%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.31",
%%% date = "16 March 2012",
%%% time = "08:08:04 MST",
%%% filename = "benfords-law.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "29683 16680 72562 716636",
%%% 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;
%%% Heaps' Law; Law of Anomalous Numbers; Lotka's
%%% Law; 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), 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
%%% 280 different journals from accounting,
%%% auditing, astronomy, biology, botany,
%%% business, chaos theory, chemistry, computer
%%% science, conflict resolution, criminology,
%%% demographics, drug design, economics,
%%% electoral studies, engineering, finance,
%%% forensics, geography, human resources,
%%% imaging science, library science, marketing,
%%% mathematics, medicine, networking,
%%% neuroscience, nuclear science, operations
%%% research, physics, probability, psychology,
%%% signal processing, and statistics, 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 decimal
%%% digit p is roughly log10(1 + (1 / p)): that
%%% is, approximately 0.301, 0.176, 0.125, 0.097,
%%% 0.079, 0.067, 0.058, 0.051, and 0.046 for
%%% digits 1 through 9, instead of the expected
%%% 1/9 ~= 0.111 for values taken from a uniform
%%% distribution of random numbers.
%%%
%%% Another common statement of Benford's Law is
%%% that the probability that a decimal number
%%% representing a measured value begins with a
%%% nonzero digit not greater than p is log10(1 +
%%% p), that is, approximately 0.301, 0.477,
%%% 0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and
%%% 1.000 for digits 1 through 9.
%%%
%%% For the second digits, the probabilities are
%%% determined by the formula (see
%%% Todter:2009:BLI)
%%%
%%% sum(q = 1:9) log10(1 + 1 / (10*q + p)),
%%%
%%% that is, approximately 0.120, 0.114, 0.109,
%%% 0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and
%%% 0.085, for second decimal digits p = 0
%%% through 9.
%%%
%%% Probabilities for later digits are even
%%% closer: see entries Newcomb:1881:NFU,
%%% Feldstein:1976:CED, and Todter:2009:BLI.
%%%
%%% Benford's Law is not restricted to decimal
%%% numbers: for base b (as long as b is not
%%% huge, according to entry Schatte:1998:BLV),
%%% just change the 10 values to b in the
%%% previous formulas. Here are some results for
%%% selected bases commonly used in computers,
%%% showing the probability of the first (D1) or
%%% second (D2) digit (first index) for base b
%%% (second index):
%%%
%%% P[D1, 2]: 1.000
%%% P[D2, 2]: 0.585, 0.415
%%%
%%% P[D1, 4]: 0.500, 0.292, 0.208
%%% P[D2, 4]: 0.304, 0.261, 0.230, 0.206
%%%
%%% P[D1, 8]: 0.333, 0.195, 0.138, 0.107,
%%% 0.088, 0.074, 0.064
%%% P[D2, 8]: 0.151, 0.141, 0.133, 0.126, 0.120,
%%% 0.115, 0.110, 0.105
%%%
%%% P[D1, 10]: 0.301, 0.176, 0.125, 0.097,
%%% 0.079, 0.067, 0.058, 0.051, 0.046
%%% P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100,
%%% 0.097, 0.093, 0.090, 0.088, 0.085
%%%
%%% P[D1, 16]: 0.250, 0.146, 0.104, 0.080,
%%% 0.066, 0.056, 0.048, 0.042, 0.038,
%%% 0.034, 0.031, 0.029, 0.027, 0.025,
%%% 0.023
%%% P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066,
%%% 0.065, 0.064, 0.062, 0.061, 0.060,
%%% 0.059, 0.058, 0.057, 0.056, 0.055,
%%% 0.054
%%%
%%% A small filter applied to the 1990 US Census
%%% data in the Project Gutenberg file
%%% uscen902.txt reports these frequencies of
%%% first and second digits for the 5148 integer
%%% values with at least 3 digits:
%%%
%%% F[D1]: 0.298, 0.215, 0.113, 0.082,
%%% 0.098, 0.056, 0.055, 0.034, 0.049
%%% F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100,
%%% 0.122, 0.076, 0.073, 0.066, 0.130
%%%
%%% For the 110 numbers in the atomic weights
%%% section of the GNU units utility data file,
%%% units.dat, we have
%%%
%%% F[D1]: 0.391, 0.309, 0.045, 0.036,
%%% 0.055, 0.036, 0.036, 0.036, 0.055
%%% F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145,
%%% 0.145, 0.055, 0.055, 0.091, 0.082
%%%
%%% From a snapshot of the country-area section
%%% of the US CIA World Factbook
%%%
%%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html
%%%
%%% taken at 18 November 2011, we find 1505
%%% numbers with these frequencies:
%%%
%%% F[D1]: 0.312, 0.275, 0.100, 0.067,
%%% 0.058, 0.062, 0.046, 0.029, 0.050
%%% F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062,
%%% 0.067, 0.075, 0.067, 0.083, 0.075
%%%
%%% From the country-population section
%%%
%%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html
%%%
%%% of that book, including only the 163 values
%%% of 1,000,000 or larger, we find
%%%
%%% F[D1]: 0.301, 0.202, 0.092, 0.135,
%%% 0.055, 0.067, 0.055, 0.037, 0.055
%%% F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098,
%%% 0.123, 0.086, 0.043, 0.049, 0.092
%%%
%%% From the section with the infant mortality
%%% rates per 1000 births,
%%%
%%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html
%%%
%%% there are 208 values with at least 4 digits,
%%% with these frequencies:
%%%
%%% F[D1]: 0.361, 0.293, 0.043, 0.072,
%%% 0.062, 0.087, 0.038, 0.014, 0.029
%%% F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077,
%%% 0.077, 0.106, 0.067, 0.043, 0.053
%%%
%%% In the 2010 annual financial report for IBM
%%% Corporation (its hundredth year of business)
%%%
%%% ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf
%%%
%%% there are 6126 numbers of two or more digits
%%% that do not look like year dates (19xx and
%%% 20xx), and they have these digit frequencies:
%%%
%%% F[D1]: 0.333, 0.160, 0.163, 0.086,
%%% 0.068, 0.053, 0.047, 0.045, 0.046
%%% F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085,
%%% 0.095, 0.079, 0.074, 0.079, 0.068
%%%
%%% For the first 100,000 primes, we have
%%%
%%% F[D1]: 0.311, 0.091, 0.090, 0.087,
%%% 0.086, 0.085, 0.084, 0.083, 0.082
%%% F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078,
%%% 0.078, 0.078, 0.079, 0.078, 0.078
%%%
%%% For the Fibonacci numbers, f(n), which
%%% satisfy the recurrence f(n) = f(n-1) + f(n-2)
%%% with f(1) = f(2) = 1, using the first 10000
%%% such numbers (the last of which has 2091
%%% digits), we find for the 9994 f(n) values
%%% with at least two digits these frequencies:
%%%
%%% F[D1]: 0.301, 0.176, 0.125, 0.097,
%%% 0.079, 0.067, 0.058, 0.051, 0.046
%%% F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100,
%%% 0.097, 0.094, 0.090, 0.088, 0.085
%%%
%%% If we take the same set of Fibonacci numbers,
%%% we find these frequencies for values output
%%% in base 4:
%%%
%%% F[D1]: 0.500, 0.292, 0.208
%%% F[D2]: 0.303, 0.262, 0.230, 0.205
%%%
%%% The Fibonacci numbers, and the members of
%%% many other such sequences, can be proved
%%% mathematically to obey Benford's Law exactly
%%% (see entries Raimi:1976:FDP, Berger:2011:BLS,
%%% and Berger:2011:BTB).
%%%
%%% 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, and Corazza:2010:CFM, 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).
%%%
%%% At version 1.30, the year coverage looked like
%%% this:
%%%
%%% 1881 ( 1) 1925 ( 1) 1969 ( 11)
%%% 1882 ( 0) 1926 ( 1) 1970 ( 7)
%%% 1883 ( 0) 1927 ( 1) 1971 ( 2)
%%% 1884 ( 0) 1928 ( 2) 1972 ( 4)
%%% 1885 ( 0) 1929 ( 1) 1973 ( 7)
%%% 1886 ( 0) 1930 ( 0) 1974 ( 10)
%%% 1887 ( 0) 1931 ( 0) 1975 ( 10)
%%% 1888 ( 0) 1932 ( 1) 1976 ( 10)
%%% 1889 ( 0) 1933 ( 0) 1977 ( 4)
%%% 1890 ( 0) 1934 ( 1) 1978 ( 7)
%%% 1891 ( 0) 1935 ( 1) 1979 ( 4)
%%% 1892 ( 0) 1936 ( 1) 1980 ( 5)
%%% 1893 ( 0) 1937 ( 0) 1981 ( 8)
%%% 1894 ( 0) 1938 ( 2) 1982 ( 5)
%%% 1895 ( 0) 1939 ( 0) 1983 ( 1)
%%% 1896 ( 1) 1940 ( 0) 1984 ( 10)
%%% 1897 ( 0) 1941 ( 0) 1985 ( 7)
%%% 1898 ( 0) 1942 ( 0) 1986 ( 5)
%%% 1899 ( 0) 1943 ( 1) 1987 ( 10)
%%% 1900 ( 0) 1944 ( 1) 1988 ( 10)
%%% 1901 ( 0) 1945 ( 2) 1989 ( 9)
%%% 1902 ( 0) 1946 ( 1) 1990 ( 5)
%%% 1903 ( 0) 1947 ( 0) 1991 ( 8)
%%% 1904 ( 0) 1948 ( 2) 1992 ( 8)
%%% 1905 ( 0) 1949 ( 2) 1993 ( 5)
%%% 1906 ( 0) 1950 ( 2) 1994 ( 2)
%%% 1907 ( 0) 1951 ( 0) 1995 ( 8)
%%% 1908 ( 0) 1952 ( 0) 1996 ( 6)
%%% 1909 ( 0) 1953 ( 1) 1997 ( 7)
%%% 1910 ( 0) 1954 ( 1) 1998 ( 8)
%%% 1911 ( 0) 1955 ( 1) 1999 ( 10)
%%% 1912 ( 1) 1956 ( 0) 2000 ( 8)
%%% 1913 ( 1) 1957 ( 5) 2001 ( 12)
%%% 1914 ( 0) 1958 ( 1) 2002 ( 11)
%%% 1915 ( 1) 1959 ( 1) 2003 ( 22)
%%% 1916 ( 1) 1960 ( 1) 2004 ( 17)
%%% 1917 ( 1) 1961 ( 2) 2005 ( 39)
%%% 1918 ( 0) 1962 ( 1) 2006 ( 33)
%%% 1919 ( 0) 1963 ( 1) 2007 ( 28)
%%% 1920 ( 1) 1964 ( 1) 2008 ( 31)
%%% 1921 ( 0) 1965 ( 4) 2009 ( 44)
%%% 1922 ( 1) 1966 ( 3) 2010 ( 43)
%%% 1923 ( 0) 1967 ( 2) 2011 ( 43)
%%% 1924 ( 0) 1968 ( 3) 2012 ( 2)
%%%
%%% Article: 496
%%% Book: 46
%%% InBook: 1
%%% InCollection: 12
%%% InProceedings: 17
%%% Misc: 5
%%% PhdThesis: 5
%%% Proceedings: 4
%%% TechReport: 17
%%% Unpublished: 3
%%%
%%% Total entries: 606
%%%
%%% Data for this bibliography have been
%%% collected from
%%%
%%% * the University of Utah Mathematics
%%% Department bibliography archives
%%%
%%% * the TeX User Group bibliography
%%% archives
%%%
%%% * the Karlsruhe Computer Science
%%% bibliography archives
%%%
%%% * the Karlsruhe virtual catalog at
%%% http://www.ubka.uni-karlsruhe.de/kvk_en.html
%%%
%%% * the US Library of Congress catalog at
%%% http://catalog.loc.gov/
%%%
%%% * the author's cattobib utility, which
%%% provides Z39.50 interfaces to many
%%% large libraries around the world, at
%%% http://www.math.utah.edu/pub/cattobib/
%%%
%%% * the American Institute of Physics
%%% Scitation database at
%%% http://scitation.aip.org/search_scitation
%%%
%%% * the American Physical Society PROLA
%%% database at
%%% http://publish.aps.org/search
%%%
%%% * the American Mathematical Society
%%% MathSciNet database at
%%% http://ams.rice.edu/mathscinet/search.html
%%%
%%% * the Bulletin of the Atomic Scientists
%%% (archives available, albeit inconveniently,
%%% via http://books.google.com/ and
%%% http://bos.sagepub.com/search)
%%%
%%% * the Canadian Journal of Physics
%%% database at
%%% http://www.nrcresearchpress.com/search/advanced
%%%
%%% * the European Mathematical Society
%%% Zentralblatt fuer Mathematik database
%%% at http://zb.msri.org/ZMATH/zmath/en/
%%%
%%% * the Europhysics journal archive at
%%% http://www.europhysicsnews.org/
%%%
%%% * the JSTOR database at
%%% http://www.jstor.org/
%%%
%%% * the Nature journal archive at
%%% http://www.nature.com/search/
%%%
%%% * the journal archives of the National
%%% Academy of Science at
%%% http://www.pnas.org/
%%%
%%% * the Project Euclid archives at
%%% http://projecteuclid.org/
%%%
%%% * the SAO/NASA Astrophysics Data System at
%%% http://adsabs.harvard.edu/
%%%
%%% * the Science journal archive at
%%% http://www.sciencemag.org/search
%%%
%%% * the SPIRES high-energy physics
%%% literature database at the Stanford
%%% Linear Accelerator at Stanford
%%% University at
%%% http://www.slac.stanford.edu/spires/hep/search/
%%%
%%% * the Springer journal database at
%%% http://www.springer.com/?SGWID=0-102-13-0-0
%%%
%%% * the Wiley journal database at
%%% http://onlinelibrary.wiley.com/
%%%
%%% * many online library catalogs, including
%%% those of the British Library, the
%%% Karlsruhe Virtual Library catalog, the
%%% Oxford University Library, the University of
%%% California library system, and the US
%%% Library of Congress.
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
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"\let \k = \c" #
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)}\fi" #
"\ifx \undefined \cprime \def \cprime{$'$} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" #
"\ifx \undefined \polhk \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}}\fi" #
"\ifx \undefined \url \input{path.sty} \fi"
}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACCOUNTANCY = "Accountancy: The journal of the {Institute of
Chartered Accountants in England and Wales}"}
@String{j-ACCOUNT-RES = "Accountability in Research"}
@String{j-ACCOUNT-REV = "The Accounting Review"}
@String{j-ACTA-ARITHMETICA = "Acta Arithmetica"}
@String{j-ADV-APPL-STAT = "Advances and Applications in Statistics"}
@String{j-ADV-COMPLEX-SYST = "Advances in Complex Systems"}
@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}
@String{j-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-ANN-APPL-PROBAB = "Annals of Applied Probability"}
@String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"}
@String{j-ANN-PROBAB = "Annals of Probability"}
@String{j-ANN-STAT = "Annals of Statistics"}
@String{j-APPL-ECON-LETT = "Applied Economics Letters"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-AQUAT-BOT = "Aquatic Botany"}
@String{j-ASLIB-PROC = "ASLIB Proceedings"}
@String{j-ASTROPART-PHYS = "Astroparticle Physics"}
@String{j-AUDITING = "Auditing: A Journal of Practice \& Theory"}
@String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"}
@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BIOINFORMATICS = "Bioinformatics"}
@String{j-BIOMETRIKA = "Biometrika"}
@String{j-BRAIN-COGN = "Brain and Cognition"}
@String{j-BULL-INST-MATH-STAT = "Bulletin --- Institute of Mathematical
Statistics"}
@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-ACAD-SCI-I = "Comptes rendus de l'Acad{\'e}mie des
sciences. S{\'e}rie I, Math{\'e}matique"}
@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-CHIN-PHYS-LETT = "Chinese Physics Letters"}
@String{j-COGNITION = "Cognition"}
@String{j-COLLOQ-MATH = "Colloquium Mathematicum"}
@String{j-COMM-PURE-APPL-MATH = "Communications on Pure and Applied
Mathematics (New York)"}
@String{j-COMM-STAT = "Communications in Statistics"}
@String{j-COMM-THEOR-PHYS = "Communications in Theoretical Physics"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-NET-AMSTERDAM = "Computer Networks (Amsterdam, Netherlands:
1999)"}
@String{j-COMP-SURV = "ACM Computing Surveys"}
@String{j-COMPOS-MATH = "Compositio Mathematica"}
@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}
@String{j-COMPUTING = "Computing: Archiv f{\"u}r Informatik und
Numerik"}
@String{j-CONTEMP-PHYS = "Contemporary Physics"}
@String{j-DEC-SUPP-SYS = "Decision Support Systems"}
@String{j-DEMOGRAPHY = "Demography"}
@String{j-DEUTSCH-MATH-V = "Jber. Deutsch. Math.--Verein"}
@String{j-DISCRETE-CONTIN-DYN-SYST = "Discrete and Continuous Dynamical Systems.
