        apr,
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00633-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2001PhyA..293..297P;
                 http://www.sciencedirect.com/science/article/pii/S0378437100006336",
  abstract =     "The distribution of first digits in numbers series
                 obtained from very different origins shows a marked
                 asymmetry in favor of small digits that goes under the
                 name of Benford's law. We analyze in detail this
                 property for different data sets and give a general
                 explanation for the origin of the Benford's law in
                 terms of multiplicative processes. We show that this
                 law can be also generalized to series of numbers
                 generated from more complex systems like the catalogs
                 of seismic activity. Finally, we derive a relation
                 between the generalized Benford's law and the popular
                 Zipf's law which characterize the rank order statistics
                 and has been extensively applied to many problems
                 ranging from city population to linguistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Reed:2001:PZO,
  author =       "William J. Reed",
  title =        "The {Pareto}, {Zipf} and other power laws",
  journal =      j-ECONOM-LETT,
  volume =       "74",
  number =       "1",
  pages =        "15--19",
  day =          "20",
  month =        dec,
  year =         "2001",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/S0165-1765(01)00524-9",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176501005249",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@TechReport{Scott:2001:BLE,
  author =       "P. D. Scott and M. Fasli",
  title =        "{Benford's Law}: An Empirical Investigation and a
                 Novel Explanation",
  type =         "CSM Technical Report",
  number =       "349",
  institution =  "Department of Computer Science, University Essex",
  address =      "Colchester, UK",
  day =          "26",
  month =        oct,
  year =         "2001",
  bibdate =      "Tue Nov 22 21:05:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.essex.ac.uk/csee/research/publications/technicalreports/2001/CSM-349.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Sellke:2001:CVT,
  author =       "Thomas Sellke and M. J. Bayarri and James O. Berger",
  title =        "Calibration of $p$ Values for Testing Precise Null
                 Hypotheses",
  journal =      j-AMER-STAT,
  volume =       "55",
  number =       "1",
  pages =        "62--71",
  month =        feb,
  year =         "2001",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/000313001300339950",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  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/i326511;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amstat.org/publications/tas/Sellke.htm;
                 http://www.jstor.org/stable/2685531;
                 http://www.tandfonline.com/doi/abs/10.1198/000313001300339950",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Snyder:2001:SAO,
  author =       "Mark A. Snyder and James H. Curry and Anne M.
                 Dougherty",
  title =        "Stochastic aspects of one-dimensional discrete
                 dynamical systems: {Benford}'s law",
  journal =      j-PHYS-REV-E,
  volume =       "64",
  number =       "2",
  pages =        "026222:1--026222:5",
  month =        aug,
  year =         "2001",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.64.026222",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Mon Nov 14 17:44:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2001PhRvE..64b6222S;
                 http://pre.aps.org/abstract/PRE/v64/i2/e026222",
  abstract =     "Benford's law owes its discovery to the ``Grubby Pages
                 Hypothesis,'' a 19th century observation made by Simon
                 Newcomb that the beginning pages of logarithm books
                 were grubbier than the last few pages, implying that
                 scientists referenced the values toward the front of
                 the books more frequently. If a data set satisfies
                 Benford's law, then its significant digits will have a
                 logarithmic distribution, which favors smaller
                 significant digits. In this article we demonstrate two
                 ways of creating discrete one-dimensional dynamical
                 systems that satisfy Benford's law. We also develop a
                 numerical simulation methodology that we use to study
                 dynamical systems when analytical results are not
                 readily available.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  pagecount =    "5",
}

@InCollection{Solomon:2001:SPZ,
  author =       "Sorin Solomon and Peter Richmond",
  booktitle =    "Economics with heterogeneous interacting agents
                 ({Marseille}, 2000)",
  title =        "Stability of {Pareto--Zipf} law in non-stationary
                 economies",
  volume =       "503",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "141--159",
  year =         "2001",
  MRclass =      "91B28 (91B62)",
  MRnumber =     "1838925",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Econom. and Math. Systems",
  acknowledgement = ack-nhfb,
}

@Article{Zanette:2001:VTC,
  author =       "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
  title =        "Vertical transmission of culture and the distribution
                 of family names",
  journal =      j-PHYSICA-A,
  volume =       "295",
  number =       "1--2",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(01)00046-2",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:03:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437101000462",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Zipf's Law",
  onlinedate =   "19 February 2013",
}

@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;
                 https://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 =   "https://doi.org/10.1177/103237320200700207",
  review-url =   "http://dro.deakin.edu.au/view/DU:30012663;
                 http://www.highbeam.com/doc/1G1-97484707.html",
}

@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 (print), 2168-8745 (electronic)",
  ISSN-L =       "0883-4237",
  bibdate =      "Fri May 30 12:48:50 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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{Brown:2002:ICF,
  author =       "Philip Brown and Angeline Chua and Jason Mitchell",
  title =        "The influence of cultural factors on price clustering:
                 Evidence from {Asia Pacific} stock markets",
  journal =      "Pacific-Basin Finance Journal",
  volume =       "10",
  number =       "3",
  pages =        "307--332",
  year =         "2002",
  DOI =          "https://doi.org/10.1016/S0927-538X(02)00049-5",
  ISSN =         "0927-538X (print), 1879-0585 (electronic)",
  ISSN-L =       "0927-538X",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "13th Annual PACAP/FMA Finance Conference",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0927538X02000495",
  abstract =     "Price clustering is the tendency of prices to be
                 observed more frequently at some numbers than others.
                 It increases with haziness, or imprecision, about
                 underlying value. Most research on price clustering has
                 been conducted in Western financial markets, where
                 there is manifest preference for trading at round
                 numbers. We focus on number preferences under Chinese
                 culture. Many Chinese believe some numbers are unlucky
                 and to be avoided. For instance, the number 4 is
                 inauspicious because the Cantonese pronunciation of 4
                 is similar to the phrase to die. We first document
                 clustering of daily closing prices on six Asia Pacific
                 stock markets, three with predominantly Chinese
                 populations. Next, we fit binomial logit models within
                 these markets to estimate the association between
                 structural and economic factors, and culture, on price
                 clustering. We find some support for the influence of
                 Chinese culture and superstition on year-round number
                 preferences of traders, but it is located solely in the
                 Hong Kong market. Furthermore, in the Hong Kong market
                 Chinese culture and superstition help explain the
                 increased avoidance of the number 4 during the
                 auspicious Chinese New Year, Dragon Boat and Mid-Autumn
                 festivals.",
  acknowledgement = ack-nhfb,
  keywords =     "Attraction; Benford's Law; Haziness; Negotiation;
                 Price clustering",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Egghe:2002:DRC,
  author =       "L. Egghe and I. K. Ravichandra Rao",
  title =        "Duality revisited: {Construction} of fractional
                 frequency distributions based on two dual {Lotka}
                 laws",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "53",
  number =       "10",
  pages =        "789--801",
  month =        "????",
  year =         "2002",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.10103",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:41:59 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "11 Jun 2002",
}

@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 =          "https://doi.org/10.1142/S0219525902000468",
  ISSN =         "0219-5259",
  bibdate =      "Sat Nov 12 11:00:23 2011",
  bibsource =    "https://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{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 =          "https://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 =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://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",
  abstract =     "We study multiplicative and affine sequences of real
                 numbers defined by $ N(j + 1) = \zeta (j) N(j) + \eta
                 (j) $, where \{\zeta(j)\} and \{\eta(j)\} are sequences
                 of positive real numbers (in the multiplicative case $
                 \eta (j) = 0 $ for all $j$). We investigate the
                 conditions under which the leading digits $k$ of
                 \{N(j)\} have the following probability distribution,
                 known as Benford's Law, $ P(k) = \log_{10}((k + 1) /
                 k)$. We present two main results. First, we show that
                 contrary to the usual assumption in the literature,
                 \{\zeta(j)\} does not necessarily need to come from a
                 chaotic or independent random process for Benford's Law
                 to hold. The multiplicative driving force may be a
                 deterministic quasiperiodic or even periodic forcing.
                 Second, we give conditions under which the distribution
                 of the first digits of an affine process displays
                 Benford's Law. Our proofs use techniques from ergodic
                 theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers;
                 Multiplicative process; Scaling laws; Zipf's Law",
}

@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 =    "https://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.",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hoyle01042002,
  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",
  year =         "2002",
  DOI =          "https://doi.org/10.1093/bioinformatics/18.4.576",
  ISSN =         "1367-4803 (print), 1367-4811 (electronic)",
  ISSN-L =       "1367-4803",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bioinformatics.oxfordjournals.org/content/18/4/576.abstract",
  abstract =     "Motivation: Typical analysis of microarray data has
                 focused on spot by spot comparisons within a single
                 organism. Less analysis has been done on the comparison
                 of the entire distribution of spot intensities between
                 experiments and between organisms.Results: Here we show
                 that mRNA transcription data from a wide range of
                 organisms and measured with a range of experimental
                 platforms show close agreement with Benford's law
                 (Benford, Proc. Am. Phil. Soc., 78, 551 572, 1938) and
                 Zipf's law (Zipf, The Psycho-biology of Language: an
                 Introduction to Dynamic Philology, 1936 and Human
                 Behaviour and the Principle of Least Effort, 1949). The
                 distribution of the bulk of microarray spot intensities
                 is well approximated by a log-normal with the tail of
                 the distribution being closer to power law. The
                 variance, 2, of log spot intensity shows a positive
                 correlation with genome size (in terms of number of
                 genes) and is therefore relatively fixed within some
                 range for a given organism. The measured value of 2 can
                 be significantly smaller than the expected value if the
                 mRNA is extracted from a sample of mixed cell types.
                 Our research demonstrates that useful biological
                 findings may result from analyzing microarray data at
                 the level of entire intensity distributions. Contact:
                 david.c.hoyle@man.ac.uk",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  journal-URL =  "http://bioinformatics.oxfordjournals.org/",
  keywords =     "Zipf's Law",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  journal-URL =  "http://bioinformatics.oxfordjournals.org/",
  keywords =     "Benford's Law; mRNA transcription data",
}

@Article{Huber:2002:NMG,
  author =       "John C. Huber",
  title =        "A new model that generates {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "53",
  number =       "3",
  pages =        "209--219",
  month =        "????",
  year =         "2002",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.10025",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:02 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "28 Dec 2001",
}

@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 =          "https://doi.org/10.1016/S0026-2714(02)00031-8",
  ISSN =         "0026-2714 (print), 1872-941X (electronic)",
  ISSN-L =       "0026-2714",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
  abstract =     "Real-life systems are complex, with many independent
                 parameters which can affect the system. Their behaviour
                 can therefore be very variable. This is especially true
                 of the more involved processes which occur in
                 reliability and degradation processes. However, there
                 are some characteristics which are observed which can
                 be understood simply because they are characteristic of
                 complex systems. These include distributions that are
                 very often logarithmic rather than uniform, log normal
                 failure distributions and $ 1 g / f $ noise. A wide
                 variety of diverse examples is given to illustrate the
                 common occurrence of such observations together with
                 the underlying unifying themes. There are several basic
                 reasons for the origin of logarithmic distributions.
                 One is that they arise from multiplicative processes.
                 Another is that although basic science is often
                 introduced as linear, with non-linear effects added as
                 a correction, complex systems are often inherently
                 non-linear. This produces multiplicative effects, such
                 as harmonic generation and fractal behaviour.",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Benford's Law; Pareto distribution; Zipf's Law",
}

@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 =          "https://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 =    "https://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)",
}