Series A"}
@String{j-DISCRETE-MATH = "Discrete Mathematics"}
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%%% ====================================================================
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%%% ====================================================================
%%% 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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2369148",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
author-dates = "March 12, 1835--July 11, 1909",
fjournal = "American Journal of Mathematics",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''. The article
contains no references to earlier work.",
remark-2 = "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are
the earliest citations of Newcomb's work that I have
yet found in connection with Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Simon_Newcomb",
}
@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 = "http://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}.",
}
@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 = "http://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",
bibdate = "Thu Nov 24 10:49:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper is reported in \cite{Newman:2005:PLP} to be
the first discovery of {\em Zipf's Law\/} in connection
with city populations (see \cite{Zipf:1932:SSP}). See
also \cite{Estoup:1916:GSM}.",
URL = "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122",
acknowledgement = ack-nhfb,
ajournal = "Petermanns Geogr. Mitteilung",
ajournal-2 = "Petermanns Geogr. Mitt.",
language = "German",
}
@Article{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 = "http://dx.doi.org/10.1007/BF01475864",
ISSN = "0025-5831",
ISSN-L = "0025-5831",
bibdate = "Sun Nov 13 10:54:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Ann.",
fjournal = "Mathematische Annalen",
language = "German",
}
@Book{Estoup:1916:GSM,
author = "J. B. Estoup",
title = "Gammes St{\'e}nographiques: m{\'e}thode \& exercices
pour l'acquisition de la vitesse ({French})
[Stenographic ranges: method and exercises for
achieving speed]",
publisher = "Institut St{\'e}nographique de France",
address = "Paris, France",
edition = "Fourth",
pages = "151",
year = "1916",
LCCN = "????",
bibdate = "Thu Nov 24 14:24:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This on shorthand writing is the earliest known
publication of the power-law distribution of word
frequencies, generally credited to
\cite{Zipf:1932:SSP}.",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
language = "French",
}
@Article{Franel:1917:PTL,
author = "J. Franel",
title = "{\`A} propos des tables de logarithmes. ({French})
[{On} tables of logarithms]",
journal = "Festschrift Naturforschenden der Gesellschaft in
Z{\"u}rich Vierteljahrsschrift",
volume = "62",
number = "??",
pages = "286--295",
month = "????",
year = "1917",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 10:09:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Boring:1920:LNL,
author = "Edwin G. Boring",
title = "The Logic of the Normal Law of Error in Mental
Measurement",
journal = j-AMER-J-PSYCHOLOGY,
volume = "31",
number = "1",
pages = "1--33",
month = jan,
year = "1920",
CODEN = "AJPCAA",
ISSN = "0002-9556 (print), 1939-8298 (electronic)",
ISSN-L = "0002-9556",
bibdate = "Thu Dec 01 21:35:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/1413989",
acknowledgement = ack-nhfb,
fjournal = "The American journal of psychology",
remark = "A citation search in Google Scholar on 1-Dec-2011
found this article as the only one citing Newcomb's
work \cite{Newcomb:1881:NFU} before it was brought to
wider view by Raimi's frequently-cited paper
\cite{Raimi:1976:FDP}. Boring's article has only brief
mention of Newcomb's work, and then solely in
connection with the believed randomness of digits of
transcendental numbers.",
}
@InCollection{Macaulay:1922:PLG,
author = "F. R. Macaulay",
editor = "W. C. Mitchell",
booktitle = "Income in the {United States}: Its Amount and
Distribution: 1909--1919",
title = "{Pareto}'s law and the general problem of mathematical
describing the frequency of distribution of income",
publisher = "National Bureau of Economic Research",
address = "New York, NY, USA",
pages = "??--??",
year = "1922",
LCCN = "????",
bibdate = "Fri Nov 25 09:06:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{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 = "http://dx.doi.org/10.1098/rstb.1925.0002",
ISSN = "0962-8436",
ISSN-L = "0962-8436",
bibdate = "Tue Nov 15 10:45:15 2011",
bibsource = "http://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",
month = dec,
year = "1926",
CODEN = "JWASA3",
ISSN = "0043-0439",
bibdate = "Thu Nov 24 14:36:11 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This is the earliest known publication on the
phenomenon known as Zipf's Law, here applied to
publication counts of chemists and physicists. Lotka's
Law (a term possibly first used in
\cite{Zipf:1949:HBP}) says that the number of authors
producing $n$ publications is about $1 / n^2$ of the
number producing only one. This `law' seems to have
been misunderstood and misapplied in other fields; see
\cite{Potter:1981:LLR}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Washington Academy of Sciences",
keywords = "Lotka's Law",
}
@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",
bibdate = "Wed Nov 23 12:29:25 2011",
bibsource = "http://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",
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 = "http://dx.doi.org/10.1126/science.67.1733.300]",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Fri Nov 25 09:04:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Science",
}
@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",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Wed Nov 23 12:16:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2331941",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
}
@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",
bibdate = "Fri Nov 25 09:02:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/310585;
http://www.jstor.org/journals/00730688.html",
acknowledgement = ack-nhfb,
}
@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;
http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper (reprinted in \cite{Bradford:1985:SIS})
introduces an observation later known as Bradford's
Law: there are exponentially-diminishing returns of
extending a search for references in journals.",
URL = "http://en.wikipedia.org/wiki/Bradford%27s_law",
acknowledgement = ack-nhfb,
}
@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 = "http://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",
}
@Book{Moon:1936:SBI,
author = "Parry Moon",
title = "The Scientific Basis of Illuminating Engineering",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xi + 608",
year = "1936",
LCCN = "TH7703 .M65",
bibdate = "Mon Nov 14 10:11:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law",
remark = "See pages 420ff.",
}
@Article{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",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
author-dates = "1883--December 4, 1948",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
xxURL = "http://en.wikipedia.org/wiki/Frank_Benford",
ZMnumber = "JFM 64.0555.03; Zbl 0018.26502",
}
@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",
bibdate = "Wed Nov 23 14:27:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper, which immediately follows Benford's
\cite{Benford:1938:LAN} in this journal issue, is
reported in \cite[p. 197]{Logan:1978:FDP} to have been
of considerable interest to scientists involved in
secret nuclear physics work in World War II. That is
how Benford's paper ``in a journal of rather limited
circulation and not usually read by mathematicians''
came to be noticed by physicists.",
URL = "http://www.jstor.org/stable/984803",
acknowledgement = ack-nhfb,
}
@Article{Benford:1943:PAG,
author = "Frank Benford",
title = "The Probable Accuracy of the General Physical
Constants",
journal = j-PHYS-REV,
volume = "63",
number = "5--6",
pages = "212--212",
month = mar,
year = "1943",
CODEN = "PHRVAO",
DOI = "http://dx.doi.org/10.1103/PhysRev.63.212",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Mon Nov 21 21:52:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.63.212",
acknowledgement = ack-nhfb,
fjournal = "Physical Review",
}
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See later work \cite{Logan:1978:FDP}, and severe
criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Nature",
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 = "http://dx.doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "{Beihefte zum Assekuranzjahrbuch}",
acknowledgement = ack-nhfb,
author-dates = "1886--",
keywords = "Benford--Furlan Law",
language = "German",
}
@Article{Geiringer:1948:RVF,
author = "Hilda Geiringer",
title = "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz
der Statistik: Eine Untersuchung {\"u}ber die metrische
Interdependenz der sozialen Erscheinungen}. ({German})
[{The} {Law of Harmony} in statistics: an investigation
of the metrical interdependence of social phenomena]",
journal = j-J-AM-STAT-ASSOC,
volume = "43",
number = "242",
pages = "325--328",
month = jun,
year = "1948",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon Nov 14 09:42:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "See \cite{Furlan:1946:HSU}.",
URL = "http://www.jstor.org/stable/2280379",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
}
@Article{Hsu:1948:ESM,
author = "E. H. Hs{\"u}",
title = "An Experimental Study on ``Mental Numbers'' and a New
Application",
journal = j-J-GEN-PSYCH,
volume = "38",
number = "1",
pages = "57--67",
month = "????",
year = "1948",
CODEN = "JGPSAY",
DOI = "http://dx.doi.org/10.1080/00221309.1948.9711768",
ISSN = "0022-1309 (print), 1940-0888 (electronic)",
ISSN-L = "0022-1309",
bibdate = "Sat Jan 07 09:29:53 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768",
acknowledgement = ack-nhfb,
fjournal = "The Journal of General Psychology",
keywords = "Benford's Law",
onlinedate = "06 Jul 2010",
}
@Book{Hardy:1949:DS,
author = "G. H. (Godfrey Harold) Hardy",
title = "Divergent series",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 396",
year = "1949",
LCCN = "QA295 .H29",
bibdate = "Wed Nov 16 08:14:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1877--1947",
}
@Book{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 = "http://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",
}
@Book{Feller:1950:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "????",
year = "1950",
LCCN = "QA273 .F37",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley series in probability and mathematical
statistics. Probability and mathematical statistics",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
}
@Article{Macon:1950:DFD,
author = "N. Macon and L. Moser",
title = "On the distribution of first digits of powers",
journal = "Scripta Math.",
volume = "16",
number = "??",
pages = "290--291",
month = "????",
year = "1950",
CODEN = "????",
ISSN = "0036-9713",
bibdate = "Sat Nov 12 16:28:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica",
}
@InProceedings{Mandelbrot:1953:ITS,
author = "Beno{\^\i}t B. Mandelbrot",
editor = "Willis Jackson",
booktitle = "{Communication theory: papers read at a Symposium on
``Applications of Communication Theory'' held at the
Institution of Electrical Engineers, London, September
22nd--26th 1952}",
title = "An Informational Theory of the Statistical Structure
of Languages",
publisher = pub-BUTTERWORTHS,
address = pub-BUTTERWORTHS:adr,
pages = "486--502",
year = "1953",
LCCN = "Q350 .S92 1952",
bibdate = "Wed Nov 16 09:37:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://lccn.loc.gov/53004215;
http://www.nytimes.com/2010/10/17/us/17mandelbrot.html",
acknowledgement = ack-nhfb,
bookpages = "xii + 532",
remark = "The paper is incorrectly referenced as a book in
\cite{Baek:2011:ZLU}. Mandelbrot got his Master's in
Mathematics at CalTech, and his Ph.D. 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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://catalog.hathitrust.org/Record/000577721",
acknowledgement = ack-nhfb,
author-dates = "David Blackwell (1919--2010)",
keywords = "Benford's Law",
remark = "Brief mention of Benford's Law on page 74, problem
2.7.2 (??).",
}
@Article{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",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Tue Nov 15 10:08:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2333389",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
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",
MRclass = "94.0X",
MRnumber = "0088412 (19,516a)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe
des Sciences. Koninklijke Belgische Academie.
Mededelingen van de Klasse der Wetenschappen. 5e
S{\'e}rie",
}
@Book{Feller:1957:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "461 (vol. 1), 626 (vol. 2)",
year = "1957",
LCCN = "QA273 .F3712",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://catdir.loc.gov/catdir/toc/onix01/57010805.html",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
}
@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 = "Bull. Inst. Internat. Stat.",
volume = "35",
number = "??",
pages = "57--76",
year = "1957",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
xxvolume = "34",
}
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "205--228",
year = "1957",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Miller:1957:SEI,
author = "George A. Miller",
title = "Some Effects of Intermittent Silence",
journal = j-AMER-J-PSYCHOLOGY,
volume = "70",
number = "2",
pages = "311--314",
month = jun,
year = "1957",
CODEN = "AJPCAA",
ISSN = "0002-9556 (print), 1939-8298 (electronic)",
ISSN-L = "0002-9556",
bibdate = "Tue Nov 15 09:40:05 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/1419346",
acknowledgement = ack-nhfb,
fjournal = "The American Journal of Psychology",
keywords = "Zipf's Law",
}
@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 = "http://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 = "http://dx.doi.org/10.1016/S0019-9958(59)90098-1",
ISSN = "0019-9958",
ISSN-L = "0019-9958",
bibdate = "Wed Nov 16 09:45:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Simon:1955:CSD}.",
abstract = "This note is a discussion of H. A. Simon's model
(1955) concerning the class of frequency distributions
generally associated with the name of G. K. Zipf. The
main purpose is to show that Simon's model is
analytically circular in the case of the linguistic
laws of Estoup--Zipf and Willis--Yule. Insofar as the
economic law of Pareto is concerned, Simon has himself
noted that his model is a particular case of that of
Champernowne; this is correct, with some reservation. A
simplified version of Simon's model is included.",
acknowledgement = ack-nhfb,
fjournal = "Information and Control",
}
@Article{Mandelbrot:1960:PLL,
author = "Beno{\^\i}t Mandelbrot",
title = "The {Pareto--Levy} law and the distribution of
income",
journal = j-INT-ECON-REV,
volume = "1",
number = "??",
pages = "79--106",
month = "????",
year = "1960",
CODEN = "INERAE",
ISSN = "0020-6598 (print), 1468-2354 (electronic)",
ISSN-L = "0020-6598",
bibdate = "Wed Nov 23 11:07:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ingenta.com/journals/browse/bpl/iere",
acknowledgement = ack-nhfb,
fjournal = "International Economic Review",
}
@Article{Cigler:1961:NET,
author = "J. Cigler and G. Helmberg",
title = "{Neuere Entwicklungen der Theorie der
Gleichverteilung}. ({German}) [{Recent} developments in
the theory of uniform distribution]",
journal = j-DEUTSCH-MATH-V,
volume = "64",
number = "??",
pages = "1--50",
month = "????",
year = "1961",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 16:33:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Jber. Deutsch. Math.--Verein",
language = "German",
}
@Article{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",
bibdate = "Sat Sep 17 10:19:00 2011",
bibsource = "http://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",
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 $d(uv) = u dv
+ v du$, 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 = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers",
}
@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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2681423",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
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 = "http://dx.doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "http://www.computer.org/tc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the low-level multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. They conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}
@Article{Konheim:1965:MDT,
author = "Alan G. Konheim",
title = "Mantissa Distributions (in {Technical Notes and Short
Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "143--144",
month = apr,
year = "1965",
CODEN = "MCMPAF",
DOI = "http://dx.doi.org/10.2307/2004111",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
}
@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 = "http://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",
}
@Book{Feller:1966:IPT,
author = "William Feller",
title = "Introduction to Probability Theory",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xviii + 626",
year = "1966",
ISSN = "0271-6232",
LCCN = "QA273 .F3727 1966",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Wiley series in probability and mathematical
statistics. Probability and mathematical statistics",
acknowledgement = ack-nhfb,
author-dates = "William Feller (1906--1970)",
remark = "Benford's Law is discussed on p. 62.",
}
@Article{Flehinger:1966:PRI,
author = "B. J. (Betty J.) Flehinger",
title = "On the probability that a random integer has initial
digit {$A$}",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "10",
pages = "1056--1061",
month = dec,
year = "1966",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2314636",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Sat Nov 12 15:33:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2314636",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
}
@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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/5-2/duncan.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@Article{Mosteller:1967:DSR,
author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
title = "The Distribution of Sums of Rounded Percentages",
journal = j-DEMOGRAPHY,
volume = "4",
number = "2",
pages = "850--858",
month = jun,
year = "1967",
CODEN = "????",
ISSN = "0070-3370 (print), 1533-7790 (electronic)",
ISSN-L = "0070-3370",
bibdate = "Thu Nov 24 08:03:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
bibdate = "Sat Nov 12 16:09:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Book{Feller:1968:IPT,
author = "William Feller",
title = "Introduction to Probability Theory and its
Applications",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Third",
pages = "xviii + 509",
year = "1968",
ISBN = "0-471-25708-7",
ISBN-13 = "978-0-471-25708-0",
LCCN = "QA273 .F3713",
bibdate = "Mon Nov 14 09:57:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/6-2/shenton.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
keywords = "Benford's Law",
}
@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",
bibdate = "Sat Nov 12 16:12:50 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Article{Bumby:1969:FAM,
author = "R. Bumby and E. Ellentuck",
title = "Finitely additive measures and the first digit
problem",
journal = j-FUNDAM-MATH,
volume = "65",
number = "??",
pages = "33--42",
month = "????",
year = "1969",
CODEN = "????",
ISSN = "0016-2736",
ISSN-L = "0016-2736",
bibdate = "Sat Nov 12 16:19:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fundamenta mathematicae",
}
@Article{Duncan:1969:NID,
author = "R. L. Duncan",
title = "Note on the Initial Digit Problem",
journal = j-FIB-QUART,
volume = "7",
number = "5",
pages = "474--475",
month = dec,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:21 MDT 2011",
bibsource = "http://www.fq.math.ca/7-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/7-5/duncan.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
}
@Article{Fairthorne:1969:PDE,
author = "Robert A. Fairthorne",
title = "Progress in Documentation: Empirical Hyperbolic
Distributions ({Bradford--Zipf--Mandelbrot}) for
Bibliometric Description and Prediction",
journal = j-J-DOC,
volume = "25",
number = "4",
pages = "313--343",
month = dec,
year = "1969",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026481",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:27:27 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprinted in \cite{Fairthorne:2005:PDE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
remark = "According to \cite{Potter:1981:LLR}, this paper is the
first to link the distributions of Bradford, Zipf,
Mandelbrot, and Lotka.",
}
@Unpublished{Hafner:1969:CSR,
author = "Everett M. Hafner",
title = "Circular slide roulette",
year = "1969",
bibdate = "Mon Nov 14 10:00:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Unpublished but dated 1969. Presented in 1975 in an
address at Hampshire College, Amherst, MA, USA",
acknowledgement = ack-nhfb,
}
@Article{Haight:1969:TPD,
author = "F. A. Haight",
title = "Two probability distributions connected with {Zipf}'s
rank-size conjecture",
journal = j-ZASTOS-MAT,
volume = "10",
pages = "225--228",
year = "1969",
CODEN = "ZAMTAK",
ISSN = "0044-1899",
MRclass = "62.31",
MRnumber = "0246425 (39 \#7729)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Polska Akademia Nauk. Instytut Matematyczny.
Zastosowania Matematyki",
}
@Book{Knuth:1969:SNM,
author = "Donald E. Knuth",
title = "Semi\-nu\-mer\-i\-cal Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is discussed on pp. 219--229.",
price = "US\$19.75",
series = "The Art of Computer Programming",
}
@Article{Kuipers:1969:RPR,
author = "L. Kuipers",
title = "Remark on a Paper by {R. L. Duncan} Concerning the
Uniform Distribution Mod $1$ of the Sequence of the
Logarithms of the {Fibonacci} Numbers",
journal = j-FIB-QUART,
volume = "7",
number = "5",
pages = "465--466",
month = dec,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:21 MDT 2011",
bibsource = "http://www.fq.math.ca/7-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://search.proquest.com/docview/302476508?accountid=14677",
acknowledgement = ack-nhfb,
}
@Article{Blum:1970:SID,
author = "M. Blum",
title = "On the Sums of Independently Distributed {Pareto}
Variates",
journal = j-SIAM-J-APPL-MATH,
volume = "19",
number = "1",
pages = "191--198",
month = jul,
year = "1970",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
}
@Article{Brown:1970:MOU,
author = "J. L. {Brown, Jr.} and R. L. Duncan",
title = "Modulo One Uniform Distribution of the Sequence of
Logarithms of Certain Recursive Sequences",
journal = j-FIB-QUART,
volume = "8",
number = "5",
pages = "482--486",
month = dec,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:31 MDT 2011",
bibsource = "http://www.fq.math.ca/8-5.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
note = "See remark \cite{Kuipers:1973:RPD}.",
URL = "http://www.fq.math.ca/Scanned/8-5/brown.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@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",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$r(x) =
1/(x \ln b) \qquad (1/b \leq x \leq 1)$$ (where $b$ is
the base of the number system). The paper also gives a
number of applications to hardware, software, and
general computing which show that this distribution is
not merely an amusing curiosity. A brief examination of
the distribution of exponents is include.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
}
@Article{Hill:1970:ZLP,
author = "Bruce M. Hill",
title = "{Zipf}'s law and prior distributions for the
composition of a population",
journal = j-J-AM-STAT-ASSOC,
volume = "65",
number = "331",
pages = "1220--1232",
month = sep,
year = "1970",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62.35",
MRnumber = "0279936 (43 \#5657)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
URL = "http://www.jstor.org/stable/2284288",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
ZMnumber = "Zbl 0224.92011",
}
@Article{Orlov:1970:GZM,
author = "Ju. K. Orlov",
title = "A generalization of the {Zipf--Mandelbrot} law",
journal = "Sakharth. SSR Mech. Akad. 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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@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",
bibdate = "Sat Nov 12 10:39:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Proc. Inst. Statist. Math.",
classmath = "68Q45 (Formal languages)",
fjournal = "Proceedings of the Institute of Statistical
Mathematics",
language = "Japanese",
ZMnumber = "0238.68026",
}
@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 = "http://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 = "http://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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://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",
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 = "http://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",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:38 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@TechReport{Diaconis:1973:LMI,
author = "Persi Diaconis",
title = "Limits of measures of the integers with applications
to random number generators and the distribution of
leading digits",
type = "Memorandum",
number = "NS-211",
institution = "Department of Statistics, Harvard University",
address = "Cambridge, MA, USA",
day = "22",
month = mar,
year = "1973",
bibdate = "Sat Nov 12 16:23:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Kuipers:1973:RPD,
author = "L. Kuipers and Jau-shyong Shiue",
title = "Remark on a Paper by {Duncan} and {Brown} on the
Sequence of Logarithms of Certain Recursive Sequences",
journal = j-FIB-QUART,
volume = "11",
number = "3",
pages = "292--293",
month = oct,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:42 MDT 2011",
bibsource = "http://www.fq.math.ca/11-3.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
note = "See \cite{Brown:1970:MOU}.",
URL = "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@Article{Murphy:1973:LLH,
author = "Larry J. Murphy",
title = "{Lotka's Law} in the Humanities?",
journal = j-J-AM-SOC-INF-SCI,
volume = "24",
number = "6",
pages = "461--462",
month = nov # "\slash " # dec,
year = "1973",
CODEN = "AISJB6",
DOI = "http://dx.doi.org/10.1002/asi.4630240607",
ISSN = "0002-8231 (print), 1097-4571 (electronic)",
ISSN-L = "0002-8231",
bibdate = "Fri Nov 25 08:09:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@Article{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",
MRclass = "92A25",
MRnumber = "0354071 (50 \#6553)",
MRreviewer = "J. S. Joel",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://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",
bibdate = "Sat Nov 12 16:29:39 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Sankhya Ser. B (Indian J. of Statist.)",
fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B.
Methodological",
}
@Article{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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
}
@PhdThesis{Diaconis:1974:WSA,
author = "Persi Diaconis",
title = "Weak and Strong Averages in probability and the theory
numbers",
type = "{Ph.D.} thesis",
school = "Department of Statistics, Harvard University",
address = "Cambridge, MA, USA",
pages = "xvii + 117",
year = "1974",
bibdate = "Mon Nov 14 10:26:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Duran:1974:ACS,
author = "J. Peter Duran",
title = "Almost convergence, summability and ergodicity",
journal = j-CAN-J-MATH,
volume = "26",
number = "??",
pages = "372--387",
month = "????",
year = "1974",
CODEN = "CJMAAB",
DOI = "http://dx.doi.org/10.4153/CJM-1974-039-6",
ISSN = "0008-414X (print), 1496-4279 (electronic)",
ISSN-L = "0008-414X",
bibdate = "Sat Sep 10 15:38:45 MDT 2011",
bibsource = "http://cms.math.ca/cjm/v26/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Mathematics = Journal canadien de
math{\'e}matiques",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
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",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
ZMnumber = "Zbl 0301.60011",
}
@Book{Kuipers:1974:UDS,
author = "Lauwerens Kuipers and Harald Niederreiter",
title = "Uniform distribution of sequences",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 390",
year = "1974",
ISBN = "0-471-51045-9",
ISBN-13 = "978-0-471-51045-1",
LCCN = "QA292 .K84",
bibdate = "Sat Nov 12 15:42:53 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "``A Wiley-Interscience publication.''.",
subject = "Sequences (Mathematics); Uniform distribution
(Probability theory)",
}
@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",
bibdate = "Fri Nov 25 08:12:46 2011",
bibsource = "http://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 = "http://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,
}
@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;
http://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",
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: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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
keywords = "Lotka's Law",
}
@Article{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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
classmath = "94A15 (General topics of information theory)",
fjournal = "IEEE Transactions on Information Theory",
ZMnumber = "0295.94048",
}
@InProceedings{Bennett:1975:SDI,
author = "John M. Bennett",
booktitle = "Int. Comput. Symp. 1975, Proc., Antibes, (1975)",
title = "Storage design for information retrieval: {Scarrott}'s
conjecture and {Zipf}'s law",
publisher = "????",
address = "????",
pages = "233--237",
year = "1975",
bibdate = "Sat Nov 12 10:49:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
classmath = "68P20 (Information storage and retrieval) 68N01
(General)",
ZMnumber = "0322.68068",
}
@Book{Hardy:1975:ITN,
author = "Godfrey H. Hardy and Edward M. Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
edition = "Fourth",
pages = "421",
year = "1975",
ISBN = "0-19-853310-1",
ISBN-13 = "978-0-19-853310-8",
LCCN = "????",
bibdate = "Fri Jun 24 12:32:14 2005",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Hill:1975:SFZ,
author = "Bruce M. Hill and Michael Woodroofe",
title = "Stronger forms of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "70",
number = "349",
pages = "212--219",
month = mar,
year = "1975",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15 (62D05)",
MRnumber = "0440763 (55 \#13633)",
MRreviewer = "I. J. Good",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
ZMnumber = "Zbl 0326.92014",
}
@Article{Kemperman:1975:BDM,
author = "J. H. B. Kemperman",
title = "Bounds on the discrepancy modulo $1$ of a real random
variable",
journal = "Inst. of Math. Stat. Bulletin",
volume = "4",
number = "??",
pages = "138--??",
month = "????",
year = "1975",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 16:26:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Abstract no. 75t-47.",
acknowledgement = ack-nhfb,
}
@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;
http://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",
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{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",
bibdate = "Fri Nov 25 08:17:00 2011",
bibsource = "http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
}
@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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/13-4/webb.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3212857",
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",
keywords = "classical occupancy problem; laws of large numbers:
weak convergence; regularly varying functions",
ZMnumber = "Zbl 0343.60012",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Billera:1976:PSC,
author = "Louis J. Billera and Robert E. Bixby",
title = "{Pareto} Surfaces of Complexity $1$",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "1",
pages = "81--89",
month = jan,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Dept. of Math., Cornell Univ., Ithaca, NY, USA",
fjournal = "SIAM Journal on Applied Mathematics",
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 = "Giorn. Econom. Ann. Econom. (N.S.)",
volume = "35",
number = "3--4",
pages = "131--153, 235",
year = "1976",
CODEN = "????",
ISSN = "????",
MRclass = "90A15",
MRnumber = "0452510 (56 \#10789)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
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",
ISSN-L = "0097-3165",
bibdate = "Thu Feb 15 16:29:51 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory (Series A)",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Davis:1976:SRI,
author = "Basil Davis",
title = "Some Remarks on Initial Digits",
journal = j-FIB-QUART,
volume = "14",
number = "1",
pages = "13--14",
month = feb,
year = "1976",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:05 MDT 2011",
bibsource = "http://www.fq.math.ca/14-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/14-1/davis.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
}
@Article{Feldstein:1976:CED,
author = "Alan Feldstein and Richard Goodman",
title = "Convergence Estimates for the Distribution of Trailing
Digits",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "287--297",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "http://doi.acm.org/10.1145/321941.321948",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "An analysis is made of the distribution of trailing
digits (tail end digits) of positive real
floating-point numbers represented in arbitrary base
$\beta$ and randomly chosen from a logarithmic
distribution. The analysis shows that the $n$th digit
for $n \geq 2$ is actually approximately uniformly
distributed. The approximation depends upon both $n$
and the base beta. It becomes better as $n$ increases,
and it is exact in the limit as $n \rightarrow \infty$.