@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 =    "https://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{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 =          "https://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 =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
  abstract =     "Throughout history, thinkers from mathematicians to
                 theologians have pondered the mysterious relationship
                 between numbers and the nature of reality. In this
                 fascinating book, the author tells the tale of a number
                 at the heart of that mystery: phi, or
                 1.6180339887\ldots{}. This curious mathematical
                 relationship, widely known as ``The Golden Ratio,'' was
                 discovered by Euclid more than two thousand years ago
                 because of its crucial role in the construction of the
                 pentagram, to which magical properties had been
                 attributed. Since then it has shown a propensity to
                 appear in the most astonishing variety of places, from
                 mollusk shells, sunflower florets, and rose petals to
                 the shape of the galaxy. Psychological studies have
                 investigated whether the Golden Ratio is the most
                 aesthetically pleasing proportion extant, and it has
                 been asserted that the creators of the Pyramids and the
                 Parthenon employed it. It is believed to feature in
                 works of art from Leonardo da Vinci's Mona Lisa to
                 Salvador Dali's The Sacrament of the Last Supper, and
                 poets and composers have used it in their works. It has
                 even been found to be connected to the behavior of the
                 stock market! This book is a captivating journey
                 through art and architecture, botany and biology,
                 physics and mathematics. It tells the human story of
                 numerous phi-fixated individuals, including the
                 followers of Pythagoras who believed that this
                 proportion revealed the hand of God; astronomer
                 Johannes Kepler, who saw phi as the greatest treasure
                 of geometry; such Renaissance thinkers as mathematician
                 Leonardo Fibonacci of Pisa; and such masters of the
                 modern world as Goethe, Cezanne, Bartok, and physicist
                 Roger Penrose. Wherever his quest for the meaning of
                 phi takes him, the author reveals the world as a place
                 where order, beauty, and eternal mystery will always
                 coexist.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Prelude to a number \\
                 The pitch and the pentagram \\
                 Under a star-Y-pointing pyramid? \\
                 The second treasure \\
                 Son of good nature \\
                 The divine proportion \\
                 Painters and poets have equal license \\
                 From the tiles to the heavens \\
                 Is God a mathematician?",
}

@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,
  bookpages =    "xviii + 482",
  pages =        "52--57",
  year =         "2002",
  DOI =          "https://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 =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=7814",
  acknowledgement = ack-nhfb,
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Mosimann:2002:TDE,
  author =       "James Mosimann and John Dahlberg and Nancy Davidian
                 and John Krueger",
  title =        "Terminal Digits and the Examination of Questioned
                 Data",
  journal =      j-ACCOUNT-RES,
  volume =       "9",
  number =       "2",
  pages =        "75--92",
  month =        "????",
  year =         "2002",
  CODEN =        "ARQAEZ",
  DOI =          "https://doi.org/10.1080/08989620212969",
  ISSN =         "0898-9621 (print), 1545-5815 (electronic)",
  ISSN-L =       "0898-9621",
  bibdate =      "Sat Sep 10 15:08:21 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/08989620212969",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountability in Research",
  journal-URL =  "http://www.tandfonline.com/toc/gacr20",
  keywords =     "Benford'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 =    "https://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",
}

@Misc{Popescu:2002:LNZ,
  author =       "Ioan-Iovitz Popescu",
  title =        "On the {Lavelette}'s nonlinear {Zipf}'s law",
  howpublished = "Web preprint.",
  month =        feb,
  year =         "2002",
  bibdate =      "Sat Feb 16 19:02:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://alpha2.infim.ro/~ltpd/Zipf's_Law.html",
  acknowledgement = ack-nhfb,
}

@Article{Reed:2002:GFG,
  author =       "William J. Reed and Barry D. Hughes",
  title =        "From gene families and genera to incomes and
                 {Internet} file sizes: Why power laws are so common in
                 nature",
  journal =      j-PHYS-REV-E,
  volume =       "66",
  number =       "6",
  pages =        "067103",
  month =        dec,
  year =         "2002",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.66.067103",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Wed Feb 27 06:58:05 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.66.067103",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Pareto's Law; rank-size property; Zipf's Law",
  pagecount =    "4",
}

@Article{Sandon:2002:DPC,
  author =       "F. Sandon",
  title =        "Do Populations Conform to the Law of Anomalous
                 Numbers?",
  journal =      "Population",
  volume =       "57",
  number =       "4",
  pages =        "755--761",
  month =        "????",
  year =         "2002",
  bibdate =      "Sat Sep 10 16:15:28 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.persee.fr/doc/pop_1634-2941_2002_num_57_4_18419",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.persee.fr/collection/pop",
  keywords =     "Benford's Law",
}

@Article{Sandron:2002:DPC,
  author =       "Fr{\'e}d{\'e}ric Sandron",
  title =        "Do populations conform to the {Law of Anomalous
                 Numbers}?",
  journal =      "Population",
  volume =       "57",
  number =       "4--5",
  pages =        "755--761",
  month =        "????",
  year =         "2002",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "1169-1018",
  ISSN-L =       "1169-1018",
  bibdate =      "Sat Feb 16 19:08:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translation from French by S. R. Hayford.",
  URL =          "http://www.cairn.info/article_p.php?ID_ARTICLE=POPE_204_0753",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.jstor.org/journals/11691018.html",
}

@Article{Sandron:2002:PSE,
  author =       "Fr{\'e}d{\'e}ric Sandron",
  title =        "Les populations suivent-elles la loi des nombres
                 anomaux? ({French}). [{Do} populations conform to the
                 {Law of Anomalous Numbers}?]",
  journal =      "Population ({French} edition)",
  volume =       "57",
  number =       "4--5",
  pages =        "761--768",
  month =        "????",
  year =         "2002",
  CODEN =        "POPUAQ",
  DOI =          "????",
  ISSN =         "0032-4663 (print), 1957-7966 (electronic)",
  ISSN-L =       "0032-4663",
  bibdate =      "Sat Feb 16 19:08:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2002_num_57_4_16873",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@TechReport{Seaman:2002:BLB,
  author =       "R. S. Seaman",
  title =        "{Benford}'s law and and background field errors in
                 data assimilation",
  type =         "Preprint",
  institution =  "Bureau of Meteorology Research Centre",
  address =      "Melbourne, Australia",
  month =        "????",
  year =         "2002",
  bibdate =      "Sun Feb 17 14:01:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://amm.bom.gov.au/amoj/docs/2002/seaman.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Seaman:2002:RBL,
  author =       "R. S. Seaman",
  title =        "The relevance of {Benford's Law} to background field
                 errors in data assimilation",
  journal =      "Australian Meteorological Magazine",
  volume =       "51",
  number =       "1",
  pages =        "25--33",
  month =        "????",
  year =         "2002",
  CODEN =        "AMMGAS",
  ISSN =         "0004-9743",
  ISSN-L =       "0004-9743",
  bibdate =      "Mon Nov 14 16:08:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.bom.gov.au/amm/docs/2002/seaman.pdf;
                 http://www.bom.gov.au/amm/docs/2002/seaman_hres.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Aust. Met. Mag.",
  ajournal-2 =   "Aust. Meteorol. Mag.",
  fjournal =     "Australian Meteorological Magazine",
  journal-URL =  "http://www.bom.gov.au/amm/",
}

@Article{Taylor:2002:STD,
  author =       "Rosemary N. Taylor and Damian J. McEntegart and
                 Eleanor C. Stillman",
  title =        "Statistical techniques to detect fraud and other data
                 irregularities in clinical questionnaire data",
  journal =      "Drug Information Journal",
  volume =       "36",
  number =       "1",
  pages =        "115--125",
  month =        jan,
  year =         "2002",
  DOI =          "https://doi.org/10.1177/009286150203600115",
  ISSN =         "0092-8615",
  ISSN-L =       "0092-8615",
  bibdate =      "Mon Feb 18 06:42:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.diahome.org/DIAHome/resources/content.aspx?type=eopdf&file=%2Fproductfiles%2F8357%2Fdiaj_11524.pdf????",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{VanCaneghem:2002:EMI,
  author =       "T. {Van Caneghem}",
  title =        "Earnings Management Induced by Cognitive Reference
                 Points",
  journal =      "The British Accounting Review",
  volume =       "34",
  number =       "2",
  pages =        "167--178",
  year =         "2002",
  DOI =          "https://doi.org/10.1006/bare.2002.0190",
  ISSN =         "0890-8389 (print), 1095-8347 (electronic)",
  ISSN-L =       "0890-8389",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0890838902901903",
  abstract =     "Previous studies (Carslaw, 1988; Thomas, 1989;
                 Niskanen \& Keloharju, 2000) have shown that companies'
                 managers tend to round-up the first digits of reported
                 earnings (i.e. for companies reporting profits).
                 According to Carslaw (1988), this type of behaviour is
                 inspired by the existence of the so-called `\$1.99'
                 phenomenon where a price of \$1.99 is perceived as
                 being abnormally lower than one of \$2.00. In the
                 current study, we try to determine whether managers of
                 UK-listed companies also engage in this type of
                 `earnings rounding-up behaviour'. Analogous to the
                 earlier studies, our study compares observed and
                 expected frequencies for the second-from-the-left digit
                 in reported earnings. Our results suggest that managers
                 of UK-listed companies tend to round-up reported
                 pre-tax income, in a way that increases the first digit
                 by one, when they are faced with a nine in the
                 second-from-the-left position for this particular
                 earnings measure. The major contribution of the current
                 study is that it introduces discretionary accruals in
                 this line of research. Discretionary accruals were
                 estimated using both the Jones model (1991) and the
                 modified Jones model as proposed by Dechow et al.
                 (1995). Our results clearly suggest that discretionary
                 accruals are used in order to round-up reported
                 earnings figures. Moreover, discretionary accruals
                 enabled us to increase the power of the tests used in
                 previous studies.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Wallace:2002:AQD,
  author =       "W. A. Wallace",
  title =        "Assessing the quality of data used for benchmarking
                 and decision making",
  journal =      "Journal of Government Financial Management",
  volume =       "51",
  number =       "3",
  pages =        "16--22",
  month =        "????",
  year =         "2002",
  DOI =          "",
  ISSN =         "1533-1385",
  ISSN-L =       "1533-1385",
  bibdate =      "Thu Oct 13 09:17:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.agacgfm.org/Resources/Journal-of-Government-Financial-Management/Archives.aspx",
  keywords =     "Benford's Law",
  remark =       "Online archive access, even for journal metadata,
                 requires member account!",
}

@Article{Yeh:2002:SMZ,
  author =       "Hsiaw-Chan Yeh",
  title =        "Six multivariate {Zipf} distributions and their
                 related properties",
  journal =      j-STAT-PROB-LETT,
  volume =       "56",
  number =       "2",
  pages =        "131--141",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/S0167-7152(01)00149-3",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "62H10",
  MRnumber =     "1881166 (2002m:62084)",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715201001493",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Zipf's Law",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@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 =    "https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@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;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "https://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 =          "https://doi.org/10.1016/S0378-4371(03)00526-0",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Fibonacci numbers; Number theory; prime
                 numbers; Probability theory; Statistical physics and
                 thermodynamics",
}

@Article{Das:2003:RRE,
  author =       "Somnath Das and Huai Zhang",
  title =        "Rounding-up in reported {EPS}, behavioral thresholds,
                 and earnings management",
  journal =      "Journal of Accounting and Economics",
  volume =       "35",
  number =       "1",
  pages =        "31--50",
  year =         "2003",
  DOI =          "https://doi.org/10.1016/S0165-4101(02)00096-4",
  ISSN =         "0165-4101 (print), 1879-1980 (electronic)",
  ISSN-L =       "0165-4101",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165410102000964",
  abstract =     "Reported earnings per share (EPS) are frequently
                 rounded to the nearest cent. This paper provides
                 evidence that firms manipulate earnings so that they
                 can round-up and report one more cent of EPS.
                 Specifically, we examine the digit immediately right of
                 the decimal in the calculated {EPS} number expressed in
                 cents. Evidence is presented that firms are more likely
                 to round-up when managers ex ante expect rounding-up to
                 meet analysts forecasts, report positive profits, or
                 sustain recent performance. Further investigation
                 provides evidence that working capital accruals are
                 used to round-up EPS.",
  acknowledgement = ack-nhfb,
  keywords =     "Behavioral threshold; Benford's Law; Earnings
                 management; Earnings per share (EPS); Rounding",
}