A table of this distribution is presented for various
$\beta$ and $n$, along with a table of the maximum
digit by digit deviation $\Delta$ of the logarithmic
distribution from the uniform distribution. Various
asymptotic results for $\Delta$ are included.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the Association for Computing Machinery",
journalabr = "J Assoc Comput Mach",
keywords = "Benford's Law; computer arithmetic; computer
programming; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Orlov:1976:CBP,
author = "Ju. K. Orlov",
title = "The connection between the {Pareto} distribution and
the generalized {Zipf--Mandelbrot} law",
journal = "Sakharth. SSR Mech. Akad. 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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2319349",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
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",
MRclass = "62E20",
MRnumber = "0423644 (54 \#11619)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://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",
MRclass = "62E20",
MRnumber = "0423645 (54 \#11620)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://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",
bibdate = "Fri Nov 25 07:56:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Prob. inf. \& doc.",
}
@Article{Brookes:1977:TBL,
author = "B. C. Brookes",
title = "Theory of the {Bradford Law}",
journal = j-J-DOC,
volume = "33",
number = "3",
pages = "180--209",
month = "????",
year = "1977",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026641",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:16:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Clark:1977:ESL,
author = "Douglas W. Clark and C. Cordell Green",
title = "An Empirical Study of List Structure in {Lisp}",
journal = j-CACM,
volume = "20",
number = "2",
pages = "78--87",
month = feb,
year = "1977",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:31:28 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Static measurements of the list structure of five
large Lisp programs are reported and analyzed. These
measurements reveal substantial regularity, or
predictability, among pointers to atoms and especially
among pointers to lists. Pointers to atoms are found to
obey, roughly, Zipf's law, which governs word
frequencies in natural languages; pointers to lists
usually point to a location physically nearby in
memory. The use of such regularities in the
space-efficient representation of list structure is
discussed.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques); C6140D (High level
languages)",
classification = "723",
comment = "Great paper; evidence pro CDR-coding, con fancy CONS",
corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA",
fjournal = "Communications of the ACM",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
keywords = "Lotka's Law",
}
@Article{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 = "????",
year = "1977",
CODEN = "APBYAE",
DOI = "http://dx.doi.org/10.1214/aop/1176995891",
ISSN = "0091-1798",
bibdate = "Sat Nov 12 15:30:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of Probability",
}
@Article{Brady:1978:MBL,
author = "W. G. Brady",
title = "More on {Benford}'s Law",
journal = j-FIB-QUART,
volume = "16",
number = "1",
pages = "51--52",
month = feb,
year = "1978",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:24 MDT 2011",
bibsource = "http://www.fq.math.ca/16-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
}
@PhdThesis{Chen:1978:ZL,
author = "Wen-Chen Chen",
title = "On {Zipf}'s law",
type = "Thesis ({Ph.D.})",
school = "University of Michigan",
address = "Ann Arbor, MI, USA",
pages = "114",
year = "1978",
MRclass = "Thesis",
MRnumber = "2627928",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871",
acknowledgement = ack-nhfb,
remark = "Available from ProQuest LLC, Ann Arbor, MI, USA.
Author given name appears as Wen-Cheng in MathSciNet
database.",
}
@Article{Elshoff:1978:SSC,
author = "James L. Elshoff",
title = "A study of the structural composition of {PL/I}
programs",
journal = j-SIGPLAN,
volume = "13",
number = "6",
pages = "29--37",
month = jun,
year = "1978",
CODEN = "SINODQ",
DOI = "http://doi.acm.org/10.1145/987515.987518",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Wed Jun 18 16:08:52 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Some research on a theory of the structural
composition of an algorithm has recently been reported.
The theory embodies models of operator and operand
distributions that have been proposed by Bayer, Zipf,
and Zweben. This paper reports a study in which the
three models of operator distributions are compared
with the measured distributions found in 34 PL/I
programs. Two of three models, one by Zipf and one by
Zweben, are shown to correlate highly with the measured
distributions. Two variations of the Zipf model are
then formulated and tested with good results. Also, the
relationship between the method of counting operators
and the models is investigated.",
acknowledgement = ack-nhfb,
classification = "C4240 (Programming and algorithm theory); C6140D
(High level languages)",
corpsource = "Computer Sci. Dept., General Motors Res. Labs.,
Warren, MI, USA",
fjournal = "ACM SIG{\-}PLAN Notices",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Library and information science",
acknowledgement = ack-nhfb,
remark = "Heaps's Law is given on pp. 206--208.",
subject = "Information storage and retrieval systems",
}
@Article{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",
bibdate = "Fri Mar 30 11:20:35 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "This paper contains derivations of both Stigler's Law
and Benford's Law, and receives strong criticism in
\cite{Raimi:1985:FDP}. This paper contains an important
historical note that is recorded in entry
\cite{Benford:1938:LAN}.",
URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
http://www.jstor.org/stable/986530",
abstract = "Forty years ago an article appeared in these
Proceedings, which has since then attracted much
attention of mathematicians and some physicists. It was
written by Frank Benford, a physicist from the General
Electric Company at Schenectady. He had examined a
large number of numerical tables, the kind that are
printed in almanacs, and in scientific and technical
handbooks. He noticed a most unusual and unexpected
property of many of these tables. Consider, for
example, the numbers representing the populations of
states or all the countries in the world, or their
areas, their budgets, their numbers of hospital beds,
etc. One would expect that on the average just as many
of these entries would begin with the digit $1$ as with
$2$ or $3$ or $4$, and so on. But Benford noticed that
small values of the first digits occur far more
often.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@Article{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",
MRclass = "62E99 (60J20 62P99)",
MRnumber = "507732 (80c:62026a)",
MRreviewer = "Bruce M. Hill",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annales de 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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://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",
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{Diaconis:1979:RP,
author = "Persi Diaconis and David Freedman",
title = "On Rounding Percentages",
journal = j-J-AM-STAT-ASSOC,
volume = "74",
number = "366",
pages = "359--364",
month = jun,
year = "1979",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Nov 23 11:24:59 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "The authors extend prior work on correctness of sums
of rounded percentages \cite{Mosteller:1967:DSR,}, and
criticize biased rounding practices in
\cite{Benford:1938:LAN}.",
URL = "http://www.jstor.org/stable/2284288",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
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{Mohanty:1979:MMQ,
author = "Siba N. Mohanty",
title = "Models and Measurements for Quality Assessment of
Software",
journal = j-COMP-SURV,
volume = "11",
number = "3",
pages = "251--275",
month = sep,
year = "1979",
CODEN = "CMSVAN",
DOI = "http://doi.acm.org/10.1145/356778.356783",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:25:12 MDT 2008",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib;
http://www.acm.org/pubs/contents/journals/surveys/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.",
acknowledgement = ack-nhfb,
annote = "Several software quality assessment methods which span
the software life cycle are discussed. The quality of a
system design can be estimated by measuring the system
entropy function or the system work function. The
quality improvement due to reconfiguration can be
determined by calculating system entropy loading
measures. Software science and Zipf's law are shown to
be useful for estimating program length and
implementation time.",
country = "USA",
date = "11/10/79",
descriptors = "Software; design; software engineering; reliability;
measurement; model; fundamentals in statistics;
performance evaluation;",
enum = "2189",
fjournal = "ACM Computing Surveys",
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Society for Information
Science",
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 = "109--130",
month = sep,
year = "1979",
CODEN = "SCNTDX",
DOI = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/0138-9130/",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
xxjournal = "Scientometrics, Bibliography Section",
}
@Article{Chen:1980:WFZ,
author = "Wen Chen Chen",
title = "On the weak form of {Zipf}'s law",
journal = j-J-APPL-PROBAB,
volume = "17",
number = "3",
pages = "611--622",
year = "1980",
CODEN = "JPRBAM",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "62E10 (62F10)",
MRnumber = "580021 (81m:62021)",
MRreviewer = "Patrick L. Brockett",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3212955",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
ZMnumber = "Zbl 0435.60017",
}
@Article{Dunn:1980:SFW,
author = "Stanley Dunn",
title = "Surveyor's Forum: {Working} on Interpretations",
journal = j-COMP-SURV,
volume = "12",
number = "2",
pages = "255--255",
month = jun,
year = "1980",
CODEN = "CMSVAN",
DOI = "http://doi.acm.org/10.1145/356810.356817",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:27:10 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
}
@Article{Leimkuhler:1980:EFB,
author = "Ferdinand F. Leimkuhler",
title = "An Exact Formulation of {Bradford's Law}",
journal = j-J-DOC,
volume = "36",
number = "4",
pages = "285--292",
month = "????",
year = "1980",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026699",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:14:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "An exact, discrete formulation of Bradford's law
describing the distribution of articles in journals is
derived by showing that Bradford's law is a special
case of the Zipf--Mandelbrot `rank frequency' law. A
relatively simple method is presented for fitting the
model to empirical data and estimating the number of
journals and articles in a subject collection. This
method is demonstrated with an example application.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{McKee:1980:POR,
author = "Arnold F. McKee",
title = "The {Pareto} Optimum: Reconcilable with Social
Thought?",
journal = "International Journal of Social Economics",
volume = "7",
number = "7",
pages = "366--375",
month = "????",
year = "1980",
CODEN = "ISLEBC",
DOI = "http://dx.doi.org/10.1108/eb013878",
ISSN = "0306-8293 (print), 1758-6712 (electronic)",
bibdate = "Fri Nov 25 07:01:57 2011",
bibsource = "http://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 = "http://doi.acm.org/10.1145/356810.356818",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:27:10 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
}
@Article{Kennard:1981:MDF,
author = "Robert W. Kennard and John E. Reith",
title = "{M32}. On the distribution of first digits",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "10",
number = "1",
pages = "97--98",
month = "????",
year = "1981",
CODEN = "CSSCDB",
DOI = "http://dx.doi.org/10.1080/03610918108812195",
ISSN = "0361-0918",
bibdate = "Sat Jan 07 09:27:42 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Simulation and
Computation",
keywords = "Benford's Law",
onlinedate = "27 Jun 2007",
}
@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",
MRclass = "10K10",
MRnumber = "631437 (83m:10093)",
MRreviewer = "Michael Keane",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia
(Moscow)",
}
@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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@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 = "http://dx.doi.org/10.1007/BF02188018",
ISSN = "0001-9054",
ISSN-L = "0001-9054",
MRclass = "Contributed Item",
MRnumber = "1553878",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Aequationes Mathematicae",
}
@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",
ISSN-L = "0024-2594",
bibdate = "Thu Nov 24 14:41:53 2011",
bibsource = "http://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 = "http://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)",
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 = "P. Schatte",
title = "On random variables with logarithmic mantissa
distribution relative to several bases",
journal = "Elektron. Inform. verarb. Kybernet. EIK",
volume = "17",
number = "??",
pages = "293--295",
month = "????",
year = "1981",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 15:53:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@Article{Pavlov:1982:DFP,
author = "A. I. Pavlov",
title = "On the Distribution of Fractional Parts and {Benford's
Law}",
journal = "Mathematics of the USSR-Izvestiya",
volume = "19",
number = "1",
pages = "65--77",
month = "????",
year = "1982",
CODEN = "????",
DOI = "http://dx.doi.org/10.1070/IM1982v019n01ABEH001411",
ISSN = "0025-5726",
bibdate = "Sun Nov 13 10:46:55 2011",
bibsource = "http://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,
}
@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 = "http://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 = "Statistica (Bologna)",
volume = "42",
number = "3",
pages = "351--370",
year = "1982",
CODEN = "STATDJ",
ISSN = "0390-590X",
MRclass = "62E99 (10K05 62A15)",
MRnumber = "695467 (84h:62032)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistica",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
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 = "http://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{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",
MRclass = "62E99 (62P99)",
MRnumber = "723296",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR",
}
@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",
bibdate = "Fri Mar 9 17:59:26 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "As software projects increase in size, the effort
required to implement them increases at a greater rate.
The use of higher level languages and adherence to
various rules of ``good programming practice'' appear
to help only marginally in reducing the impact of this
non-linear effect, and progress can only be made by
calling on techniques for managing complexity which
have emerged in other fields. Hierarchical structures
are discussed with particular reference to software as
is the effect which appears to be common to a wide
range of human activities, and which is known as Zipf's
law. The effects of variation in individual programming
skills, the roles of creativity, invention and
innovation and lessons to be learned from case studies
of past failure are also examined.",
acknowledgement = ack-nhfb,
fjournal = "Australian Computer Journal",
keywords = "creativity; innovation; invention; large software
projects; project failures; structured programming;
Zipf's law",
}
@Article{Boroda:1984:ZML,
author = "M. G. Boroda and A. A. Polikarpov",
title = "The {Zipf--Mandelbrot} law and units of different
levels of text organization",
journal = "Tartu Riikl. {\"U}l. Toimetised",
volume = "??",
number = "689",
pages = "35--60",
year = "1984",
CODEN = "????",
ISSN = "????",
MRclass = "92A25",
MRnumber = "781731 (86c:92030)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
et Commentationes Universitatis Tartuensis",
}
@Article{Bunt:1984:MPL,
author = "Richard B. Bunt and Jennifer M. Murphy and Shikharesh
Majumdar",
title = "A measure of program locality and its application",
journal = j-SIGMETRICS,
volume = "12",
number = "3",
pages = "28--40",
month = aug,
year = "1984",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1031382.809311",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Thu Jun 26 11:00:50 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Although the phenomenon of locality has long been
recognized as the single most important characteristic
of program behaviour, relatively little work has been
done in attempting to measure it. Recent work has led
to the development of an intrinsic measure of program
locality based on the Bradford--Zipf distribution.
Potential applications for such a measure are many, and
include the evaluation of program restructuring methods
(manual and automatic), the prediction of system
performance, the validation of program behaviour
models, and the enhanced understanding of the phenomena
that characterize program behaviour. A consideration of
each of these areas is given in connection with the
proposed measure, both to increase confidence in the
validity of the measure and to illustrate a methodology
for dealing with such problems.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
}
@Article{Cohen:1984:PNF,
author = "D. I. A. Cohen and T. M. Katz",
title = "Prime numbers and the first digit phenomenon",
journal = j-J-NUMBER-THEORY,
volume = "18",
number = "3",
pages = "261--268",
month = jun,
year = "1984",
CODEN = "JNUTA9",
DOI = "http://dx.doi.org/10.1016/0022-314X(84)90061-1",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Fri Nov 25 13:58:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
}
@Article{Fedorowicz:1984:DEU,
author = "Jane Fedorowicz",
title = "Database evaluation using multiple regression
techniques",
journal = j-SIGMOD,
volume = "14",
number = "2",
pages = "70--76",
year = "1984",
CODEN = "SRECD8",
ISBN = "0-89791-128-8",
ISBN-13 = "978-0-89791-128-3",
ISSN = "0163-5808 (print), 1943-5835 (electronic)",
ISSN-L = "0163-5808",
bibdate = "Mon Dec 9 07:58:51 MST 1996",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A model of the inverted file of an automated
bibliographic system is constructed using the Zipf
distribution of word frequency. By ascertaining the
parameters of the Zipfian model of the inverted file
system, one can estimate the minimum data storage
requirements of the database. In addition, given a few
additional system parameters, access time for a
specified query can be estimated. The estimation
procedures are accomplished using logarithmic
transformations and multiple regression techniques.
This paper introduces the Zipfian models, their
regression formulation, and their results and
interpretation for application to database
evaluation.",
acknowledgement = ack-nhfb,
affiliation = "Northwestern Univ, Kellogg Graduate Sch of Management,
Evanston, IL, USA",
affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of
Management, Evanston, IL, USA",
classification = "723; 901; 922",
conference = "SIGMOD '84, Proceedings of Annual Meeting (ACM Special
Interest Group on Management of Data).",
fjournal = "SIGMOD Record (ACM Special Interest Group on
Management of Data)",
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{Kohyama:1984:TIC,
author = "Tamotsu Kohyama and Y{\=o}ji Aizawa",
title = "Theory of the intermittent chaos. {$1/f$} spectrum and
the {Pareto--Zipf} law",
journal = j-PROG-THEOR-PHYS,
volume = "71",
number = "5",
pages = "917--929",
year = "1984",
CODEN = "PTPKAV",
DOI = "http://dx.doi.org/10.1143/PTP.71.917",
ISSN = "0033-068X (print), 1347-4081 (electronic)",
ISSN-L = "0033-068X",
MRclass = "58F13 (76F99)",
MRnumber = "756214 (86a:58063)",
MRreviewer = "Joseph Ford",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Progress of Theoretical Physics",
}
@Article{Maia:1984:UBL,
author = "M. J. F. Maia and M. D. Maia",
title = "On the Unity of {Bradford's Law}",
journal = j-J-DOC,
volume = "40",
number = "3",
pages = "206--216",
month = "????",
year = "1984",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026765",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:11:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Nagasaka:1984:BL,
author = "Kenji Nagasaka",
title = "On {Benford}'s law",
journal = "Ann. Inst. Statist. Math.",
volume = "36",
number = "2",
pages = "337--352",
year = "1984",
CODEN = "AISXAD",
DOI = "http://dx.doi.org/10.1007/BF02481974",
ISSN = "0020-3157",
MRclass = "60F99 (11K06 11K36 62E99)",
MRnumber = "758506 (86a:60052)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of the Institute of Statistical Mathematics",
}
@Article{Schatte:1984:AUD,
author = "P. 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 = "http://dx.doi.org/10.1002/mana.19841150121",
ISSN = "0025-584X",
bibdate = "Sat Nov 12 15:54:14 2011",
bibsource = "http://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",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://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,
keywords = "l. s. d. (leading significant digits)",
}
@Article{Barlow:1985:RED,
author = "J. L. Barlow and E. H. Bareiss",
title = "On Roundoff Error Distributions in Floating Point and
Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "325--347",
month = dec,
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65045",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ, Computer Science Dep,
University Park, PA, USA",
affiliationaddress = "USA",
classification = "723",
fjournal = "Computing",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory; floating
point arithmetic; logarithmic arithmetic; roundoff
error distributions",
reviewer = "N. N. Abdelmalek",
}
@Article{Bradford:1985:SIS,
author = "Samuel C. Bradford",
title = "Sources of Information on Specific Subjects",
journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE,
volume = "10",
number = "4",
pages = "173--180",
month = oct,
year = "1985",
CODEN = "JISCDI",
ISSN = "0165-5515 (print), 1741-6485 (electronic)",
ISSN-L = "0165-5515",
bibdate = "Fri Nov 25 11:49:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprint of \cite{Bradford:1934:SIS}, the source of
Bradford's Law.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Information Science, Principles and
Practice",
}
@Article{Egghe:1985:CLL,
author = "L. Egghe",
title = "Consequences of {Lotka's Law} for the {Law of
Bradford}",
journal = j-J-DOC,
volume = "41",
number = "3",
pages = "173--189",
month = "????",
year = "1985",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/eb026780",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:23:22 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
keywords = "Bradford's Law",
}
@Article{Lagarias:1985:PG,
author = "Jeffrey C. Lagarias",
title = "The $3x + 1$ Problem and Its Generalizations",
journal = j-AMER-MATH-MONTHLY,
volume = "92",
number = "1",
pages = "3--23",
month = jan,
year = "1985",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K55 (11K31)",
MRnumber = "86i:11043",
MRreviewer = "A. D. Pollington",
bibdate = "Mon Jun 28 12:37:47 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing and Management",
}
@Article{Raimi:1985:FDP,
author = "R. 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",
bibdate = "Sat Nov 12 16:56:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.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",
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{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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
et Commentationes Universitatis Tartuensis",
}
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = "Overflow, underflow, and severe loss of significance
in floating-point addition and subtraction",
journal = j-IMA-J-NUMER-ANAL,
volume = "6",
number = "2",
pages = "241--251",
month = apr,
year = "1986",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05",
MRnumber = "89h:65065",
bibdate = "Sat Dec 23 14:52:49 2000",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this paper it is shown that, under the assumption
of the logarithmic distribution of numbers,
floating-point addition and subtraction can result in
overflow or underflow with alarming frequency --- a
frequency that increases rapidly with machine speed
unless the range of the exponent is also increased. If
numbers are assumed to be distributed in accordance
with Sweeney's (1965) experiments, then severe loss of
significance occurs with large probability in floating
point subtraction. These results have implications for
computer design and lead to the suggestion of a long
word format which will reduce the risks to acceptable
levels.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
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)",
bibdate = "Sat Apr 21 10:24:36 MDT 2001",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
JSTOR database",
acknowledgement = ack-nhfb,
}
@Article{Katz:1986:FDP,
author = "Talbot M. Katz and Daniel I. A. Cohen",
title = "The First Digit Property for Exponential Sequences is
Independent of the Underlying Distribution",
journal = j-FIB-QUART,
volume = "24",
number = "1",
pages = "2--7",
month = feb,
year = "1986",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:45 MDT 2011",
bibsource = "http://www.fq.math.ca/24-1.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/24-1/katz.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@Article{Lemons:1986:NTD,
author = "Don S. Lemons",
title = "On the number of things and the distribution of first
digits",
journal = j-AMER-J-PHYSICS,
volume = "54",
number = "9",
pages = "816--817",
month = sep,
year = "1986",
CODEN = "AJPIAS",
DOI = "http://dx.doi.org/10.1119/1.14453",
ISSN = "0002-9505",
bibdate = "Wed Nov 23 12:03:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ajp.aapt.org/",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
keywords = "Benford's Law",
remark = "Lemons gives a derivation of Benford's Law that does
not assume scale invariance, unlike other widely-cited
derivations
\cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.",
}
@Book{Lines:1986:NYT,
author = "Malcolm E. Lines",
title = "A number for your thoughts: facts and speculations
about numbers from {Euclid} to the latest computers",
publisher = pub-ADAM-HILGER,
address = pub-ADAM-HILGER:adr,
pages = "vi + 214",
year = "1986",
ISBN = "0-85274-495-1 (paperback)",
ISBN-13 = "978-0-85274-495-6 (paperback)",
LCCN = "QA241 .L617 1986",
bibdate = "Wed Nov 23 11:34:02 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.gbv.de:20011/gvk",
URL = "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html",
acknowledgement = ack-nhfb,
remark = "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law
of Benford''.",
subject = "number theory",
}
@Article{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 = "??",
pages = "171--182",
month = "????",
year = "1987",
CODEN = "IPMADK",
DOI = "http://dx.doi.org/10.1016/0306-4573(87)90002-1",
ISSN = "0306-4573 (print), 1873-5371 (electronic)",
ISSN-L = "0306-4573",
bibdate = "Sat Nov 12 10:49:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A rigorous analysis of Zipf's law is made using an
index for the sequence of observed values of the
variables in a Zipf-type relationship. Three important
properties relating rank, count, and frequency are
identified. Using this approach, the shape of Zipf-type
curves can be described in terms of three distinct
regions and two parameters of the Mandelbrot--Zipf law.