@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 =          "https://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 =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
  abstract =     "Benford's law assigns the probability $ \log_{10}(1 +
                 1 / d) $ for finding a number starting with specific
                 significant digit $d$. We show that exponentially
                 distributed numbers obey this law approximatively,
                 i.e., within bounds of $ 0.03$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; Exponential distribution; Significant
                 digit 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 =          "https://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 =    "https://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",
}

@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 =    "https://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{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 =          "https://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 =    "https://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: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 =          "https://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 =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$29.95",
  URL =          "http://www.loc.gov/catdir/description/prin031/2002192453.html",
  abstract =     "Among the myriad of constants that appear in
                 mathematics, $ \pi $, $e$, and $i$ are the most
                 familiar. Following closely behind is $ \gamma $ or
                 gamma, a constant that arises in many mathematical
                 areas yet maintains a profound sense of mystery. In a
                 tantalizing blend of history and mathematics, Julian
                 Havil takes the reader on a journey through logarithms
                 and the harmonic series, the two defining elements of
                 gamma, toward the first account of gamma's place in
                 mathematics. Introduced by the Swiss mathematician
                 Leonhard Euler (1707--1783), who figures prominently in
                 this book, gamma is defined as the limit of the sum of
                 $ 1 + 1 / 2 + 1 / 3 + \cdots + 1 / n - \ln n$, the
                 numerical value being $ 0.5772156 \ldots {}$. But
                 unlike its more celebrated colleagues $ \pi $ and $e$,
                 the exact nature of gamma remains a mystery --- we
                 don't even know if it can be expressed as a fraction.
                 Among the numerous topics that arise during this
                 historical odyssey into fundamental mathematical ideas
                 are the Prime Number Theorem and the most important
                 open problem in mathematics today, the Riemann
                 Hypothesis (though no proof of either is offered!).
                 Sure to be popular with not only students and
                 instructors but all math aficionados, Gamma takes us
                 through countries, centuries, lives, and works,
                 unfolding along the way the stories of some remarkable
                 mathematics from some remarkable mathematicians.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword / xv \\
                 Acknowledgements / xvii \\
                 Introduction / xix \\
                 Chapter One: The Logarithmic Cradle / 1 \\
                 1.1 A Mathematical Nightmare- and an Awakening / 1 \\
                 1.2 The Baron's Wonderful Canon / 4 \\
                 1.3 A Touch of Kepler / 11 \\
                 1.4 A Touch of Euler / 13 \\
                 1.5 Napier's Other Ideas / 16 \\
                 Chapter Two: The Harmonic Series / 21 \\
                 2.1 The Principle / 21 \\
                 2.2 Generating Function for $H_n$ / 21 \\
                 2.3 Three Surprising Results / 22 \\
                 Chapter Three: Sub-Harmonic Series / 27 \\
                 3.1 A Gentle Start / 27 \\
                 3.2 Harmonic Series of Primes / 28 \\
                 3.3 The Kempner Series / 31 \\
                 3.4 Madelung's Constants / 33 \\
                 Chapter Four: Zeta Functions / 37 \\
                 4.1 Where $n$ Is a Positive Integer / 37 \\
                 4.2 Where $x$ Is a Real Number / 42 \\
                 4.3 Two Results to End With / 44 \\
                 Chapter Five: Gamma's Birthplace / 47 \\
                 5.1 Advent / 47 \\
                 5.2 Birth / 49 \\
                 Chapter Six: The Gamma Function / 53 \\
                 6.1 Exotic Definitions / 53 \\
                 6.2 Yet Reasonable Definitions / 56 \\
                 6.3 Gamma Meets Gamma / 57 \\
                 6.4 Complement and Beauty / 58 \\
                 Chapter Seven: Euler's Wonderful Identity / 61 \\
                 7.1 The All-Important Formula / 61 \\
                 7.2 And a Hint of Its Usefulness / 62 \\
                 Chapter Eight: A Promise Fulfilled / 65 \\
                 Chapter Nine: What Is Gamma Exactly? / 69 \\
                 9.1 Gamma Exists / 69 \\
                 9.2 Gamma Is What Number? 739.3 A Surprisingly Good
                 Improvement / 75 \\
                 9.4 The Germ of a Great Idea / 78 \\
                 Chapter Ten: Gamma as a Decimal / 81 \\
                 10.1 Bernoulli Numbers / 81 \\
                 10.2 Euler--Maclaurin Summation / 85 \\
                 10.3 Two Examples / 86 \\
                 10.4 The Implications for Gamma / 88 \\
                 Chapter Eleven: Gamma as a Fraction / 91 \\
                 11.1 A Mystery / 91 \\
                 11.2 A Challenge / 91 \\
                 11.3 An Answer / 93 \\
                 11.4 Three Results / 95 \\
                 11.5 Irrationals / 95 \\
                 11.6 Pell's Equation Solved / 97 \\
                 11.7 Filling the Gaps / 98 \\
                 11.8 The Harmonic Alternative / 98 \\
                 Chapter Twelve: Where Is Gamma? / 101 \\
                 12.1 The Alternating Harmonic Series Revisited / 101
                 \\
                 12.2 In Analysis / 105 \\
                 12.3 In Number Theory / 112 \\
                 12.4 In Conjecture / 116 \\
                 12.5 In Generalization / 116 \\
                 Chapter Thirteen: It's a Harmonic World / 119 \\
                 13.1 Ways of Means / 119 \\
                 13.2 Geometric Harmony / 121 \\
                 13.3 Musical Harmony / 123 \\
                 13.4 Setting Records / 125 \\
                 13.5 Testing to Destruction / 126 \\
                 13.6 Crossing the Desert / 127 \\
                 13.7 Shuffiing Cards / 127 \\
                 13.8 Quicksort / 128 \\
                 13.9 Collecting a Complete Set / 130 \\
                 13.10 A Putnam Prize Question / 131 \\
                 13.11 Maximum Possible Overhang / 132 \\
                 13.12 Worm on a Band / 133 \\
                 13.13 Optimal Choice / 134 \\
                 Chapter Fourteen: It's a Logarithmic World / 139 \\
                 14.1 A Measure of Uncertainty / 139 \\
                 14.2 Benford's Law / 145 \\
                 14.3 Continued-Fraction Behaviour / 155 \\
                 Chapter Fifteen: Problems with Primes / 163 \\
                 15.1 Some Hard Questions about Primes / 163 \\
                 15.2 A Modest Start / 164 \\
                 15.3 A Sort of Answer / 167 \\
                 15.4 Picture the Problem / 169 \\
                 15.5 The Sieve of Eratosthenes / 171 \\
                 15.6 Heuristics / 172 \\
                 15.7 A Letter / 174 \\
                 15.8 The Harmonic Approximation / 179 \\
                 15.9 Different-and Yet the Same / 180 \\
                 15.10 There are Really Two Questions, Not Three / 182
                 \\
                 15.11 Enter Chebychev with Some Good Ideas / 183 \\
                 15.12 Enter Riemann, Followed by Proof(s) / 186 \\
                 Chapter Sixteen: The Riemann Initiative / 189 \\
                 16.1 Counting Primes the Riemann Way / 189 \\
                 16.2 A New Mathematical Tool / 191 \\
                 16.3 Analytic Continuation / 191 \\
                 16.4 Riemann's Extension of the Zeta Function / 193 \\
                 16.5 Zeta's Functional Equation / 193 \\
                 16.6 The Zeros of Zeta / 193 \\
                 16.7 The Evaluation of $\Pi(x)$ and $\pi(x)$ / 196 \\
                 16.8 Misleading Evidence / 197 \\
                 16.9 The Von Mangoldt Explicit Formula --- and How It
                 Is Used to Prove the Prime Number Theorem / 200 \\
                 16.10 The Riemann Hypothesis / 202 \\
                 16.11 Why Is the Riemann Hypothesis Important? / 204
                 \\
                 16.12 Real Alternatives / 206 \\
                 16.13 A Back Route to Immortality-Partly Closed / 207
                 \\
                 16.14 Incentives, Old and New / 210 \\
                 16.15 Progress / 213 \\
                 Appendix A: The Greek Alphabet / 217 \\
                 Appendix B: Big Oh Notation / 219 \\
                 Appendix C: Taylor Expansions / 221 \\
                 C.1 Degree 1 / 221 \\
                 C.2 Degree 2 / 221 \\
                 C.3 Examples / 223 \\
                 C.4 Convergence / 223 \\
                 Appendix D: Complex Function Theory / 225 \\
                 D.1 Complex Differentiation / 225 \\
                 D.2 Weierstrass Function / 230 \\
                 D.3 Complex Logarithms / 231 \\
                 D.4 Complex Integration / 232 \\
                 D.5 A Useful Inequality / 235 \\
                 D.6 The Indefinite Integral / 235 \\
                 D.7 The Seminal Result / 237 \\
                 D.8 An Astonishing Consequence / 238 \\
                 D.9 Taylor Expansions-and an Important Consequence /
                 239 \\
                 D.10 Laurent Expansions --- and Another Important
                 Consequence / 242 \\
                 D.11 The Calculus of Residues / 245 \\
                 D.12 Analytic Continuation / 247 \\
                 Appendix E: Application to the Zeta Function / 249 \\
                 E.1 Zeta Analytically Continued / 249 \\
                 E.2 Zeta's Functional Relationship / 253",
}