This result has considerable practical significance,
since it provides rigorous foundations for the
application of Zipf's law.",
acknowledgement = ack-nhfb,
classmath = "62P99 (Appl. of statistics)",
fjournal = "Information Processing and Management",
keywords = "index approach; Mandelbrot-Zipf law; Zipf's law",
ZMnumber = "0614.62150",
}
@Article{Fedorowicz:1987:DPE,
author = "Jane Fedorowicz",
title = "Database Performance Evaluation in an Indexed File
Environment",
journal = j-TODS,
volume = "12",
number = "1",
pages = "85--110",
month = mar,
year = "1987",
CODEN = "ATDSD3",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Sat Apr 14 10:34:48 MDT 2001",
bibsource = "Compendex database; Database/Graefe.bib;
Database/Wiederhold.bib; http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf;
http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/;
http://www.acm.org/pubs/toc/Abstracts/tods/13675.html",
abstract = "The use of database systems for managerial decision
making often incorporates information-retrieval
capabilities with numeric report generation. Of great
concern to the user of such a system is the response
time associated with issuing a query to the database.
This study presents a procedure for estimating response
time for one of the most frequently encountered
physical storage mechanisms, the indexed file. The
model provides a fairly high degree of accuracy, but is
simple enough so that the cost of applying the model is
not exorbitant. The model incorporates the knowledge
that the distribution of access key occurrences is
known to follow Zipf's law. It first estimates the
access time required to complete the query, which
includes the time needed for all input and output
transactions, and CPU time used in performing the
search. The effects of multiple users on an
individual's response time are then assessed using a
simple regression estimation technique. The two-step
procedure allows for the separation of access time from
multiuser influences.",
acknowledgement = ack-nhfb,
affiliation = "Boston Univ, Boston, MA, USA",
affiliationaddress = "Boston Univ, Boston, MA, USA",
annote = "a procedure for estimating response time; distribution
of access key occurrences follow Zipf's law. Early
version with Kellogg, J. L. Model provides a fairly
high degree of accuracy but is simple. The effects of
multiple users are assessed using simple regression
estimation.",
classification = "723; 912; 922",
fjournal = "ACM Transactions on Database Systems",
generalterms = "Design; Performance",
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",
ISSN-L = "0040-1706",
bibdate = "Fri Nov 25 16:39:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
}
@Article{Kunoff:1987:FDP,
author = "Sharon Kunoff",
title = "{$N!$} has the First Digit Property",
journal = j-FIB-QUART,
volume = "25",
number = "4",
pages = "365--367",
month = nov,
year = "1987",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:01:00 MDT 2011",
bibsource = "http://www.fq.math.ca/25-4.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@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",
MRclass = "60E99 (11B37)",
MRnumber = "926460 (88m:60047)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Tsukuba Journal of Mathematics",
}
@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 = "http://dx.doi.org/10.1108/eb008188",
ISSN = "0736-3761",
bibdate = "Fri Nov 25 06:56:30 2011",
bibsource = "http://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 = "http://dx.doi.org/10.1108/eb024706",
ISSN = "0887-6045",
bibdate = "Fri Nov 25 06:56:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1987:ABM,
author = "P. 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",
bibdate = "Sat Nov 12 15:58:50 2011",
bibsource = "http://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 = "P. Schatte",
title = "Some estimates of the {$\mathcal{H}_\infty$}-uniform
distribution",
journal = j-MONAT-MATH,
volume = "103",
number = "??",
pages = "233--249",
month = "????",
year = "1987",
CODEN = "MNMTA2",
ISSN = "0026-9255 (print), 1436-5081 (electronic)",
ISSN-L = "0026-9255",
bibdate = "Sat Nov 12 15:57:05 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
}
@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 = "http://dx.doi.org/10.2307/3616283",
ISSN = "0025-5572",
bibdate = "Tue Oct 30 23:36:58 2007",
bibsource = "http://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",
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",
MRclass = "92A90",
MRnumber = "1016850 (90g:92114)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annales de la Societ{\'e} Scientifique de Bruxelles.
S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques
et Physiques",
language = "French",
}
@Article{Carslow:1988:AIN,
author = "C. Carslow",
title = "Anomalies in Income Numbers. {Evidence} of Goal
Oriented Behavior",
journal = j-ACCOUNT-REV,
volume = "63",
number = "2",
pages = "321--327",
month = apr,
year = "1988",
CODEN = "ACRVAS",
ISSN = "0001-4826 (print), 1558-7967 (electronic)",
ISSN-L = "0001-4826",
bibdate = "Sat Dec 10 11:19:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/248109",
acknowledgement = ack-nhfb,
fjournal = "The Accounting Review",
keywords = "Benford's Law",
remark = "This paper references neither Newcomb nor Benford, but
it uses their digit-frequency formula from
\cite{Feller:1966:IPT} to compare with data on revenues
of New Zealand companies.",
}
@InCollection{Kanemitsu:1988:BLF,
author = "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard
Rauzy and Jau-Shyong Shiue",
booktitle = "Probability theory and mathematical statistics
({Kyoto}, 1986)",
title = "On {Benford}'s law: the first digit problem",
volume = "1299",
publisher = pub-SV,
address = pub-SV:adr,
pages = "158--169",
year = "1988",
DOI = "http://dx.doi.org/10.1007/BFb0078471",
MRclass = "11K06 (60E99)",
MRnumber = "935987 (89d:11059)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Math.",
acknowledgement = ack-nhfb,
}
@InCollection{Nicolis:1988:PBZ,
author = "John S. Nicolis",
booktitle = "Synergetics, order and chaos ({Madrid}, 1987)",
title = "On the parallel between {Zipf}'s law and {$1 / f$}
processes in chaotic systems possessing coexisting
attractors",
publisher = "World Sci. Publ.",
address = "Teaneck, NJ, USA",
pages = "723--734",
year = "1988",
MRclass = "58F13 (00A69)",
MRnumber = "1115922 (92g:58087)",
MRreviewer = "Dieter H. Mayer",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{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;
http://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",
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 = "http://dx.doi.org/10.1108/eb006057",
ISSN = "0885-8624",
bibdate = "Fri Nov 25 07:04:53 2011",
bibsource = "http://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 = "http://dx.doi.org/10.1002/mana.19881350108",
ISSN = "0025-584X",
MRclass = "60F15 (11K31)",
MRnumber = "944219 (89g:60114)",
MRreviewer = "S. A. Book",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
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",
year = "1988",
CODEN = "PTRFEU",
DOI = "http://dx.doi.org/10.1007/BF00334035",
ISSN = "0178-8051",
ISSN-L = "0178-8051",
MRclass = "60F15 (11K31)",
MRnumber = "927235 (89b:60081)",
MRreviewer = "L. Kuipers",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Probability Theory and Related Fields",
}
@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",
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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
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 = "http://dx.doi.org/10.1002/mana.19881360119",
ISSN = "0025-584X",
MRclass = "11K06 (11K31)",
MRnumber = "952478 (89j:11075)",
MRreviewer = "O. P. Stackelberg",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
onlinedate = "11 Nov 2006",
}
@Article{Arnold:1989:BEP,
author = "Barry C. Arnold and S. James Press",
title = "{Bayesian} estimation and prediction for {Pareto}
data",
journal = j-J-AM-STAT-ASSOC,
volume = "84",
number = "408",
pages = "1079--1084",
month = "????",
year = "1989",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62F15 (62F10)",
MRnumber = "92f:62034",
bibdate = "Mon May 5 12:36:01 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
}
@Article{Chen:1989:ZLT,
author = "Ye-Sho Chen",
title = "{Zipf}'s laws in text modeling",
journal = "Internat. J. Gen. Systems",
volume = "15",
number = "3",
pages = "233--252",
year = "1989",
CODEN = "IJGSAX",
DOI = "http://dx.doi.org/10.1080/03081078908935048",
ISSN = "0308-1079",
MRclass = "92A90",
MRnumber = "1015844",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of General Systems. Methodology,
Applications, Education",
}
@InProceedings{Kitsuregawa:1989:EBS,
author = "Masaru Kitsuregawa and Masaya Nakayama and Mikio
Takagi",
title = "The Effect of Bucket Size Tuning in the Dynamic Hybrid
{GRACE} Hash Join Method",
crossref = "Apers:1989:VLD",
pages = "257--266",
month = aug,
year = "1989",
CODEN = "VLDBDP",
bibdate = "Sat Jan 25 17:38:12 MST 1997",
bibsource = "Compendex database;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/hash.bib",
abstract = "In this paper, we show detailed analysis and
performance evaluation of the Dynamic Hybrid GRACE Hash
Join Method (DHGH Method) when the tuple distribution
in buckets is unbalanced. The conventional Hash Join
Methods specify the tuple distribution in buckets
statically. However it may differ from estimation since
join operations are applied with selection operations.
When the tuple distribution in buckets is unbalanced,
the processing cost of join operation becomes more
costly than the ideal case when you use Hybrid Hash
Join Method (HH Method). On the other hand, when you
use the DHGH Method, the destaging buckets are selected
dynamically, gives the same performance as the ideal
case even if the tuple distribution in buckets is
unbalanced such as Zipf-like distributions.",
acknowledgement = ack-nhfb,
affiliation = "Univ of Tokyo",
affiliationaddress = "Tokyo, Jpn",
classification = "723",
journalabr = "Very Large Data Bases Int Conf Very Large Data Bases",
keywords = "Computer Metatheory --- Programming Theory; Computer
Programming --- Algorithms; Database Systems; Query
Processing; Relational; Relational Algebra; VLDB",
}
@Article{Lang:1989:UAB,
author = "Sheau-Dong Lang and James R. Driscoll and Jiann H.
Jou",
title = "A Unified Analysis of Batched Searching of Sequential
and Tree-Structured Files",
journal = j-TODS,
volume = "14",
number = "4",
pages = "604--618",
month = dec,
year = "1989",
CODEN = "ATDSD3",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
MRclass = "68P10 (68P20)",
MRnumber = "1 073 204",
bibdate = "Sat Apr 14 10:34:48 MDT 2001",
bibsource = "Database/Graefe.bib; Database/Wiederhold.bib;
http://www.acm.org/pubs/toc/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf;
http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/;
http://www.acm.org/pubs/toc/Abstracts/tods/76908.html",
abstract = "A direct and unified approach is used to analyze the
efficiency of batched searching of sequential and
tree-structured files. The analysis is applicable to
arbitrary search distributions, and closed-form
expressions are obtained for the expected batched
searching cost and savings. In particular, we consider
a search distribution satisfying Zipf's law for
sequential files and four types of uniform (random)
search distribution for sequential and tree-structured
files. These results unify and extend earlier research
on batched searching and estimating block accesses for
database systems.",
acknowledgement = ack-nhfb,
affiliation = "Central Florida Univ., Orlando, FL, USA",
annote = "closed-form expressions for the number of accesses
needed given arbitrary search distributions.",
fjournal = "ACM Transactions on Database Systems",
generalterms = "Algorithms; Design; Performance; Theory",
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{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",
year = "1989",
CODEN = "JSTPSB",
ISSN = "0022-4715",
ISSN-L = "0022-4715",
MRclass = "58F13 (58F14 58F20)",
MRnumber = "988565 (90b:58184)",
MRreviewer = "Shi Hai Li",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Physics",
}
@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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Progress of Theoretical Physics",
}
@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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Monatshefte f{\"u}r Mathematik",
}
@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",
year = "1989",
CODEN = "ECLEDS",
DOI = "http://dx.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 = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
}
@Article{Katsikas:1990:CDG,
author = "A. A. Katsikas and J. S. Nicolis",
title = "Chaotic dynamics of generating {Markov} partitions and
linguistic sequences mimicking {Zipf}'s law",
journal = "Nuovo Cimento D (1)",
volume = "12",
number = "2",
pages = "177--195",
year = "1990",
CODEN = "NCSDDN",
DOI = "http://dx.doi.org/10.1007/BF02450454",
ISSN = "0392-6737",
MRclass = "92A90 (58F13 92A08 94A15)",
MRnumber = "1049338 (90m:92114)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D.
Serie 1",
}
@InCollection{Nagasaka:1990:BLL,
author = "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong
Shiue",
booktitle = "Number theory, {Vol}.\ {I} ({Budapest}, 1987)",
title = "{Benford}'s law: the logarithmic law of first digit",
volume = "51",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "361--391",
year = "1990",
MRclass = "11K06",
MRnumber = "1058225 (92b:11048)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Colloq. Math. Soc. J{\'a}nos Bolyai",
acknowledgement = ack-nhfb,
}
@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",
MRclass = "11K50 (11K06)",
MRnumber = "1127337 (92m:11077)",
MRreviewer = "Harald Niederreiter",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
}
@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 = "http://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.zentralblatt-math.org/zmath/en/search/?an=0743.60004;
http://www.gbv.de/dms/hbz/toc/ht003363686.pdf",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Yeh:1990:ODT,
author = "Hsiaw-Chan Yeh",
title = "One discrete time series model for fat-tailed integer
random variables: {Zipf} process",
journal = "Bull. Inst. Math. Acad. Sinica",
volume = "18",
number = "1",
pages = "19--33",
year = "1990",
CODEN = "BIMSDG",
ISSN = "0304-9825",
MRclass = "60J10 (62M10)",
MRnumber = "1072827 (91i:60175)",
MRreviewer = "Ed McKenzie",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
}
@Article{Burke:1991:BLP,
author = "John Burke and Eric Kincanon",
title = "{Benford}'s law and physical constants: The
distribution of initial digits",
journal = j-AMER-J-PHYSICS,
volume = "59",
number = "10",
pages = "952--952",
month = oct,
year = "1991",
CODEN = "AJPIAS",
DOI = "http://dx.doi.org/10.1119/1.16838",
ISSN = "0002-9505",
bibdate = "Mon Nov 14 17:31:11 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B;
http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
}
@Article{Chen:1991:ZLN,
author = "Ye-Sho Chen",
title = "{Zipf}'s law in natural languages, programming
languages, and command languages: the {Simon--Yule}
approach",
journal = j-INT-J-SYST-SCI,
volume = "22",
number = "11",
pages = "2299--2312",
year = "1991",
CODEN = "IJSYA9",
DOI = "http://dx.doi.org/10.1080/00207729108910791",
ISSN = "0020-7721",
ISSN-L = "0020-7721",
bibdate = "Sat Nov 12 10:50:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
ZMnumber = "0793.68020",
}
@Book{Durrett:1991:PTE,
author = "Richard Durrett",
title = "Probability: theory and examples",
publisher = "Wadsworth and Brooks\slash Cole Advanced Books and
Software",
address = "Pacific Grove, CA, USA",
pages = "ix + 453",
year = "1991",
ISBN = "0-534-13206-5",
ISBN-13 = "978-0-534-13206-4",
LCCN = "QA273 .D865 1991",
bibdate = "Mon Nov 21 10:06:18 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$49.95",
series = "The Wadsworth and Brooks\slash Cole statistics\slash
probability series",
acknowledgement = ack-nhfb,
remark = "Benford's Law is treated on pp. 300ff. Hill \cite[page
893]{Hill:1995:BII} reports that Durrett has a proof
that the $k$-th digit of powers of integers follows
Benford's Law.",
subject = "Probabilities",
}
@Book{Hardy:1991:DS,
author = "G. H. (Godfrey Harold) Hardy",
title = "Divergent series",
publisher = "Chelsea Pub. Co.",
address = "New York, NY, USA",
edition = "Second",
pages = "xvi + 396",
year = "1991",
ISBN = "0-8284-0334-1",
ISBN-13 = "978-0-8284-0334-4",
LCCN = "QA295 .H29 1991",
bibdate = "Wed Nov 16 08:17:27 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1877--1947",
remark = "Unaltered reprint of \cite{Hardy:1949:DS}, despite
label of second edition.",
subject = "Divergent series",
}
@Article{Katsikas:1991:CDG,
author = "A. A. Katsikas and J. S. Nicolis",
title = "Chaotic Dynamics of Generating {Markov} Partitions,
and Linguistic Sequences Mimicking {Zipf}'s Law",
journal = j-LECT-NOTES-COMP-SCI,
volume = "565",
pages = "335--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon May 13 08:51:55 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
}
@Article{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",
ISSN-L = "0232-2064",
MRclass = "11K31",
MRnumber = "1155374 (93b:11101)",
MRreviewer = "F. Schweiger",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://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 = "http://dx.doi.org/10.1007/BF00972327",
ISSN = "0132-2818",
MRclass = "60F15 (11K99)",
MRnumber = "1161363 (93g:60067)",
MRreviewer = "O. P. Stackelberg",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://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",
}
@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",
MRclass = "00A69 (92K20)",
MRnumber = "1153554",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii Nauk SSSR",
}
@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",
MRclass = "11K36",
MRnumber = "1272624 (95c:11097)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Journal of Okayama University",
}
@Article{Gunther:1992:PCZ,
author = "R. G{\"u}nther and B. Schapiro and P. Wagner",
title = "Physical complexity and {Zipf}'s law",
journal = j-INT-J-THEOR-PHYS,
volume = "31",
number = "3",
pages = "525--543",
year = "1992",
CODEN = "IJTPBM",
DOI = "http://dx.doi.org/10.1007/BF00740003",
ISSN = "0020-7748 (print), 1572-9575 (electronic)",
ISSN-L = "0020-7748",
MRclass = "58F40",
MRnumber = "1154668 (92k:58252)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Theoretical Physics",
}
@Article{Jech:1992:LDL,
author = "Thomas Jech",
title = "The logarithmic distribution of leading digits and
finitely additive measures",
journal = j-DISCRETE-MATH,
volume = "108",
number = "1--3",
pages = "53--57",
month = "????",
year = "1992",
CODEN = "DSMHA4",
ISSN = "0012-365X (print), 1872-681X (electronic)",
ISSN-L = "0012-365X",
bibdate = "Fri Nov 18 12:12:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete Mathematics",
}
@Article{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 = "??",
pages = "329--361",
month = "????",
year = "1992",
ISSN = "1050-5164",
bibdate = "Mon Nov 21 07:49:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of applied probability",
}
@Article{Li:1992:RTE,
author = "W. Li",
title = "Random texts exhibit {Zipf}'s-law-like word frequency
distribution",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "38",
number = "6",
pages = "1842--1845",
month = "????",
year = "1992",
CODEN = "IETTAW",
DOI = "http://dx.doi.org/10.1109/18.165464",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Nov 18 12:32:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
}
@PhdThesis{Nigrini:1992:DIE,
author = "Mark J. Nigrini",
title = "The detection of income tax evasion through an
analysis of digital distributions",
type = "Thesis ({Ph.D.})",
school = "Department of Accounting, University of Cincinnati",
address = "Cincinnati, OH, USA",
pages = "????",
month = "????",
year = "1992",
bibdate = "Sat Nov 12 15:47:41 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.doi.org/10.1108/10610429210036762",
ISSN = "1061-0421",
bibdate = "Fri Nov 25 06:50:32 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Product \& Brand Management",
keywords = "80/20 rule",
}
@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 = "http://dx.doi.org/10.1109/24.159803",
ISSN = "0018-9529",
ISSN-L = "0018-9529",
bibdate = "Sat Nov 12 10:50:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
classmath = "68M15 (Reliability and testing of computer systems)
68N01 (General)",
fjournal = "IEEE Transactions on Reliability",
ZMnumber = "0825.68222",
}
@Article{Buck:1993:IBF,
author = "B. Buck and A. C. Merchant and S. M. Perez",
title = "An illustration of {Benford}'s first digit law using
alpha decay half lives",
journal = j-EUR-J-PHYS,
volume = "14",
number = "2",
pages = "59--63",
month = "????",
year = "1993",
CODEN = "EJPHD4",
ISSN = "0143-0807 (print), 1361-6404 (electronic)",
ISSN-L = "0143-0807",
bibdate = "Mon Nov 14 17:32:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/1993EJPh...14...59B",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Physics",
}
@Article{Deakin:1993:ADB,
author = "Michael A. B. Deakin",
title = "Another derivation of {Benford}'s law",
journal = j-AUSTRALIAN-MATH-SOC-GAZ,
volume = "20",
number = "5",
pages = "162--163",
year = "1993",
CODEN = "????",
ISSN = "0311-0729",
ISSN-L = "0311-0729",
MRclass = "11K36",
MRnumber = "1268513 (95j:11072)",
MRreviewer = "Jean-Loup Mauclaire",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Mathematical Society Gazette",
}
@Article{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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://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",
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 = "http://dx.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;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://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",
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",
}
@Article{Boyle:1994:AFS,
author = "Jeff Boyle",
title = "An application of {Fourier} series to the most
significant digit problem",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "9",
pages = "879--886",
month = nov,
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "60F99",
MRnumber = "1 300 493",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@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/;
http://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",
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{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",
bibdate = "Sat Dec 10 11:17:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Wall Street Journal",
}
@Book{Bologna:1995:FAF,
author = "Jack Bologna and Robert J. Lindquist",
title = "Fraud auditing and forensic accounting: new tools and
techniques",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xv + 249",
year = "1995",
ISBN = "0-471-10646-1 (hardcover)",
ISBN-13 = "978-0-471-10646-3 (hardcover)",
LCCN = "HV8079.W47 B65 1995",
bibdate = "Tue Nov 22 10:31:53 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley042/95005510.html;
http://www.loc.gov/catdir/description/wiley033/95005510.html;
http://www.loc.gov/catdir/toc/onix04/95005510.html",
acknowledgement = ack-nhfb,
remark = "This book does not discuss Benford's Law, but may be
helpful background for application of that law to the
detection of fraud.",
subject = "white collar crime investigation; United States;
forensic accounting; fraud investigation",
}
@Article{Hill:1995:BII,
author = "Theodore P. Hill",
title = "Base-invariance implies {Benford's Law}",
journal = j-PROC-AM-MATH-SOC,
volume = "123",
number = "3",
pages = "887--895",
month = mar,
year = "1995",
CODEN = "PAMYAR",
DOI = "http://dx.doi.org/10.2307/2160815",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "60A10 (28D05)",
MRnumber = "1233974 (95d:60006)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/2160815",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
}
@Article{Hill:1995:SDP,
author = "Theodore P. Hill",
title = "The significant-digit phenomenon",
journal = j-AMER-MATH-MONTHLY,
volume = "102",
number = "4",
pages = "322--327",
month = apr,
year = "1995",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.2307/2974952",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11K99 (60E99)",
MRnumber = "96f:11101",
MRreviewer = "Jean-Loup Mauclaire",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
}
@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",
MRclass = "60E99 (60A10 62E99)",
MRnumber = "1421567 (98a:60021)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 10:09:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "2-P&origin=MSN;
http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science. A Review Journal of the Institute
of Mathematical Statistics",
ZMnumber = "Zbl 0955.60509",
}
@Article{Mosimann:1995:DFC,
author = "James E. Mosimann and Claire V. Wiseman and Ruth E.