@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 =      "Wed Aug 16 07:36:50 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances and Applications in Statistics",
}

@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 =          "https://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 =    "https://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{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 =    "https://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}",
  journal-URL =  "http://www.degruyter.com/view/j/zna",
}

@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,
  bookpages =    "ix + 177",
  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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lagarias:2003:PAB,
  author =       "Jeffrey C. Lagarias",
  title =        "The $ 3 x + 1 $ problem: An annotated bibliography
                 (1963--1999) (sorted by author)",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  month =        sep,
  year =         "2003",
  bibdate =      "Sat Sep 10 12:58:10 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math/0309224",
  abstract =     "The $ 3 x + 1 $ problem concerns iteration of the map
                 on the integers given by $ T(n) = (3 n + 1) / 2 $ if
                 $n$ is odd; $ T(n) = n / 2$ if $n$ is even. The $ 3 x +
                 1$ Conjecture asserts that for every positive integer $
                 n > 1$ the forward orbit of $n$ under iteration by $T$
                 includes the integer 1. This paper is an annotated
                 bibliography of work done on the $ 3 x + 1$ problem and
                 related problems from 1963 through 1999. At present the
                 $ 3 x + 1$ Conjecture remains unsolved.",
  acknowledgement = ack-nhfb,
  pagecount =    "74",
  remark =       "At least 13 updates have been made up to
                 11-Jan-2011.",
}

@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 =    "https://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",
}