Edelman",
title = "Data Fabrication: Can People Generate Random Digits?",
journal = j-ACCOUNT-RES,
volume = "4",
number = "1",
pages = "31--55",
month = "????",
year = "1995",
CODEN = "ARQAEZ",
ISSN = "0898-9621 (print), 1545-5815 (electronic)",
ISSN-L = "0898-9621",
bibdate = "Sat Dec 10 11:56:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866",
acknowledgement = ack-nhfb,
fjournal = "Accountability in Research",
keywords = "Benford's Law",
remark = "The abstract ends with: ``The difficulty that people
have in creating random error digits supports the
utility of examining such digits in investigations of
scientific misconduct.''",
}
@Article{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 = "http://dx.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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@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",
year = "1995",
CODEN = "CSDADW",
DOI = "http://dx.doi.org/10.1016/0167-9473(94)00009-8",
ISSN = "0167-9473",
ISSN-L = "0167-9473",
MRclass = "62E10 (62F10)",
MRnumber = "1333065 (96f:62029)",
MRreviewer = "Friedrich Liese",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
}
@Book{Bak:1996:HNW,
author = "Per Bak",
title = "How nature works: the science of self-organized
criticality",
publisher = "Copernicus",
address = "New York, NY, USA",
pages = "xiii + 212 + 8",
year = "1996",
ISBN = "0-387-94791-4 (hardcover)",
ISBN-13 = "978-0-387-94791-4 (hardcover)",
LCCN = "QC173.4.C74 B34 1996",
bibdate = "Thu Nov 24 13:34:22 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "Zipf's Law",
subject = "Critical phenomena (Physics); Complexity (Philosophy);
Physics; Philosophy",
}
@Article{Beirlant:1996:TIE,
author = "Jan Beirlant and Petra Vynckier and Jozef L. Teugels",
title = "Tail Index Estimation, {Pareto} Quantile Plots, and
Regression Diagnostics",
journal = j-J-AM-STAT-ASSOC,
volume = "91",
number = "436",
pages = "1659--??",
month = "????",
year = "1996",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon May 5 08:26:17 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
}
@Article{Campanino:1996:IIM,
author = "Massimo Campanino and Stefano Isola",
title = "Infinite invariant measures for non-uniformly
expanding transformations of $[0, 1]$: Weak law of
large numbers with anomalous scaling",
journal = j-FORUM-MATH,
volume = "8",
number = "1",
pages = "71--92",
year = "1996",
CODEN = "FOMAEF",
DOI = "http://dx.doi.org/10.1515/form.1996.8.71",
ISSN = "0933-7741 (print), 1435-5337 (electronic)",
ISSN-L = "0933-7741",
bibdate = "Sat Nov 12 10:33:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
ZMnumber = "0837.60022",
}
@Article{Gunther:1996:ZLE,
author = "R. G{\"u}nther and L. Levitin and B. Schapiro and P.
Wagner",
title = "{Zipf}'s law and the effect of ranking on probability
distributions",
journal = j-INT-J-THEOR-PHYS,
volume = "35",
number = "2",
pages = "395--417",
year = "1996",
CODEN = "IJTPBM",
DOI = "http://dx.doi.org/10.1007/BF02083823",
ISSN = "0020-7748 (print), 1572-9575 (electronic)",
ISSN-L = "0020-7748",
bibdate = "Sat Nov 12 10:53:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
keywords = "numerical simulations; ranking procedures; Zipf's
law",
ZMnumber = "0843.60002",
}
@Article{Ley:1996:PDU,
author = "Eduardo Ley",
title = "On the Peculiar Distribution of the {U.S.} Stock
Indexes' Digits",
journal = j-AMER-STAT,
volume = "50",
number = "4",
pages = "311--313",
month = nov,
year = "1996",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Nov 14 15:09:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2684926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@Article{Nigrini:1996:TCA,
author = "M. Nigrini",
title = "A Taxpayer Compliance Application of {Benford's Law}",
journal = "J. Amer. Tax. Assoc.",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Taxation Association",
}
@Article{Allaart:1997:ISC,
author = "Pieter C. Allaart",
title = "An Invariant-Sum Characterization of {Benford's Law}",
journal = j-J-APPL-PROBAB,
volume = "34",
number = "1",
pages = "288--291",
month = mar,
year = "1997",
CODEN = "JPRBAM",
DOI = "http://dx.doi.org/10.2307/3215195",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "60E05",
MRnumber = "1429075 (98d:60029)",
MRreviewer = "Peter Schatte",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/3215195",
abstract = "The accountant Nigrini remarked that in tables of data
distributed according to Benford's law, the sum of all
elements with first digit $d (d = 1, 2, \cdots, 9)$ 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 $d_{1}, \cdots, d_{k}$ is constant
for every fixed $k$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Castillo:1997:FGP,
author = "Enrique Castillo and Ali S. Hadi",
title = "Fitting the Generalized {Pareto} Distribution to
Data",
journal = j-J-AM-STAT-ASSOC,
volume = "92",
number = "440",
pages = "1609--1620",
month = dec,
year = "1997",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Mon Oct 30 06:57:36 MST 2000",
bibsource = "http://www.amstat.org/publications/jasa/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
URL = "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM;
http://www.jstor.org/stable/2965432",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
}
@Article{Chen:1997:NHS,
author = "Weishing Chen and Tai-Hsi Wu",
title = "A non-homogeneous software reliability model based on
{Zipf}'s law",
journal = "International Journal of Quality \& Reliability
Management",
volume = "14",
number = "4",
pages = "409--431",
month = "????",
year = "1997",
DOI = "http://dx.doi.org/10.1108/02656719710170666",
ISSN = "0265-671X (print), 1758-6682 (electronic)",
bibdate = "Fri Nov 25 07:08:17 2011",
bibsource = "http://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 = "http://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/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02664769723594",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
keywords = "Benford's Law; Zipf's Law",
xxpages = "383--394",
}
@Book{Knuth:1997:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xiii + 762",
year = "1997",
ISBN = "0-201-89684-2",
ISBN-13 = "978-0-201-89684-8",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See section 4.2.4V, The Fraction Parts, pages
254--262, for a discussion of Benford's Law.",
price = "US\$52.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
}
@Article{Nigrini:1997:UBL,
author = "M. 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 = "http://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",
}
@Article{Browne:1998:FBL,
author = "Malcolm W. Browne",
title = "Following {Benford's Law}, or Looking Out for {No.
1}",
journal = j-NY-TIMES,
day = "4",
month = aug,
year = "1998",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibdate = "Wed Nov 16 10:26:48 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "New York Times",
}
@Article{Busta:1998:UBL,
author = "Bruce Busta and Randy Weinberg",
title = "Using {Benford's Law} and Neural Networks as a Review
Procedure",
journal = "Managerial Auditing Journal",
volume = "13",
number = "6",
pages = "356--366",
month = "????",
year = "1998",
CODEN = "????",
DOI = "http://dx.doi.org/10.1108/02686909810222375",
ISSN = "0268-6902 (print), 1758-7735 (electronic)",
ISSN-L = "0268-6902",
bibdate = "Tue Nov 22 18:50:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{DeCeuster:1998:HPB,
author = "M. J. K. DeCeuster and G. Dhaene and T. Schatteman",
title = "On the hypothesis of psychological barriers in stock
markets and {Benford}'s law",
journal = j-J-EMPIR-FINANCE,
volume = "5",
number = "3",
pages = "263--279",
month = sep,
year = "1998",
CODEN = "JEFIEC",
DOI = "http://dx.doi.org/10.1016/S0927-5398(97)00024-8",
ISSN = "0927-5398 (print), 1879-1727 (electronic)",
ISSN-L = "0927-5398",
bibdate = "Sun Nov 13 11:33:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
acknowledgement = ack-nhfb,
fjournal = "Journal of Empirical Finance",
}
@Article{Hill:1998:FDP,
author = "Theodore P. Hill",
title = "The First Digit Phenomenon",
journal = j-AM-SCI,
volume = "86",
number = "4",
pages = "358--363",
month = jul # "\slash " # aug,
year = "1998",
CODEN = "AMSCAC",
DOI = "http://dx.doi.org/10.1511/1998.4.358",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Sat Dec 10 11:54:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf;
http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.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",
keywords = "Benford's Law; Law of Anomalous Numbers; 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 = "http://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{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 = "http://dx.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 = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/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",
keywords = "Benford's Law",
}
@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",
month = "????",
year = "1998",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.57.1347",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Wed Nov 23 11:14:21 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "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)",
}
@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 = "http://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{Barabasi:1999:ESR,
author = "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka
Albert",
title = "Emergence of scaling in random networks",
journal = j-SCIENCE,
volume = "286",
number = "5439",
pages = "509--512",
day = "15",
month = oct,
year = "1999",
CODEN = "SCIEAS",
DOI = "http://dx.doi.org/10.1126/science.286.5439.509",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Tue Nov 15 09:57:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/286/5439/509",
acknowledgement = ack-nhfb,
fjournal = "Science",
keywords = "power-law distribution; Zipf's Law",
}
@Article{Coderre:1999:FDU,
author = "David Coderre",
title = "Fraud Detection Using Digital Analysis",
journal = j-EDPACS,
volume = "27",
number = "3",
pages = "1--8",
month = "????",
year = "1999",
CODEN = "EDPCDF",
DOI = "http://dx.doi.org/10.1201/1079/43249.27.3.19990901/30268.1",
ISSN = "0736-6981 (print), 1936-1009 (electronic)",
ISSN-L = "0736-6981",
bibdate = "Sat Jan 07 09:20:49 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1",
acknowledgement = ack-nhfb,
fjournal = "EDPACS",
keywords = "Benford's Law",
onlinedate = "21 Dec 2006",
}
@Article{Gabaix:1999:ZLC,
author = "Xavier Gabaix",
title = "{Zipf}'s law for cities: An explanation",
journal = j-Q-J-ECON,
volume = "114",
number = "3",
pages = "739--767",
year = "1999",
CODEN = "QJECAT",
DOI = "http://dx.doi.org/10.1162/003355399556133",
ISSN = "0033-5533 (print), 1531-4650 (electronic)",
ISSN-L = "0033-5533",
bibdate = "Sat Nov 12 10:57:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
ZMnumber = "0952.91059",
}
@Article{Hill:1999:DFD,
author = "T. P. Hill",
title = "The Difficulty of Faking Data",
journal = j-CHANCE,
volume = "12",
number = "3",
pages = "27--31",
month = "????",
year = "1999",
CODEN = "CNDCE4",
ISSN = "0933-2480 (print), 1867-2280 (electronic)",
bibdate = "Tue Nov 22 18:54:44 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://chance.amstat.org/",
acknowledgement = ack-nhfb,
fjournal = "Chance: a magazine for people interested in the
analysis of data",
keywords = "Benford's Law",
}
@Article{Huberman:1999:IGD,
author = "Bernardo A. Huberman and Lada A. Adamic",
title = "{Internet}: Growth dynamics of the {World-Wide Web}",
journal = j-NATURE,
volume = "401",
number = "6749",
pages = "131--131",
day = "9",
month = sep,
year = "1999",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/43604",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Tue Nov 15 09:52:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf;
http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html",
acknowledgement = ack-nhfb,
lastaccess = "23 November 2011",
}
@Article{Matthews:1999:PO,
author = "Robert Matthews",
title = "The Power of One",
journal = j-NEW-SCIENTIST,
volume = "163",
number = "2194",
pages = "27--30",
day = "10",
month = jul,
year = "1999",
CODEN = "NWSCAL",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Mon Nov 14 16:04:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.fortunecity.com/emachines/e11/86/one.html;
http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
xxISSN = "0262-4079, 0028-6664",
}
@Article{Nigrini:1999:IGY,
author = "M. Nigrini",
title = "{I}'ve Got Your Number",
journal = j-J-ACCOUNTANCY,
volume = "187",
number = "??",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accountancy",
}
@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 = "http://dx.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 = "http://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{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",
ISSN = "0764-4442 (print), 1778-3577 (electronic)",
ISSN-L = "0764-4442",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0764444299802651",
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{Drake:2000:CAA,
author = "P. D. Drake and M. J. Nigrini",
title = "Computer assisted analytical procedures using
{Benford}'s law",
journal = j-J-ACCOUNT-EDUC,
volume = "18",
number = "2",
pages = "127--146",
month = "Spring",
year = "2000",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S0748-5751(00)00008-7",
ISSN = "0748-5751 (print), 1873-1996 (electronic)",
ISSN-L = "0748-5751",
bibdate = "Tue Nov 22 10:36:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/journal/07485751;
http://www.sciencedirect.com/science/article/pii/S0748575100000087",
acknowledgement = ack-nhfb,
fjournal = "Journal of Accounting Education",
}
@Article{Lanza:2000:UDA,
author = "R. B. Lanza",
title = "Using digital analysis to detect fraud: Review of the
{DATAS\reg} statistical analysis tool",
journal = j-J-FORENSIC-ACCOUNT,
volume = "1",
number = "??",
pages = "291--296",
month = "????",
year = "2000",
CODEN = "????",
ISSN = "1524-5586",
bibdate = "Tue Nov 22 10:47:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.rtedwards.com/journals/JFA/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Forensic Accounting",
}
@Article{Leemis:2000:SDS,
author = "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
Evans",
title = "Survival Distributions Satisfying {Benford's Law}",
journal = j-AMER-STAT,
volume = "54",
number = "4",
pages = "236--241",
month = nov,
year = "2000",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62E15 (62N05)",
MRnumber = "1803620",
bibdate = "Fri Jan 27 18:16:34 MST 2012",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326510;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.amstat.org/publications/tas/Leemis.htm;
http://www.jstor.org/stable/2685773",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@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 = "????",
LCCN = "????",
bibdate = "Tue Nov 22 20:48:29 MST 2011",
bibsource = "amicus.nlc-bnc.ca:210/NL;
http://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 = "http://doi.acm.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/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://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",
}
@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 = "http://dx.doi.org/10.1063/1.166498",
ISSN = "1054-1500",
ISSN-L = "1054-1500",
bibdate = "Mon Nov 14 17:35:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2000Chaos..10..331T;
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)",
}
@Article{Urzua:2000:SET,
author = "C. 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",
year = "2000",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/S0165-1765(99)00215-3",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
bibdate = "Sat Nov 12 10:56:07 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
ZMnumber = "0951.91059",
}
@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",
bibdate = "Wed Nov 23 11:30:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Accountancy",
}
@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 = "??",
month = dec,
year = "2001",
CODEN = "????",
ISSN = "1389-1286",
ISSN-L = "1389-1286",
bibdate = "Wed Feb 20 06:34:11 MST 2002",
bibsource = "http://www.elsevier.com/locate/issn/13891286;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html",
acknowledgement = ack-nhfb,
fjournal = "Computer Networks (Amsterdam, Netherlands: 1999)",
}
@Article{Gelbukh:2001:ZHL,
author = "Alexander Gelbukh and Grigori Sidorov",
title = "{Zipf} and {Heaps Laws}' Coefficients Depend on
Language",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2004",
pages = "332--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:22 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
}
@TechReport{Gent:2001:BL,
author = "Ian Gent and Toby Walsh",
title = "{Benford's Law}",
type = "Report",
institution = "School of Computer Science, University of St. Andrews,
and Department of Computer Science, University of
York",
address = "St. Andrews, Scotland and York, England",
pages = "7",
day = "2",
month = feb,
year = "2001",
bibdate = "Fri Nov 18 08:37:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf",
abstract = "Benford's Law predicts the frequency of the leading
digit in numbers met in a wide range of naturally
occurring phenomena. In data following Benford's Law,
numbers start with a small leading digit more often
those with a large leading digit. Here we demonstrate
that Benford's Law also describes a wide range of
computational phenomena. In particular, we show that a
number of different statistics associated with
computation like space and runtime often follow
Benford's Law. We also show that search cost on input
data that follows Benford's Law is often very different
to that on more uniform data. These results could be
used to improve algorithm performance (for example, for
load balancing or disk de-fragmentation), as well as to
help model algorithm performance. Benford's Law can
also be used to generate data for benchmarking
algorithms that may be more realistic than purely
random data.",
acknowledgement = ack-nhfb,
remark = "PDF file no longer at the St. Andrews URL on 18
November 2011, but recovered from
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.",
}
@Article{Hobza:2001:NBL,
author = "Tom{\'a}{\v{s}} Hobza and Igor Vajda",
title = "On the {Newcomb--Benford} law in models of statistical
data",
journal = "Rev. Mat. Complut.",
volume = "14",
number = "2",
pages = "407--420",
year = "2001",
CODEN = "????",
ISSN = "1139-1138",
MRclass = "62E10",
MRnumber = "1871305 (2002j:62015)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Revista Matem{\'a}tica Complutense",
}
@Article{Jansen:2001:RNP,
author = "C. J. M. Jansen and M. M. W. Pollmann",
title = "On Round Numbers: Pragmatic Aspects of Numerical
Expressions",
journal = j-J-QUANT-LINGUISTICS,
volume = "8",
number = "3",
pages = "187--201",
month = "????",
year = "2001",
DOI = "http://dx.doi.org/10.1076/jqul.8.3.187.4095",
ISSN = "1744-5035",
bibdate = "Sat Jan 07 09:51:05 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095",
abstract = "This paper describes and explains some regularities in
the frequency of numbers in text. An analysis of number
frequencies in text corpora in Dutch, English, German,
and French confirms the expectation that frequency is
highly dependent on two factors: magnitude and
roundness. Roundness (defined as number frequency in an
approximation context) proves to be related to three
arithmetical properties: `10-ness', `2-ness', and
`5-ness'. In predicting the frequency of numbers
irrespective of their context `$2 1/2$-ness' should be
added to these factors, as is suggested in the work of
Sigurd (1988). The role of the four number
characteristics found in this study can be explained by
the preference of the language user for using base
numbers, and for doubling and halving quantities.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Linguistics",
onlinedate = "09 Aug 2010",
}
@Article{Jolion:2001:IBL,
author = "Jean-Michel Jolion",
title = "Images and {Benford}'s law",
journal = j-J-MATH-IMAG-VIS,
volume = "14",
number = "1",
pages = "73--81",
year = "2001",
CODEN = "JMIVEK",
DOI = "http://dx.doi.org/10.1023/A:1008363415314",
ISSN = "0924-9907 (print), 1573-7683 (electronic)",
ISSN-L = "0924-9907",
MRclass = "94A08 (68U10)",
MRnumber = "1818436 (2001m:94007)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Imaging and Vision: JMIV",
}
@Article{Levene:2001:ZLW,
author = "Mark Levene and Jos{\'e} Borges and George Loizou",
title = "{Zipf}'s law for {Web} surfers",
journal = j-KNOWL-INFO-SYS,
volume = "3",
number = "1",
pages = "120--129",
year = "2001",
CODEN = "KISNCR",
DOI = "http://dx.doi.org/10.1007/PL00011657",
ISSN = "0219-1377",
bibdate = "Sat Nov 12 11:00:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
ZMnumber = "0991.68622",
}
@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 = "http://dx.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 = "http://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",
month = apr,
year = "2001",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(00)00633-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Thu Feb 15 16:36:18 2007",
bibsource = "http://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",
keywords = "Benford's Law; Law of Anomalous Numbers; 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 = "http://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{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",
month = aug,
year = "2001",
CODEN = "PLEEE8",
DOI = "http://dx.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 = "http://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)",
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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Econom. and Math. Systems",
acknowledgement = ack-nhfb,
}
@TechReport{Diekmann:2002:DFM,
author = "Andreas Diekmann",
title = "{Diagnose von Fehlerquellen und methodische
Qualit{\"a}t in der sozialwissenschaftlichen
Forschung}. ({German}) [{Diagnosis} of errors and
methodological quality in social science research]",
type = "Report",
number = "ITA-02-04",
institution = "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung",
address = "Vienna, Austria",
pages = "????",
year = "2002",
bibdate = "Thu Nov 17 19:11:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{FerreriCancho:2002:ZLR,
author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
title = "{Zipf}'s law and random texts",
journal = j-ADV-COMPLEX-SYST,
volume = "5",
number = "1",
pages = "1--6",
year = "2002",
CODEN = "????",
DOI = "http://dx.doi.org/10.1142/S0219525902000468",
ISSN = "0219-5259",
bibdate = "Sat Nov 12 11:00:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
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",
keywords = "Human language; monkey languages; random texts;
scaling; Zipf's law",
ZMnumber = "1090.91595",
}
@Article{Gottwald:2002:NBL,
author = "Georg A. Gottwald and Matthew Nicol",
title = "On the nature of {Benford's Law}",
journal = j-PHYSICA-A,
volume = "303",
number = "3--4",
pages = "387--396",
day = "15",
month = jan,
year = "2002",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/S0378-4371(01)00497-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "60C05 (28D05 60E05 82B05)",
MRnumber = "1917635 (2003d:60015)",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://adsabs.harvard.edu/abs/2002PhyA..303..387G;
http://www.sciencedirect.com/science/article/pii/S0378437101004976",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Hoyle:2002:MSM,
author = "David C. Hoyle and Magnus Rattray and Ray Jupp and
Andrew Brass",
title = "Making sense of microarray data distributions",
journal = j-BIOINFORMATICS,
volume = "18",
number = "4",
pages = "576--584",
month = apr,
year = "2002",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Fri Nov 25 11:16:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Bioinformatics",
keywords = "Benford's Law; mRNA transcription data",
}
@Article{Jones:2002:LDR,
author = "B. K. Jones",
title = "Logarithmic distributions in reliability analysis",
journal = j-MICROELECT-RELIABILITY,
volume = "42",
number = "4--5",
pages = "779--786",
month = apr # "\slash " # may,
year = "2002",
CODEN = "MCRLAS",
DOI = "http://dx.doi.org/10.1016/S0026-2714(02)00031-8",
ISSN = "0026-2714 (print), 1872-941X (electronic)",
ISSN-L = "0026-2714",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics and Reliability",
keywords = "Benford's Law; Pareto distribution; Zipf's Law",
}
@Article{Kawamura:2002:UZL,
author = "Kenji Kawamura and Naomichi Hatano",
title = "Universality of {Zipf}'s law",
journal = j-J-PHYS-SOC-JAP,
volume = "71",
number = "5",
pages = "1211--1213",
year = "2002",
CODEN = "JUPSAU",
DOI = "http://dx.doi.org/10.1143/JPSJ.71.1211",
ISSN = "0031-9015 (print), 1347-4073 (electronic)",
ISSN-L = "0031-9015",
bibdate = "Sat Nov 12 11:00:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jpsj.ipap.jp/",
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",
ZMnumber = "1063.60114",
ZMreviewer = "Neculai Curteanu (Ia\c si)",
}
@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. Theoret. Biol.",
volume = "219",
number = "4",
pages = "539--551",
year = "2002",
CODEN = "JTBIAP",
DOI = "http://dx.doi.org/10.1006/jtbi.2002.3145",
ISSN = "0022-5193",
MRclass = "92C40 (92D10)",
MRnumber = "2044066",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Theoretical Biology",
}
@Book{Livio:2002:GRS,
author = "Mario Livio",
title = "The golden ratio: the story of phi, the world's most
astonishing number",
publisher = "Broadway Books",
address = "New York, NY, USA",
pages = "viii + 294",
year = "2002",
ISBN = "0-7679-0815-5",
ISBN-13 = "978-0-7679-0815-3",
LCCN = "QA466 .L58 2002",
bibdate = "Tue Jul 08 12:29:44 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is treated on pages 231--237.",
price = "US\$24.95, CAN\$37.95",
acknowledgement = ack-nhfb,
}
@Article{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",
bibdate = "Thu Nov 17 19:20:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{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 = "??",
pages = "25--33",
month = "????",
year = "2002",
CODEN = "AMMGAS",
ISSN = "0004-9743",
bibdate = "Mon Nov 14 16:08:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bom.gov.au/amm/docs/2002/seaman.pdf",
acknowledgement = ack-nhfb,
ajournal = "Aust. Met. Mag.",
ajournal-2 = "Aust. Meteorol. Mag.",
fjournal = "Australian Meteorological Magazine",
}
@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",
year = "2002",
CODEN = "SPLTDC",
DOI = "http://dx.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 = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
}
@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)",
bibdate = "Fri Jan 9 08:41:12 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
}
@Book{Anastasi:2003:NFI,
author = "Joe Anastasi",
title = "The new forensics: investigating corporate fraud and
the theft of intellectual property",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiv + 270",
year = "2003",
ISBN = "0-471-26994-8 (hardcover)",
ISBN-13 = "978-0-471-26994-6 (hardcover)",
LCCN = "HV8079.W47 A5 2003",
bibdate = "Tue Nov 22 11:42:36 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/bios/wiley044/2003001697.html;
http://www.loc.gov/catdir/description/wiley037/2003001697.html;
http://www.loc.gov/catdir/toc/wiley031/2003001697.html",
acknowledgement = ack-nhfb,
remark = "Brief mention of Benford's Law on pp. 184--185.",
subject = "white collar crime investigation; data processing;
case studies; fraud investigation; forensic accounting;
computer security",
}
@Article{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",
year = "2003",
CODEN = "PHYSAG",
DOI = "http://dx.doi.org/10.1016/S0378-4371(02)01845-9",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B82",
MRnumber = "2030919",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "International Econophysics Conference IEC2002 (Bali)",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Book{Baldi:2003:MIW,
author = "Pierre Baldi and Paolo Frasconi and Padhraic Smyth",
title = "Modeling the {Internet} and the {Web}: probabilistic
methods and algorithms",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 285",
year = "2003",
ISBN = "0-470-86492-3 (e-book), 0-470-84906-1",
ISBN-13 = "978-0-470-86492-0 (e-book), 978-0-470-84906-4",
LCCN = "TK5105.875.I57 B35 2003eb",
bibdate = "Fri Jun 3 10:03:23 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/pagerank.bib",
acknowledgement = ack-nhfb,
subject = "Internet; Mathematical models; Telecommunication;
Traffic; World Wide Web; Cyberspace; Probabilities;
Computers; Web; General; Networking; Intranets and
Extranets",
tableofcontents = "Mathematical Background \\
Probability and Learning from a Bayesian Perspective
\\
Parameter Estimation from Data \\
Basic principles \\
A simple die example \\
Mixture Models and the Expectation Maximization
Algorithm \\
Graphical Models \\
Bayesian networks \\
Belief propagation \\
Learning directed graphical models from data \\
Classification \\
Clustering \\
Power-Law Distributions \\
Scale-free properties (80/20 rule) \\
Applications to Languages: Zipf's and Heaps' Laws \\
Origin of power-law distributions and Fermi's model \\
Basic WWW Technologies \\
Web Documents \\
SGML and HTML \\
General structure of an HTML document \\
Links \\
Resource Identifiers: URI, URL, and URN \\
Protocols \\
Reference models and TCP/IP \\
The domain name system \\
The Hypertext Transfer Protocol \\
Programming examples \\
Log Files \\
Search Engines \\
Coverage \\
Basic crawling \\
Web Graphs \\
Internet and Web Graphs \\
Power-law size \\
Power-law connectivity \\
Small-world networks \\
Power law of PageRank \\
The bow-tie structure \\
Generative Models for the Web Graph and Other Networks
\\
Web page growth \\
Lattice perturbation models: between order and disorder
\\
Preferential attachment models, or the rich get richer
\\
Copy models \\
PageRank models \\
Applications \\
Distributed search algorithms \\
Subgraph patterns and communities \\
Robustness and vulnerability \\
Notes and Additional Technical References \\
Text Analysis \\
Indexing \\
Compression techniques \\
Lexical Processing \\
Tokenization",
}
@Article{Canessa:2003:TAFa,
author = "Enrique Canessa",
title = "Theory of Analogous Force on Number Sets",
journal = "ArXiv e-prints",
year = "2003",
bibdate = "Mon Nov 21 06:56:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/cond-mat/0307703",
abstract = "A general statistical thermodynamic theory that
considers given sequences of $x$-integers to play the
role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit
discrete probability distributions $p_x$ for natural
numbers, we claim that they lead to a better
understanding of probabilistic laws associated with
number theory. Sequences of numbers are treated as the
size measure of finite sets. By considering $p_x$ to
describe complex phenomena, the theory leads to derive
a distinct analogous force $f_x$ on number sets
proportional to $(\frac{\partial p_{x}}{\partial x}
)_{T}$ at an analogous system temperature $T$. In
particular, this yields to an understanding of the
uneven distribution of integers of random sets in terms
of analogous scale invariance and a screened inverse
square force acting on the significant digits. The
theory also allows to establish recursion relations to
predict sequences of Fibonacci numbers and to give an
answer to the interesting theoretical question of the
appearance of the Benford's law in Fibonacci numbers. A
possible relevance to prime numbers is also analyzed.",
acknowledgement = ack-nhfb,
remark = "To appear in Phys. A.",
}
@Article{Canessa:2003:TAFb,
author = "Enrique Canessa",
title = "Theory of analogous force on number sets",
journal = j-PHYSICA-A,
volume = "328",
number = "1--2",
pages = "44--52",
month = oct,
year = "2003",
CODEN = "PHYADX",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437103005260",
abstract = "A general statistical thermodynamic theory that
considers given sequences of $x$-integers to play the
role of particles of known type in an isolated elastic
system is proposed. By also considering some explicit
discrete probability distributions $p_x$ for natural
numbers, we claim that they lead to a better
understanding of probabilistic laws associated with
number theory. Sequences of numbers are treated as the
size measure of finite sets. By considering $p_x$ to
describe complex phenomena, the theory leads to derive
a distinct analogous force $f_x$ on number sets
proportional to $(\partial p_x/\partial x)T$ at an
analogous system temperature $T$. In particular, this
leads to an understanding of the uneven distribution of
integers of random sets in terms of analogous scale
invariance and a screened inverse square force acting
on the significant digits. The theory also allows to
establish recursion relations to predict sequences of
Fibonacci numbers and to give an answer to the
interesting theoretical question of the appearance of
the Benford's law in Fibonacci numbers. A possible
relevance to prime numbers is also analyzed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law; Fibonacci numbers; prime numbers",
}
@Article{Engel:2003:BLE,
author = "Hans-Andreas Engel and Christoph Leuenberger",
title = "{Benford}'s law for exponential random variables",
journal = j-STAT-PROB-LETT,
volume = "63",
number = "4",
pages = "361--365",
day = "15",
month = jul,
year = "2003",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/S0167-7152(03)00101-9",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60E99 (60C05)",
MRnumber = "1996184 (2004d:60050)",
MRreviewer = "Ulrich M. Hirth",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
keywords = "Benford's Law",
}
@Article{FerreriCancho:2003:LEO,
author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
title = "Least effort and the origins of scaling in human
language",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "100",
number = "3",
pages = "788--791",
day = "4",
month = feb,
year = "2003",
CODEN = "PNASA6",
DOI = "http://dx.doi.org/10.1073/pnas.0335980100",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue Nov 15 09:44:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
keywords = "Zipf's Law",
onlinedate = "January 22, 2003",
}
@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)",
bibdate = "Fri Nov 25 11:07:59 2011",
bibsource = "http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Benford's Law is the subject of Section 14.2, pages
145--155.",
price = "US\$29.95",
URL = "http://www.loc.gov/catdir/description/prin031/2002192453.html",
acknowledgement = ack-nhfb,
}
@Article{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",
MRclass = "11K31 (11B73)",
MRnumber = "2034405 (2004k:11125)",
MRreviewer = "Vydas {\v{C}}ekanavi{\v{c}}ius",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances and Applications in Statistics",
}
@InCollection{Kumar:2003:BLA,
author = "Kuldeep Kumar and Sukanto Bhattacharya",
editor = "Cheng-Few Lee",
booktitle = "Advances in Financial Planning and Forecasting",
title = "{Benford}'s law and its application in financial fraud
detection",
volume = "11",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "57--70",
year = "2003",
ISBN = "0-7623-1016-2",
ISBN-13 = "978-0-7623-1016-6",
ISSN = "1046-5847",
LCCN = "????",
bibdate = "Wed Nov 23 16:45:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
bookpages = "ix + 177",
}
@Article{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",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:57 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See replies
\cite{Twardy:2005:EDS,McAllister:2005:ACE}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0039368103000475",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
}
@Article{Mitzenmacher:2003:BHG,
author = "Michael Mitzenmacher",
title = "A Brief History of Generative Models for Power Law and
Lognormal Distributions",
journal = j-INTERNET-MATH,
volume = "1",
number = "2",
pages = "226--251",
month = dec,
year = "2003",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/15427951.2004.10129088",
ISSN = "1542-7951 (print), 1944-9488 (electronic)",
ISSN-L = "1542-7951",
bibdate = "Thu Nov 24 13:38:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.im/1089229510;
http://www.tandfonline.com/toc/uinm20/1/2;
http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf",
acknowledgement = ack-nhfb,
ajournal = "Internet Math.",
fjournal = "Internet Mathematics",
keywords = "Fibonacci sequence; lognormal distribution; monkeys
typing randomly; Pareto distribution; power-law
distribution; Yule distribution; Zipf's Law",
remark = "This is a survey article with a six-page bibliography
of earlier work, and a clear description of the
differences between lognormal and power-law
distributions, which otherwise look similar on log-log
plots. Lognormal distributions have finite means and
moments, while power-law distributions may have
infinite means and/or moments, depending on the
exponent. The preprint at author's Web site (last URL)
contains additional material on the acrimonious debate
between Beno{\^\i}t Mandelbrot and Herbert A. Simon
(see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and
other references in Mitzenmacher's paper) on the
derivation and modeling of Zipf's Law distributions.",
}
@Article{Naldi:2003:CIZ,
author = "M. Naldi",
title = "Concentration indices and {Zipf}'s law",
journal = j-ECONOM-LETT,
volume = "78",
number = "3",
pages = "329--334",
year = "2003",
CODEN = "ECLEDS",
DOI = "http://dx.doi.org/10.1016/S0165-1765(02)00251-3",
ISSN = "0165-1765 (print), 1873-7374 (electronic)",
ISSN-L = "0165-1765",
MRclass = "91B82",
MRnumber = "1959355",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Economics Letters",
}
@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",
bibdate = "Sat Dec 10 12:01:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
remark = "Betriebswirtschaftliche Forschung und Praxis ==
Business Research and Practice.",
}
@Article{Sinai:2003:SP,
author = "Ya. G. Sinai",
title = "Statistical $(3 x + 1)$ problem",
journal = j-COMM-PURE-APPL-MATH,
volume = "56",
number = "??",
pages = "1016--1028",
month = "????",
year = "2003",
CODEN = "CPAMAT, CPMAMV",
ISSN = "0010-3640",
ISSN-L = "0010-3640",
bibdate = "Mon Nov 21 07:52:19 2011",
bibsource = "http://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)",
}
@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 = "http://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,
}
@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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://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 = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
}
@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 = "http://doi.acm.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/;
http://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",
}
@TechReport{Diekmann:2004:DEE,
author = "Andreas Diekmann",
title = "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit
der Benford Verteilung}. ({German}) [{Data}
falsification. {Results} from experiments with the
{Benford} distribution]",
type = "Report",
institution = "ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
year = "2004",
bibdate = "Fri Nov 18 12:09:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@TechReport{Diekmann:2004:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! {Using} {Benford's Law} to Detect
Fraudulent Scientific Data",
type = "Report",
institution = "ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "26",
month = oct,
year = "2004",
bibdate = "Sat Dec 10 11:12:29 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by ``Benford's law''. Recently, a test
against this distribution was used to identify
fraudulent accounting data. This test is based on the
supposition that real data follow the Benford
distribution while fabricated data do not. Is it
possible to apply Benford tests to detect fabricated or
falsified scientific data as well as fraudulent
financial data? We approached this question in two
ways. First, we examined the use of the Benford
distribution as a standard by checking digit
frequencies in published statistical estimates. Second,
we conducted experiments in which subjects were asked
to fabricate statistical estimates (regression
coefficients). These experimental data were scrutinized
for possible deviations from the Benford distribution.