@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 =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@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 =          "https://doi.org/10.1016/S0039-3681(03)00047-5",
  ISSN =         "0039-3681 (print), 1879-2510 (electronic)",
  ISSN-L =       "0039-3681",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://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",
  abstract =     "According to a traditional view, scientific laws and
                 theories constitute algorithmic compressions of
                 empirical data sets collected from observations and
                 measurements. This article defends the thesis that, to
                 the contrary, empirical data sets are algorithmically
                 incompressible. The reason is that individual data
                 points are determined partly by perturbations, or
                 causal factors that cannot be reduced to any pattern.
                 If empirical data sets are incompressible, then they
                 exhibit maximal algorithmic complexity, maximal entropy
                 and zero redundancy. They are therefore maximally
                 efficient carriers of information about the world.
                 Since, on algorithmic information theory, a string is
                 algorithmically random just if it is incompressible,
                 the thesis entails that empirical data sets consist of
                 algorithmically random strings of digits. Rather than
                 constituting compressions of empirical data, scientific
                 laws and theories pick out patterns that data sets
                 exhibit with a certain noise.",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part
                 {A}",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00393681",
  keywords =     "Algorithmic randomness; Benford's Law; Compression;
                 Empirical data; Information; Law; Pattern",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://projecteuclid.org/info/euclid.im",
  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.",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://permalink.obvsg.at/wuw/AC03895842",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@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 =          "https://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 =    "https://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{Newby:2003:OSS,
  author =       "Gregory B. Newby and Jane Greenberg and Paul Jones",
  title =        "Open source software development and {Lotka's Law}:
                 {Bibliometric} patterns in programming",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "54",
  number =       "2",
  pages =        "169--178",
  day =          "15",
  month =        jan,
  year =         "2003",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.10177",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:09 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  note =         "See comments \cite{Burrell:2004:LEF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "10 Dec 2002",
}

@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 =          "https://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 =    "https://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{Peter:2003:ADE,
  author =       "Manfred Peter",
  title =        "The asymptotic distribution of elements in automatic
                 sequences",
  journal =      j-THEOR-COMP-SCI,
  volume =       "301",
  number =       "1 3",
  pages =        "285--312",
  year =         "2003",
  CODEN =        "TCSCDI",
  DOI =          "https://doi.org/10.1016/S0304-3975(02)00587-X",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S030439750200587X",
  abstract =     "In an automatic sequence an element need not have an
                 asymptotic density. In this paper a necessary and
                 sufficient criterion is proved for the existence of the
                 asymptotic density of a given element. If it does not
                 exist the asymptotic distribution of the element can be
                 described in terms of a function H whose graph is
                 self-similar. An algorithm is given to decide whether H
                 is piecewise continuously differentiable, and in this
                 case it can be computed effectively. Finally, it is
                 shown that the H -density of an element in an automatic
                 sequence always exists and equals its logarithmic
                 density.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "Asymptotics; Automata; Benford's Law; Density;
                 H{\"o}lder mean; Oscillating sum; Self-similarity",
}

@Article{Quick:2003:BLD,
  author =       "Reiner Quick and Matthias Wolz",
  title =        "{Benford's Law in deutschen Rechnungslegungsdaten}.
                 ({German}) [{Benford's Law} in {German} accounting
                 data]",
  journal =      "Betriebswirtschaftliche Forschung und Praxis",
  volume =       "55",
  number =       "2",
  pages =        "208--224",
  month =        "????",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0340-5370",
  ISSN-L =       "0340-5370",
  bibdate =      "Sat Dec 10 12:01:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "Betriebswirtschaftliche Forschung und Praxis ==
                 Business Research and Practice.",
}

@Article{Reed:2003:PLI,
  author =       "William J. Reed",
  title =        "The {Pareto} law of incomes---an explanation and an
                 extension",
  journal =      j-PHYSICA-A,
  volume =       "319",
  number =       "1--4",
  pages =        "469--486",
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(02)01507-8",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B70",
  MRnumber =     "1965596",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Rose:2003:TEF,
  author =       "Anna M. Rose and Jacob M. Rose",
  title =        "Turn {Excel} into a financial sleuth: an easy-to-use
                 digital analysis tool can red-flag irregularities",
  journal =      j-J-ACCOUNTANCY,
  volume =       "196",
  number =       "2",
  pages =        "58--??",
  month =        aug,
  year =         "2003",
  CODEN =        "JACYAD",
  ISSN =         "0021-8448 (print), 1945-0729 (electronic)",
  ISSN-L =       "0021-8448",
  bibdate =      "Sat Feb 16 19:07:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.journalofaccountancy.com/Issues/2003/Aug/TurnExcelIntoAFinancialSleuth",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accountancy",
  journal-URL =  "http://www.journalofaccountancy.com/",
}

@Article{Sinai:2003:SP,
  author =       "Ya. G. Sinai",
  title =        "Statistical $ (3 x + 1) $ problem",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "56",
  number =       "7",
  pages =        "1016--1028",
  month =        jul,
  year =         "2003",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.10084",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  bibdate =      "Mon Nov 21 07:52:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Dedicated to the memory of J{\"u}rgen K. Moser.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}

@InProceedings{Swanson:2003:DPF,
  author =       "David Swanson and Moon Jung Cho and John Eltinge",
  editor =       "????",
  booktitle =    "Proceedings of the Survey Research Section",
  title =        "Detecting possibly fraudulent or error-prone survey
                 data using {Benford's Law}",
  publisher =    "American Statistical Association",
  address =      "Washington, DC, USA",
  pages =        "4172--4177",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Nov 16 10:21:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amstat.org/sections/srms/proceedings/y2003/Files/JSM2003-000205.pdf.",
  acknowledgement = ack-nhfb,
}