There were two main findings. First, the digits of the
published regression coefficients were approximately
Benford distributed. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. At least in the case of regression
coefficients, there were indications that checks for
digit-preference anomalies should focus less on the
first and more on the second and higher-digits",
acknowledgement = ack-nhfb,
}
@Article{Durtschi:2004:EUB,
author = "C. Durtschi and W. Hillison and C. Pacini",
title = "The Effective Use of {Benford's Law} to Assist in
Detecting Fraud in Accounting Data",
journal = j-J-FORENSIC-ACCOUNT,
volume = "5",
number = "1",
pages = "17--34",
month = "????",
year = "2004",
CODEN = "????",
ISSN = "1524-5586",
bibdate = "Sun Nov 13 11:35:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Forensic Accounting",
}
@Article{Fujiwara:2004:ZLF,
author = "Yoshi Fujiwara",
title = "{Zipf} law in firms' bankruptcy",
journal = j-PHYSICA-A,
volume = "337",
number = "1-2",
pages = "219--230",
year = "2004",
CODEN = "PHYSAG",
DOI = "http://dx.doi.org/10.1016/j.physa.2004.01.037",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "91B38",
MRnumber = "2092316",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Article{Geyer:2004:DFD,
author = "Christina Lynn Geyer and Patricia Pepple Williamson",
title = "Detecting fraud in data sets using {Benford's Law}",
journal = j-COMM-STAT,
volume = "B33",
number = "1",
pages = "229--246",
month = "????",
year = "2004",
CODEN = "CSSCDB",
DOI = "http://dx.doi.org/10.1081/SAC-120028442",
ISSN = "0361-0918",
MRclass = "62-07",
MRnumber = "2044866",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Statist. Simulation Comput.",
fjournal = "Communications in Statistics. Simulation and
Computation",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Hurlimann:2004:IPB,
author = "Werner H{\"u}rlimann",
title = "Integer powers and {Benford}'s law",
journal = j-INT-J-PURE-APPL-MATH,
volume = "11",
number = "1",
pages = "39--46",
year = "2004",
CODEN = "????",
ISSN = "1311-8080",
ISSN-L = "1314-3395",
MRclass = "62E15 (11B83 11K31 62E20)",
MRnumber = "2033394 (2005c:62030)",
MRreviewer = "I. N. Volodin",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Pure and Applied
Mathematics",
}
@Article{Ismail:2004:SES,
author = "Sanaa Isma{\"\i}l",
title = "A Simple Estimator for the Shape Parameter of the
{Pareto} Distribution with Economics and Medical
Applications",
journal = j-J-APPL-STAT,
volume = "31",
number = "1",
pages = "3--13",
month = jan,
year = "2004",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Sat Dec 4 12:10:37 MST 2004",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
}
@Article{Janvresse:2004:UDB,
author = "{\'E}lise Janvresse and Thierry de la Rue",
title = "From uniform distributions to {Benford}'s law",
journal = j-J-APPL-PROBAB,
volume = "41",
number = "4",
pages = "1203--1210",
year = "2004",
CODEN = "JPRBAM",
DOI = "http://dx.doi.org/10.1239/jap/1101840566",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
MRclass = "60J20 (60J10)",
MRnumber = "2122815 (2006b:60161)",
MRreviewer = "Michael Drmota",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566;
http://www.jstor.org/stable/4141393",
abstract = "We provide a new, probabilistic explanation for the
appearance of Benford's law in everyday-life numbers,
by showing that it arises naturally when we consider
mixtures of uniform distributions. Then we connect our
result to a result of Flehinger, for which we provide a
shorter proof, and the speed of convergence.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
}
@Article{Kristiansen:2004:EOZ,
author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
Skjeltorp",
title = "Experimental observation of {Zipf--Mandelbrot}
relation",
journal = j-PHYSICA-A,
volume = "335",
number = "3-4",
pages = "413--420",
year = "2004",
CODEN = "PHYSAG",
DOI = "http://dx.doi.org/10.1016/j.physa.2003.12.024",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "82D10 (76T99 82-05)",
MRnumber = "2044153",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Article{Kulikova:2004:OSS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "One-sided stable distributions and {Benford}'s law",
journal = "Teor. Veroyatn. Primen.",
volume = "49",
number = "1",
pages = "178--184",
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1137/S0040585X97980944",
ISSN = "0040-361X",
MRclass = "60E07 (60F05)",
MRnumber = "2141338 (2005m:60028)",
MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
Veroyatnoste{\u\i} i ee Primeneniya",
}
@Article{Li:2004:DBL,
author = "Zhi-peng Li and Lin Cong and Hua-jia Wang",
title = "Discussion on {Benford's Law} and its Application",
journal = "ArXiv e-prints",
pages = "1--13",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 16:17:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2004math......8057L;
http://arxiv.org/abs/math/0408057",
abstract = "The probability that a number in many naturally
occurring tables of numerical data has first
significant digit $d$ is predicted by Benford's Law
${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over
d}}), d = 1, 2 > \cdots, 9$. Illustrations of Benford's
Law from both theoretical and real-life sources on both
science and social science areas are shown in detail
with some novel ideas and generalizations developed
solely by the authors of this paper. Three tests,
Chi-Square test, total variation distance, and maximum
deviations are adopted to examine the fitness of the
datasets to Benford's distribution. Finally,
applications of Benford's Law are summarized and
explored to reveal the power of this mathematical
principle.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "math/0408057",
}
@Article{Molchanov:2004:BEL,
author = "Stanislav Molchanov and Xian Wang",
title = "On the {Benford}'s empirical law",
journal = "Random Oper. Stochastic Equations",
volume = "12",
number = "3",
pages = "201--210",
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1163/1569397042222495",
ISSN = "0926-6364",
MRclass = "11K16 (11B39 60B15)",
MRnumber = "2084074 (2005h:11162)",
MRreviewer = "A. N. Philippou",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Random Operators and Stochastic Equations",
}
@Article{Nguyen:2004:DPL,
author = "Hung T. Nguyen and Vladik Kreinovich and Luc
Longpr{\'e}",
title = "Dirty Pages of Logarithm Tables, Lifetime of the
Universe, and (Subjective) Probabilities on Finite and
Infinite Intervals",
journal = j-RELIABLE-COMPUTING,
volume = "10",
number = "2",
pages = "83--106",
month = apr,
year = "2004",
CODEN = "RCOMF8",
DOI = "http://dx.doi.org/10.1023/B:REOM.0000015848.19449.12",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon Feb 6 07:42:05 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/rc.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
}
@Article{Pustet:2004:ZHH,
author = "Regina Pustet",
title = "{Zipf} and his heirs",
journal = "Language Sciences",
volume = "26",
number = "1",
pages = "1--25",
month = jan,
year = "2004",
CODEN = "????",
ISSN = "0388-0001 (print), 1873-5746 (electronic)",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0388000103000184",
acknowledgement = ack-nhfb,
fjournal = "Language Sciences",
keywords = "Benford's Law",
}
@Article{Rodriguez:2004:FSD,
author = "Ricardo J. Rodriguez",
title = "First Significant Digit Patterns From Mixtures of
Uniform Distributions",
journal = j-AMER-STAT,
volume = "58",
number = "1",
pages = "64--71",
month = feb,
year = "2004",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/0003130042782",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Feb 20 06:14:28 MST 2004",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://oberon.ingentaselect.com/cgi-bin/linker?ini=asa&reqidx=/cw/asa/00031305/v58n1/s13/p64",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
keywords = "Benford's Law",
}
@Article{Skousen:2004:AUP,
author = "Christopher J. Skousen and Liming Guan and T. Sterling
Wetzel",
title = "Anomalies and Unusual Patterns in Reported Earnings:
{Japanese} Managers Round Earnings",
journal = j-J-INT-FINANC-MANAG-ACCOUNT,
volume = "15",
number = "3",
pages = "212--234",
month = oct,
year = "2004",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1467-646X.2004.00108.x",
ISSN = "0954-1314 (print), 1467-646X (electronic)",
ISSN-L = "0954-1314",
bibdate = "Fri Nov 25 11:11:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of International Financial Management and
Accounting",
}
@Article{Vanichpun:2004:OCU,
author = "Sarut Vanichpun and Armand M. Makowski",
title = "The output of a cache under the independent reference
model: where did the locality of reference go?",
journal = j-SIGMETRICS,
volume = "32",
number = "1",
pages = "295--306",
month = jun,
year = "2004",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1012888.1005722",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:21:18 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "We consider a cache operating under a demand-driven
replacement policy when document requests are modeled
according to the Independent Reference Model (IRM). We
characterize the popularity pmf of the stream of misses
from the cache, the so-called output of the cache, for
a large class of demand-driven cache replacement
policies. We measure strength of locality of reference
in a stream of requests through the skewness of its
popularity distribution. Using the notion of
majorization to capture this degree of skewness, we
show that for the policy $A_0$ and the random policy,
the output always has less locality of reference than
the input. However, we show by counterexamples that
this is not always the case under the LRU and CLIMB
policies when the input is selected according to a
Zipf-like pmf. In that case, conjectures are offered
(and supported by simulations) as to when LRU or CLIMB
caching indeed reduces locality of reference.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
keywords = "locality of reference; majorization; output of a
cache; popularity",
}
@Article{Antonini:2005:RSC,
author = "Rita Giuliano Antonini and Georges Grekos",
title = "Regular sets and conditional density: an extension of
{Benford}'s law",
journal = j-COLLOQ-MATH,
volume = "103",
number = "2",
pages = "173--192",
year = "2005",
CODEN = "CQMAAQ",
DOI = "http://dx.doi.org/10.4064/cm103-2-3",
ISSN = "0010-1354",
ISSN-L = "0010-1354",
MRclass = "11B05 (11K99)",
MRnumber = "2197847 (2006j:11012)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Colloquium Mathematicum",
}
@Article{Berger:2005:BLP,
author = "Arno Berger",
title = "{Benford}'s law in power-like dynamical systems",
journal = "Stoch. Dyn.",
volume = "5",
number = "4",
pages = "587--607",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.1142/S0219493705001602",
ISSN = "0219-4937",
MRclass = "37B55 (11K06 37A50 37E05)",
MRnumber = "2185507 (2008i:37029)",
MRreviewer = "Peter Raith",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Stochastics and Dynamics",
}
@InCollection{Berger:2005:DDU,
author = "A. Berger",
booktitle = "{EQUADIFF} 2003",
title = "Dynamics and digits: on the ubiquity of {Benford}'s
law",
publisher = "World Sci. Publ., Hackensack, NJ",
pages = "693--695",
year = "2005",
DOI = "http://dx.doi.org/10.1142/9789812702067_0115",
MRclass = "37A45 (11K55)",
MRnumber = "2185113",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Berger:2005:MDD,
author = "Arno Berger",
title = "Multi-dimensional dynamical systems and {Benford}'s
law",
journal = j-DISCRETE-CONTIN-DYN-SYST,
volume = "13",
number = "1",
pages = "219--237",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.3934/dcds.2005.13.219",
ISSN = "1078-0947 (print), 1553-5231 (electronic)",
ISSN-L = "1078-0947",
MRclass = "37A45 (11K36 28D05 37A50 60F05)",
MRnumber = "2128801 (2005m:37016)",
MRreviewer = "Reinhard Winkler",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Continuous Dynamical Systems. Series A",
}
@Article{Berger:2005:ODD,
author = "Arno Berger and Leonid A. Bunimovich and Theodore P.
Hill",
title = "One-dimensional dynamical systems and {Benford}'s
law",
journal = j-TRANS-AM-MATH-SOC,
volume = "357",
number = "1",
pages = "197--219",
year = "2005",
CODEN = "TAMTAM",
DOI = "http://dx.doi.org/10.1090/S0002-9947-04-03455-5",
ISSN = "0002-9947",
ISSN-L = "0002-9947",
MRclass = "37A45 (11K06 37A50 37E05 60F05 82B05)",
MRnumber = "2098092 (2005m:37017)",
MRreviewer = "Peter Raith",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
}
@Article{Bhattacharya:2005:CPA,
author = "Sukanto Bhattacharya and Kuldeep Kumar and Florentin
Smarandache",
title = "Conditional probability of actually detecting a
financial fraud --- a neutrosophic extension to
{Benford}'s law",
journal = "Int. J. Appl. Math.",
volume = "17",
number = "1",
pages = "7--14",
year = "2005",
CODEN = "????",
ISSN = "1311-1728",
MRclass = "62G10 (91B28)",
MRnumber = "2170667",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0504520",
abstract = "This study actually draws from and builds on an
earlier paper (Kumar and Bhattacharya, 2002). Here we
have basically added a neutrosophic dimension to the
problem of determining the conditional probability that
a financial fraud has been actually committed, given
that no Type I error occurred while rejecting the null
hypothesis H0: The observed first-digit frequencies
approximate a Benford distribution; and accepting the
alternative hypothesis H1: The observed first-digit
frequencies do not approximate a Benford distribution.
We have also suggested a conceptual model to implement
such a neutrosophic fraud detection system.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Applied Mathematics",
}
@Article{Cleary:2005:ADA,
author = "Richard Cleary and Jay C. Thibodeau",
title = "Applying Digital Analysis Using {Benford's Law} to
Detect Fraud: The Dangers of Type {I} Errors",
journal = j-AUDITING,
volume = "24",
number = "1",
pages = "77--81",
month = may,
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.2308/aud.2005.24.1.77",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Tue Nov 15 09:17:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt;
http://link.aip.org/link/AJPTXX/v24/i1/p77/s1",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@Article{Cohen:2005:PCL,
author = "Edith Cohen and Carsten Lund",
title = "Packet classification in large {ISPs}: design and
evaluation of decision tree classifiers",
journal = j-SIGMETRICS,
volume = "33",
number = "1",
pages = "73--84",
month = jun,
year = "2005",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1064212.1064222",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:21:27 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Packet classification, although extensively studied,
is an evolving problem. Growing and changing needs
necessitate the use of larger filters with more complex
rules. The increased complexity and size pose
implementation challenges on current hardware solutions
and drive the development of software classifiers, in
particular, decision-tree based classifiers. Important
performance measures for these classifiers are time and
memory due to required high throughput and use of
limited fast memory. We analyze Tier 1 ISP data that
includes filters and corresponding traffic from over a
hundred edge routers and thousands of interfaces. We
provide a comprehensive view on packet classification
in an operational network and glean insights that help
us design more effective classification algorithms. We
propose and evaluate decision tree classifiers with
{\em common branches}. These classifiers have linear
worst-case memory bounds and require much less memory
than standard decision tree classifiers, but
nonetheless, we show that on our data have similar
average and worst-case time performance. We argue that
common-branches exploit structure that is present in
real-life data sets. We observe a strong Zipf-like
pattern in the usage of rules in a classifier, where a
very small number of rules resolves the bulk of traffic
and most rules are essentially never used. Inspired by
this observation, we propose {\em traffic-aware\/}
classifiers that obtain superior average-case and
bounded worst-case performance. Good average-case can
boost performance of software classifiers that can be
used in small to medium sized routers and are also
important for traffic analysis and traffic
engineering.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
keywords = "access control lists; decision trees; packet
filtering; routing",
}
@InProceedings{DelAcebo:2005:BLN,
author = "Esteve {Del Acebo} and Mateu Sbert",
title = "{Benford's Law} for Natural and Synthetic Images",
crossref = "Neumann:2005:CAE",
pages = "169--176",
year = "2005",
DOI = "http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
bibdate = "Tue Nov 15 08:46:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf",
acknowledgement = ack-nhfb,
}
@Book{Durrett:2005:PTE,
author = "Richard Durrett",
title = "Probability: theory and examples",
publisher = "Thomson Brooks\slash Cole",
address = "Belmont, CA, USA",
edition = "Third",
pages = "xi + 497",
year = "2005",
ISBN = "0-534-42441-4",
ISBN-13 = "978-0-534-42441-1",
LCCN = "QA273 .D865 2005",
bibdate = "Mon Nov 21 10:00:11 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Duxbury advanced series",
acknowledgement = ack-nhfb,
remark = "Benford's Law is treated on pp. 337ff. Hill \cite[page
893]{Hill:1995:BII} reports that the 1991 edition has a
proof that the $k$-th digit of powers of integers
follows Benford's Law.",
subject = "Probabilities",
}
@Article{elSehity:2005:PDA,
author = "Tarek el Sehity and Erik Hoelzl and Erich Kirchler",
title = "Price developments after a nominal shock: {Benford's
Law} and psychological pricing after the euro
introduction",
journal = j-INT-J-RES-MARK,
volume = "22",
number = "4",
pages = "471--480",
month = dec,
year = "2005",
CODEN = "IJRME6",
ISSN = "0167-8116 (print), 1873-8001 (electronic)",
ISSN-L = "0167-8116",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167811605000522",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Research in Marketing",
keywords = "Benford's Law",
}
@Article{Fairthorne:2005:PDE,
author = "Robert A. Fairthorne",
title = "Progress in Documentation: Empirical Hyperbolic
Distributions ({Bradford--Zipf--Mandelbrot}) for
Bibliometric Description and Prediction",
journal = j-J-DOC,
volume = "61",
number = "2",
pages = "171--193",
month = "????",
year = "2005",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/00220410510585179",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:27:27 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Reprint of \cite{Fairthorne:1969:PDE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
remark = "According to \cite{Potter:1981:LLR}, this paper is the
first to link the distributions of Bradford, Zipf,
Mandelbrot, and Lotka.",
}
@Article{FerreriCancho:2005:CZL,
author = "Ramon {Ferrer i Cancho} and Oliver Riordan and
B{\'e}la Bollob{\'a}s",
title = "The consequences of {Zipf}'s law for syntax and
symbolic reference",
journal = j-PROC-R-SOC-LOND-SER-B-BIO-SCI,
volume = "272",
number = "1562",
pages = "561--565",
day = "7",
month = mar,
year = "2005",
CODEN = "PRLBA4",
DOI = "http://dx.doi.org/10.1098/rspb.2004.2957",
ISSN = "0962-8452 (print), 1471-2954 (electronic)",
ISSN-L = "0962-8452",
bibdate = "Tue Nov 15 11:27:26 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://rspb.royalsocietypublishing.org/content/272/1562/561.full",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series B.
Biological sciences",
}
@TechReport{Giles:2005:BLN,
author = "David E. Giles",
title = "{Benford's Law} and Naturally Occurring Prices in
Certain {ebaY} Auctions",
type = "Econometrics Working Paper",
number = "EWP0505",
institution = "Department of Economics, University of Victoria",
address = "Victoria, BC, Canada",
month = may,
year = "2005",
ISSN = "1485-6441",
bibdate = "Thu Feb 15 16:24:39 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://web.uvic.ca/econ/ewp0505.pdf",
abstract = "We show that certain the winning bids for certain ebaY
auctions obey Benford's Law. One implication of this is
that it is unlikely that these bids are subject to
collusion among bidders, or ``shilling'' on the part of
sellers. Parenthetically, we also show that numbers
from the naturally occurring Fibonacci and Lucas
sequences also obey Benford's Law.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@InCollection{Harremoes:2005:ZLH,
author = "Peter Harremo{\"e}s and Flemming Topsoe",
editor = "Rudolf Ahlswede and others",
booktitle = "General theory of information transfer and
combinatorics.",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
volume = "21",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "315--318",
year = "2005",
DOI = "http://dx.doi.org/10.1016/j.endm.2005.07.075",
bibdate = "Sat Nov 12 11:07:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Electronic Notes in Discrete Mathematics",
abstract = "Zipf's law --- or Estoup-Zipf's law --- is an
empirical fact of computational linguistics which
relates rank and frequency of words in natural
languages. The law suggests modelling by distributions
of ``hyperbolic type''. We present a satisfactory
general definition and an information-theoretical
characterization of the resulting hyperbolic
distributions. When applied to linguistics this leads
to a property of stability and flexibility, explaining
that a language can develop towards higher and higher
expressive powers without changing its basic
structure.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics) 94A15 (General topics of
information theory) 94A17 (Measures of information)",
keywords = "entropy loss; hyperbolic distributions; Zipf's law",
ZMnumber = "1158.91482",
}
@Article{Hill:2005:RDS,
author = "Theodore P. Hill and Klaus Sch{\"u}rger",
title = "Regularity of digits and significant digits of random
variables",
journal = j-STOCH-PROC-APPL,
volume = "115",
number = "10",
pages = "1723--1743",
month = oct,
year = "2005",
CODEN = "STOPB7",
DOI = "http://dx.doi.org/10.1016/j.spa.2005.05.003",
ISSN = "0304-4149 (print), 1879-209X (electronic)",
ISSN-L = "0304-4149",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0304414905000657",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Processes and Their Applications",
keywords = "Benford's Law; digit-regular random variable;
floating-point numbers; law of least significant
digits; nonleading digits; normal numbers; significant
digits; significant-digit-regular random variable;
trailing digits",
}
@InProceedings{Hjorland:2005:BLS,
author = "Birger Hj{\o}rland and Jeppe Nicolaisen",
editor = "Fabio Crestani and Ian Ruthven",
booktitle = "Context: nature, impact, and role: {5th International
Conference on Conceptions of Library and Information
Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005;
proceedings}",
title = "{Bradford}'s law of scattering: ambiguities in the
concept of ``subject''",
volume = "3507",
publisher = pub-SV,
address = pub-SV:adr,
pages = "96--106",
year = "2005",
ISBN = "3-540-26178-8",
ISBN-13 = "978-3-540-26178-0",
LCCN = "Z672.5 .I5616 2005",
bibdate = "Fri Nov 25 11:52:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
bookpages = "xiii + 250",
}
@Article{Ioannidis:2005:WMP,
author = "John P. A. Ioannidis",
title = "Why Most Published Research Findings Are False",
journal = j-PLOS-MED,
volume = "2",
number = "8",
pages = "696--701",
month = aug,
year = "2005",
CODEN = "PMLEAC",
DOI = "http://dx.doi.org/10.1371/journal.pmed.0020124",
ISSN = "1549-1277 (print), 1549-1676 (electronic)",
ISSN-L = "1549-1277",
bibdate = "Fri Nov 18 12:42:05 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124",
abstract = "There is increasing concern that most current
published research findings are false. The probability
that a research claim is true may depend on study power
and bias, the number of other studies on the same
question, and, importantly, the ratio of true to no
relationships among the relationships probed in each
scientific field. In this framework, a research finding
is less likely to be true when the studies conducted in
a field are smaller; when effect sizes are smaller;
when there is a greater number and lesser preselection
of tested relationships; where there is greater
flexibility in designs, definitions, outcomes, and
analytical modes; when there is greater financial and
other interest and prejudice; and when more teams are
involved in a scientific field in chase of statistical
significance. Simulations show that for most study
designs and settings, it is more likely for a research
claim to be false than true. Moreover, for many current
scientific fields, claimed research findings may often
be simply accurate measures of the prevailing bias. In
this essay, I discuss the implications of these
problems for the conduct and interpretation of
research.",
acknowledgement = ack-nhfb,
articleno = "e124",
fjournal = "PLoS Medicine",
remark = "This article does not discuss Benford's Law, but is
related to the use of that law in the detection of
fraud in research data. Ioannidis discusses the abuse
of statistics for limited experimental data, a topic
that receives book-length treatment in
\cite{Ziliak:2008:CSS}.",
}
@Article{Jolissaint:2005:LBR,
author = "Paul Jolissaint",
title = "Loi de {Benford}, relations de r{\'e}currence et
suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s
Law, recurrence relations, and equidistributed
sequences]",
journal = j-ELEM-MATH,
volume = "60",
number = "1",
pages = "10--18",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.4171/EM/2",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "11K36 (37A45 60E99)",
MRnumber = "2188341 (2006j:11109)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{Kechedzhi:2005:RDW,
author = "K. E. Kechedzhi and O. V. Usatenko and V. A.
Yampol{\cprime}skii",
title = "Rank distributions of words in correlated symbolic
systems and the {Zipf} law",
journal = j-PHYS-REV-E,
volume = "72",
number = "4",
pages = "046138",
year = "2005",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.72.046138",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82C31",
MRnumber = "2183723 (2006f:82069)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
pagecount = "6",
}
@Article{Kontorovich:2005:BLV,
author = "Alex V. Kontorovich and Steven J. Miller",
title = "{Benford}'s law, values of {$L$}-functions and the {$3
x + 1$} problem",
journal = j-ACTA-ARITHMETICA,
volume = "120",
number = "3",
pages = "269--297",
year = "2005",
CODEN = "AARIA9",
DOI = "http://dx.doi.org/10.4064/aa120-3-4",
ISSN = "0065-1036 (print), 1730-6264 (electronic)",
ISSN-L = "0065-1036",
MRclass = "11K06 (11B37 11M06 37A45)",
MRnumber = "2188844 (2007c:11085)",
MRreviewer = "J. C. Lagarias",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2005AcAri.120..269K;
http://arxiv.org/abs/math/0412003",
abstract = "We show the leading digits of a variety of systems
satisfying certain conditions follow Benford's Law. For
each system proving this involves two main ingredients.