@Article{Wales:2003:IWI,
  author =       "Elspeth Wales",
  title =        "Is it Worth Investing in Software to Combat Fraud?",
  journal =      "Computer Fraud \& Security",
  volume =       "2003",
  number =       "5",
  pages =        "6--8",
  year =         "2003",
  DOI =          "https://doi.org/10.1016/S1361-3723(03)05009-7",
  ISSN =         "1361-3723 (print), 1873-7056 (electronic)",
  ISSN-L =       "1361-3723",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1361372303050097",
  abstract =     "Despite the tendency for businesses to keep fraud to
                 themselves, the consensus is that the problem is
                 becoming worse. On the plus side though software
                 solutions that can detect potential fraudulent activity
                 are evolving in their scope and ability to
                 automatically track transactions in real-time.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InCollection{Warren:2003:DLD,
  author =       "Henry S. Warren",
  title =        "The distribution of leading digits",
  crossref =     "Warren:2003:HD",
  chapter =      "15.3",
  pages =        "264--267",
  year =         "2003",
  bibdate =      "Fri Mar 16 08:02:56 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wu:2003:IPD,
  author =       "Shuo-Jye Wu and Chun-Tao Chang",
  title =        "Inference in the {Pareto} distribution based on
                 progressive {Type II} censoring with random removals",
  journal =      j-J-APPL-STAT,
  volume =       "30",
  number =       "2",
  pages =        "163--172",
  month =        "????",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Dec 16 15:40:48 MST 2003",
  bibsource =    "https://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{Wu:2003:PDC,
  author =       "Wei Biao Wu and Chinya V. Ravishankar",
  title =        "The performance of difference coding for sets and
                 relational tables",
  journal =      j-J-ACM,
  volume =       "50",
  number =       "5",
  pages =        "665--693",
  month =        sep,
  year =         "2003",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/876638.876641",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Mon Sep 8 17:55:23 MDT 2003",
  bibsource =    "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "We characterize the performance of difference coding
                 for compressing sets and database relations through an
                 analysis of the problem of estimating the number of
                 bits needed for storing the spacings between values in
                 sets of integers. We provide analytical expressions for
                 estimating the effectiveness of difference coding when
                 the elements of the sets or the attribute fields in
                 database tuples are drawn from the uniform and Zipf
                 distributions. We also examine the case where a
                 uniformly distributed domain is combined with a Zipf
                 distribution, and with an arbitrary distribution. We
                 present limit theorems for most cases, and
                 probabilistic convergence results in other cases. We
                 also examine the effects of attribute domain reordering
                 on the compression ratio. Our simulations show
                 excellent agreement with theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@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 =    "https://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{Burrell:2004:LEF,
  author =       "Quentin L. Burrell",
  title =        "Letters to the {Editor}: Fitting {Lotka's Law}: {Some}
                 cautionary observations on a recent paper by {Newby} et
                 al. (2003)",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "55",
  number =       "13",
  pages =        "1209--1210",
  month =        nov,
  year =         "2004",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20086",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:16 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  note =         "See \cite{Newby:2003:OSS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "17 Aug 2004",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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{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 =    "https://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,
}

@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 =    "https://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 =    "https://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{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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@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 =          "https://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 =    "https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Garcia-Berthou:2004:IBT,
  author =       "Emili Garc{\'i}a-Berthou and Carles Alcaraz",
  title =        "Incongruence between test statistics and {$P$} values
                 in medical papers",
  journal =      "BMC Medical Research Methodology",
  volume =       "4",
  number =       "1",
  pages =        "1--5",
  year =         "2004",
  DOI =          "https://doi.org/10.1186/1471-2288-4-13",
  ISSN =         "1471-2288",
  ISSN-L =       "1471-2288",
  bibdate =      "Sat Sep 10 11:16:07 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Given an observed test statistic and its degrees of
                 freedom, one may compute the observed P value with most
                 statistical packages. It is unknown to what extent test
                 statistics and P values are congruent in published
                 medical papers.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://bmcmedresmethodol.biomedcentral.com/",
  keywords =     "Benford's Law; digit frequencies",
}

@Article{Geyer:2004:DFD,
  author =       "Christina Lynn Geyer and Patricia Pepple Williamson",
  title =        "Detecting fraud in data sets using {Benford's Law}",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "B33",
  number =       "1",
  pages =        "229--246",
  month =        "????",
  year =         "2004",
  CODEN =        "CSSCDB",
  DOI =          "https://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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Statist. Simulation Comput.",
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@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 (print), 1314-3395 (electronic)",
  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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
  journal-URL =  "http://ijpam.eu/",
}

@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 =    "https://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{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 =          "https://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 =    "https://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",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
}

@Book{Judson:2004:GBF,
  author =       "Horace Freeland Judson",
  title =        "The Great Betrayal: Fraud in Science",
  publisher =    "Harcourt",
  address =      "Orlando, FL, USA",
  pages =        "xiv + 463",
  year =         "2004",
  ISBN =         "0-15-100877-9",
  ISBN-13 =      "978-0-15-100877-3",
  LCCN =         "Q175.37 .J84 2004",
  bibdate =      "Sat Sep 10 12:29:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/har051/2004005906.html;
                 http://www.loc.gov/catdir/description/har051/2004005906.html;
                 http://www.loc.gov/catdir/samples/har051/2004005906.html;
                 http://www.loc.gov/catdir/toc/ecip0416/2004005906.html",
  acknowledgement = ack-nhfb,
  remark =       "No mention of Benford's Law or first digit phenomenon,
                 but nevertheless relevant for applications of Benford's
                 Law to detection of fraud in data.",
  subject =      "Fraud in science",
  tableofcontents = "Preface / xi \\
                 Prologue / 1 \\
                 1: A Culture of Fraud / 9 \\
                 2: What's It Like? A Typology of Scientific Fraud / 43
                 \\
                 3: Patterns of Complicity: Recent Cases / 98 \\
                 4: Hard to Measure, Hard to Define: The Incidence of
                 Scientific Fraud and the Struggle Over Its Definition /
                 155 \\
                 5: The Baltimore Affair / 191 \\
                 6: The Problems of Peer Review / 244 \\
                 7: Authorship, Ownership: The Problems of Credit,
                 Plagiarism, and Property / 287 \\
                 8: The Rise of Open Publication on the Internet / 325
                 \\
                 9: Laboratory to Law: The Problems of Institutions When
                 Misconduct is Charged / 369 \\
                 Epilogue / 404 \\
                 Notes / 419 \\
                 Index / 447",
}

@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 =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{