One is a structure theorem of the limiting
distribution, specific to the system. The other is a
general technique of applying Poisson Summation to the
limiting distribution. We show the distribution of
values of $L$-functions near the central line and (in
some sense) the iterates of the $3 x + 1$ Problem are
Benford.",
acknowledgement = ack-nhfb,
fjournal = "Acta Arithmetica",
}
@Article{Kulikova:2005:CAS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "Completely Asymmetric Stable Laws and {Benford's
Law}",
journal = j-THEORY-PROBAB-APPL,
volume = "49",
number = "1",
pages = "163--169",
month = mar,
year = "2005",
CODEN = "TPRBAU",
DOI = "http://dx.doi.org/10.1137/S0040585X97980944",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Thu Jul 7 19:15:48 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/98094",
acknowledgement = ack-nhfb,
fjournal = "Theory of probability and its applications",
keywords = "Benford's Law; Zipf's Law",
}
@Article{Kulikova:2005:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H. F. D.} ({$H$}-function distribution) and the
{Benford} law. {I}",
journal = "Teor. Veroyatn. Primen.",
volume = "50",
number = "2",
pages = "366--371",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.1137/S0040585X97981706",
ISSN = "0040-361X",
MRclass = "60E07 (60F05)",
MRnumber = "2221718 (2007b:60029)",
MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
Veroyatnoste{\u\i} i ee Primeneniya",
}
@Article{Lagarias:2005:BLF,
author = "J. C. Lagarias and K. Soundararajan",
title = "{Benford}'s law for the $3 x + 1$ function",
journal = "ArXiv Mathematics e-prints",
month = sep,
year = "2005",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2005math......9175L;
http://arxiv.org/abs/math/0509175",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0509175",
keywords = "Mathematics - Number Theory, Mathematics -
Probability",
}
@Article{Li:2005:ZLP,
author = "Yujian Li and Chuangbai Xiao",
title = "{Zipf}'s law probably existing in protein sequences",
journal = "J. Beijing Univ. Technol.",
volume = "31",
number = "4",
pages = "366--368",
year = "2005",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Nov 12 11:10:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In order to analyze whether Zipf's law in linguistics
exists in protein sequences, this paper uses
$1.735\,7\times 10^4$ protein sequences labeled with
secondary structures which are selected from the DSSP
database. The segments of successive amino acid
residues with a same code of secondary structure are
defined as words. The results show that the
distribution of words emerging frequency follows Zipf's
law with the exponent $0.981$.",
acknowledgement = ack-nhfb,
classmath = "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics
to biology): 92D20 (Protein sequences, DNA sequences)",
language = "Chinese. English summary",
ZMnumber = "1084.92019",
}
@InProceedings{Lu:2005:DFH,
author = "Fletcher Lu and J. Efrim Boritz",
title = "Detecting Fraud in Health Insurance Data: Learning to
Model Incomplete {Benford's Law} Distributions",
crossref = "Gama:2005:MLE",
pages = "633--640",
year = "2005",
DOI = "http://dx.doi.org/10.1007/11564096_63",
bibdate = "Tue Nov 15 08:55:45 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Article{Maslov:2005:GTS,
author = "V. P. Maslov",
title = "On a general theorem of set theory that leads to the
{Gibbs}, {Bose--Einstein}, and {Pareto} distributions
and to the {Zipf--Mandelbrot} law for the stock
market",
journal = j-MAT-ZAMETKI,
volume = "78",
number = "6",
pages = "870--877",
year = "2005",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11006-005-0186-9",
ISSN = "0025-567X",
MRclass = "91B28 (90C29)",
MRnumber = "2249037 (2007b:91077)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
}
@Article{Maslov:2005:RZLa,
author = "V. P. Maslov",
title = "Refining {Zipf}'s law for frequency dictionaries",
journal = j-DOKL-AKAD-NAUK,
volume = "405",
number = "5",
pages = "591--594",
year = "2005",
CODEN = "DANKAS",
ISSN = "0869-5652",
MRclass = "94A15 (60C05)",
MRnumber = "2340762",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
Nauk",
}
@Article{Maslov:2005:RZLb,
author = "V. P. Maslov",
title = "Refinement of {Zipf}'s law for frequency
dictionaries",
journal = j-DOKL-MATH,
volume = "72",
number = "3",
pages = "942--945",
year = "2005",
CODEN = "????",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Sat Nov 12 11:05:14 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
classmath = "82B10 (Quantum equilibrium statistical mechanics
(general)) 68T50 (Natural language processing) 68Q45
(Formal languages)",
fjournal = "Doklady Mathematics",
keywords = "Bose--Einstein statistics",
language = "English. Russian original",
ZMnumber = "1206.82009",
}
@Article{Maslov:2005:ZML,
author = "V. P. Maslov",
title = "The {Zipf--Mandelbrot} law: quantization and an
application to the stock market",
journal = j-RUSS-J-MATH-PHYS,
volume = "12",
number = "4",
pages = "483--488",
year = "2005",
CODEN = "RJMPEL",
ISSN = "1061-9208",
ISSN-L = "1061-9208",
MRclass = "91B28 (82B99)",
MRnumber = "2201312 (2006i:91053)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Russian Journal of Mathematical Physics",
}
@Article{McAllister:2005:ACE,
author = "James W. McAllister",
title = "Algorithmic compression of empirical data: reply to
Twardy, Gardner, and Dowe",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "36",
number = "2",
pages = "403--410",
month = jun,
year = "2005",
CODEN = "SHPSB5",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:58 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.",
URL = "http://www.sciencedirect.com/science/article/pii/S0039368105000221",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
}
@Article{Newman:2005:PLP,
author = "M. E. J. Newman",
title = "Power laws, {Pareto} distributions and {Zipf}'s law",
journal = j-CONTEMP-PHYS,
volume = "46",
number = "5",
pages = "323--351",
month = sep,
year = "2005",
CODEN = "CTPHAF",
DOI = "http://dx.doi.org/10.1080/00107510500052444",
ISSN = "0010-7514 (print), 1366-5812 (electronic)",
ISSN-L = "0010-7514",
bibdate = "Fri Jul 09 16:33:18 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "When the probability of measuring a particular value
of some quantity varies inversely as a power of that
value, the quantity is said to follow a power law, also
known variously as Zipf's law or the Pareto
distribution. Power laws appear widely in physics,
biology, earth and planetary sciences, economics and
finance, computer science, demography and the social
sciences. For instance, the distributions of the sizes
of cities, earthquakes, forest fires, solar flares,
moon craters and people's personal fortunes all appear
to follow power laws. The origin of power-law behaviour
has been a topic of debate in the scientific community
for more than a century. Here we review some of the
empirical evidence for the existence of power-law forms
and the theories proposed to explain them.",
acknowledgement = ack-nhfb,
fjournal = "Contemporary physics",
keywords = "Benford's Law; critical phenomena; Legendre beta
function; Pareto distribution; percolation; phase
transitions; power-law distributions; random walks;
Riemann zeta function; scale-free distributions; Yule
process; Zipf's Law",
remark = "This article is an excellent survey of continuous and
discrete distributions that follow a power law, and
some that do not. It is well worth reading.",
subject = "astrophysics; atomic and nuclear physics; chemical
physics; computational physics; condensed matter
physics; environmental physics; experimental physics;
general physics; particle and high energy physics;
plasma physics; space science; theoretical physics",
}
@Article{Perline:2005:SWF,
author = "Richard Perline",
title = "Strong, weak and false inverse power laws",
journal = j-STAT-SCI,
volume = "20",
number = "1",
pages = "68--88",
month = "????",
year = "2005",
CODEN = "STSCEP",
ISSN = "0883-4237",
bibdate = "Fri Nov 18 12:15:56 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Statistical Science",
keywords = "Benford's Law",
}
@Article{Rousseau:2005:RFE,
author = "Ronald Rousseau",
title = "{Robert Fairthorne} and the empirical power laws",
journal = j-J-DOC,
volume = "61",
number = "2",
pages = "194--202",
month = "????",
year = "2005",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/00220410510585188",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 06:42:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
remark = "Review of
\cite{Fairthorne:1969:PDE,Fairthorne:2005:PDE}.",
}
@Article{Rowlands:2005:EAD,
author = "Ian Rowlands",
title = "{Emerald} authorship data, {Lotka}'s law and research
productivity",
journal = j-ASLIB-PROC,
volume = "57",
number = "1",
pages = "5--10",
month = "????",
year = "2005",
CODEN = "ASLPAO",
DOI = "http://dx.doi.org/10.1108/00012530510579039",
ISSN = "0001-253X (print), 1758-3748 (electronic)",
ISSN-L = "0001-253X",
bibdate = "Fri Nov 25 07:25:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "ASLIB Proceedings",
keywords = "brand loyalty; publishing; research results",
remark = "This paper applies Lotka's Law to the question of the
likelihood of an author remaining with a particular
publisher.",
}
@Article{Twardy:2005:EDS,
author = "Charles Twardy and Steve Gardner and David L. Dowe",
title = "Empirical data sets are algorithmically compressible:
reply to {McAllister}?",
journal = j-STUD-HIST-PHILOS-SCI,
volume = "36",
number = "2",
pages = "391--402",
month = jun,
year = "2005",
CODEN = "SHPSB5",
ISSN = "0039-3681 (print), 1879-2510 (electronic)",
ISSN-L = "0039-3681",
bibdate = "Mon Nov 7 12:11:58 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/shps-a.bib;
http://www.sciencedirect.com/science/journal/00393681",
note = "See \cite{McAllister:2003:ARE,McAllister:2005:ACE}.",
URL = "http://www.sciencedirect.com/science/article/pii/S003936810500021X",
acknowledgement = ack-nhfb,
fjournal = "Studies in History and Philosophy of Science Part A",
}
@Article{vanLeijenhorst:2005:FDH,
author = "D. C. van Leijenhorst and Th. P. van der Weide",
title = "A formal derivation of {Heaps}' law",
journal = "Inform. Sci.",
volume = "170",
number = "2-4",
pages = "263--272",
year = "2005",
CODEN = "ISIJBC",
DOI = "http://dx.doi.org/10.1016/j.ins.2004.03.006",
ISSN = "0020-0255",
MRclass = "60C05",
MRnumber = "2120894 (2005h:60024)",
bibdate = "Sat Nov 12 10:28:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Word frequencies in text documents can be reasonably
described by the Mandelbrot distribution, which has
Zipf's law as a special case. Furthermore, the growth
of vocabulary size as a function of the text size (its
number of words) has been described in Heaps' law. It
has been shown that these two experimental laws are
related. In this paper we go a step further, and
provide a (formal) derivation of Heaps' law from the
Mandelbrot distribution. We also provide a
specification of the validity area for applying Heaps'
law.",
acknowledgement = ack-nhfb,
fjournal = "Information Sciences. An International Journal",
}
@Article{Aban:2006:PET,
author = "Inmaculada B. Aban and Mark M. Meerschaert and Anna K.
Panorska",
title = "Parameter Estimation for the Truncated {Pareto}
Distribution",
journal = j-J-AM-STAT-ASSOC,
volume = "101",
number = "473",
pages = "270--277",
month = mar,
year = "2006",
CODEN = "JSTNAL",
DOI = "http://dx.doi.org/10.1198/016214505000000411",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Thu Aug 26 11:26:31 MDT 2010",
bibsource = "http://www.amstat.org/publications/jasa/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib",
acknowledgement = ack-nhfb,
}
@Article{Bohachevsky:2006:DBL,
author = "Ihor O. Bohachevsky and Mark E. Johnson and Myron L.
Stein",
title = "A derivation of {Benford}'s law",
journal = j-AM-J-MATH-MANAGE-SCI,
volume = "26",
number = "3--4",
pages = "355--370",
year = "2006",
CODEN = "AMMSDX",
ISSN = "0196-6324",
MRclass = "60E99 (11K36)",
MRnumber = "2312400 (2008h:60062)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematical and Management
Sciences",
}
@Article{Dorogovtsev:2006:FON,
author = "S. N. Dorogovtsev and J. F. F. Mendes and J. G.
Oliveira",
title = "Frequency of occurrence of numbers in the {World Wide
Web}",
journal = j-PHYSICA-A,
volume = "360",
number = "2",
pages = "548--556",
month = feb,
year = "2006",
CODEN = "PHYADX",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437105006874",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law",
}
@Article{Egghe:2006:DHL,
author = "L. Egghe",
title = "The dependence of the height of a {Lorenz} curve of a
{Zipf} function on the size of the system",
journal = j-MATH-COMP-MODELLING,
volume = "43",
number = "7-8",
pages = "870--879",
year = "2006",
CODEN = "MCMOEG",
DOI = "http://dx.doi.org/10.1016/j.mcm.2005.09.033",
ISSN = "0895-7177",
ISSN-L = "0895-7177",
MRclass = "94A15 (91B82)",
MRnumber = "2218323 (2006k:94033)",
MRreviewer = "Ulrich Tamm",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical and Computer Modelling",
}
@Article{Gaite:2006:CSZ,
author = "Jos{\'e} Gaite",
title = "Cut-out sets and the {Zipf} law for fractal voids",
journal = "Phys. D",
volume = "223",
number = "2",
pages = "248--255",
year = "2006",
CODEN = "PDNPDT",
DOI = "http://dx.doi.org/10.1016/j.physd.2006.09.021",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
MRclass = "28A80",
MRnumber = "2307212",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica D. Nonlinear Phenomena",
}
@Article{Handurukande:2006:PSB,
author = "S. B. Handurukande and A.-M. Kermarrec and F. {Le
Fessant} and L. Massouli{\'e} and S. Patarin",
title = "Peer sharing behaviour in the {eDonkey} network, and
implications for the design of server-less file sharing
systems",
journal = j-OPER-SYS-REV,
volume = "40",
number = "4",
pages = "359--371",
month = oct,
year = "2006",
CODEN = "OSRED8",
DOI = "http://doi.acm.org/10.1145/1218063.1217970",
ISSN = "0163-5980",
ISSN-L = "0163-5980",
bibdate = "Fri Jun 20 17:14:10 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this paper we present an empirical study of a
workload gathered by crawling the eDonkey network --- a
dominant peer-to-peer file sharing system --- for over
50 days. We first confirm the presence of some known
features, in particular the prevalence of free-riding
and the Zipf-like distribution of file popularity. We
also analyze the evolution of document popularity. We
then provide an in-depth analysis of several clustering
properties of such workloads. We measure the
geographical clustering of peers offering a given file.
We find that most files are offered mostly by peers of
a single country, although popular files don't have
such a clear home country. We then analyze the overlap
between contents offered by different peers. We find
that peer contents are highly clustered according to
several metrics of interest. We propose to leverage
this property by allowing peers to search for content
without server support, by querying suitably identified
semantic neighbours. We find via trace-driven
simulations that this approach is generally effective,
and is even more effective for rare files. If we
further allow peers to query both their semantic
neighbours, and in turn their neighbours' neighbours,
we attain hit rates as high as over 55\% for neighbour
lists of size 20.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGOPS Operating Systems Review",
keywords = "file sharing; peer-to-peer; simulation; trace",
}
@InCollection{Harremoes:2006:ZLH,
author = "P. Harremo{\"e}s and F. Topsoe",
editor = "Rudolf Ahlswede and others",
booktitle = "General theory of information transfer and
combinatorics",
title = "{Zipf}'s law, hyperbolic distributions and entropy
loss",
volume = "4123",
publisher = pub-SV,
address = pub-SV:adr,
pages = "788--792",
year = "2006",
DOI = "http://dx.doi.org/10.1007/11889342_50",
bibdate = "Sat Nov 12 11:15:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
abstract = "Zipf's law --- or Estoup-Zipf's law --- is an
empirical fact of computational linguistics which
relates rank and frequency of words in natural
languages. The law suggests modelling by distributions
of ``hyperbolic type''. We present a satisfactory
general definition and an information-theoretical
characterization of the resulting hyperbolic
distributions. When applied to linguistics this leads
to a property of stability and flexibility, explaining
that a language can develop towards higher and higher
expressive powers without changing its basic
structure.",
acknowledgement = ack-nhfb,
classmath = "91F20 (Linguistics) 94A15 (General topics of
information theory) 94A17 (Measures of information)",
keywords = "entropy loss; hyperbolic distributions; Zipf's law",
ZMnumber = "1158.91481",
}
@TechReport{Hurlimann:2006:BLB,
author = "Werner H{\"u}rlimann",
title = "{Benford's Law} from 1881 to 2006: a bibliography",
type = "Report",
address = "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
pages = "15",
day = "5",
month = jul,
year = "2006",
bibdate = "Fri Mar 30 11:32:30 2007",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/pdf/math.ST/0607168",
abstract = "On the occasion of the 125-th anniversary of Newcomb's
paper, a bibliography of academic work related to
Benford's law from its year of origin 1881 to 2006 has
been compiled.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "This bibliography lists 325 references on the title
subject, with these (years) and counts: (1881) 1,
(1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
(1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
(1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
(1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
(1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
(1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
(1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
(1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
(1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
(1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
(1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
(2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
(2005) 34, (2006) 18.",
}
@Article{Hurlimann:2006:GBL,
author = "W. Hurlimann",
title = "Generalizing {Benford}'s law using power laws:
application to integer sequences",
journal = "ArXiv Mathematics e-prints",
month = jul,
year = "2006",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......7166H",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0607166",
keywords = "Mathematics - Statistics, Mathematics - Number Theory,
11B73, 11B83, 11K31, 62E15, 62E17",
}
@Article{Izsak:2006:MLE,
author = "F. Izs{\'a}k",
title = "Maximum likelihood estimation for constrained
parameters of multinomial distributions --- application
to {Zipf--Mandelbrot} models",
journal = j-COMPUT-STAT-DATA-ANAL,
volume = "51",
number = "3",
pages = "1575--1583",
year = "2006",
CODEN = "CSDADW",
DOI = "http://dx.doi.org/10.1016/j.csda.2006.05.008",
ISSN = "0167-9473",
ISSN-L = "0167-9473",
MRnumber = "2307527",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics \& Data Analysis",
}
@Article{Kossovsky:2006:TBU,
author = "Alex Ely Kossovsky",
title = "Towards a Better Understanding of the Leading Digits
Phenomena",
journal = "CoRR",
year = "2006",
bibdate = "Mon Nov 21 06:46:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/math/0612627",
abstract = "This article on leading digits (Benford's Law)
contains the following: (I) An attempt at a
comprehensive account on the leading digits phenomena,
incorporating many of its existing explanations,
proofs, and differing points of view. (II) The finding
that leading digits of random numbers derived from a
chain of distributions that are linked via parameter
selection are logarithmic in the limit as the number of
sequences approaches infinity, and that empirically
only around 5 or 6 sequences of such a distribution
chain are needed to obtain results that are close
enough to the logarithmic (i.e., rapid convergence).
(III) An outright exact logarithmic behavior for a
2-sequence chain whenever parametrical density is
exactly logarithmic. (IV) An account on the existence
of singularities in exponential growth rates with
regards to the leading digits distributions of their
series. (V) An account on several distributions that
are intrinsically logarithmic or approximately so. (VI)
A conceptual justification of Flehinger's iterated
averaging scheme --- an algorithm that was presented
without any clear motivation. (VII) A note on the close
relationship of Flehinger's scheme and the chain of
distribution to Hill's super distribution. (VIII) A
conceptual argument justifying the scale invariance
principle --- a principle invoked in derivations of
Benford's law. (IX) A note on the intimate connection
between one-sided tail to the right in density
distributions and logarithmic leading digit behavior.",
acknowledgement = ack-nhfb,
}
@Book{Kuipers:2006:UDS,
author = "Lauwerens Kuipers and Harald Niederreiter",
title = "Uniform distribution of sequences",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xviii + 390",
year = "2006",
ISBN = "0-486-45019-8 (paperback)",
ISBN-13 = "978-0-486-45019-3 (paperback)",
LCCN = "QA292 .K84 2006",
bibdate = "Sat Nov 12 15:42:53 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html;
http://www.loc.gov/catdir/toc/fy0612/2005056064.html",
acknowledgement = ack-nhfb,
remark = "Originally published in \cite{Kuipers:1974:UDS}.",
subject = "Sequences (Mathematics); Uniform distribution
(Probability theory)",
}
@Article{Kulikova:2006:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H.F.D.} ({$H$}-function Distribution) and {Benford's
Law}. {I}",
journal = j-THEORY-PROBAB-APPL,
volume = "50",
number = "2",
pages = "311--315",
month = jan,
year = "2006",
CODEN = "TPRBAU",
DOI = "http://dx.doi.org/10.1137/S0040585X97981706",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Wed May 19 18:14:51 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1",
acknowledgement = ack-nhfb,
fjournal = "Theory of probability and its applications",
}
@Article{Lagarias:2006:BLF,
author = "Jeffrey C. Lagarias and K. Soundararajan",
title = "{Benford}'s law for the $3 x + 1$ function",
journal = "J. London Math. Soc. (2)",
volume = "74",
number = "2",
pages = "289--303",
year = "2006",
CODEN = "JLMSAK",
DOI = "http://dx.doi.org/10.1112/S0024610706023131",
ISSN = "0024-6107 (print), 1469-7750 (electronic)",
MRclass = "37A45",
MRnumber = "2269630 (2007h:37007)",
MRreviewer = "Radhakrishnan Nair",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the London Mathematical Society. Second
Series",
}
@InCollection{Lu:2006:AFD,
author = "Fletcher Lu and J. Efrim Boritz and Dominic Covvey",
booktitle = "Advances in artificial intelligence",
title = "Adaptive fraud detection using {Benford}'s law",
volume = "4013",
publisher = pub-SV,
address = pub-SV:adr,
pages = "347--358",
year = "2006",
DOI = "http://dx.doi.org/10.1007/11766247_30",
MRnumber = "2280590",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Article{Marchi:2006:AAS,
author = "Scott Marchi and James Hamilton",
title = "Assessing the Accuracy of Self-Reported Data: an
Evaluation of the Toxics Release Inventory",
journal = "Journal of Risk and Uncertainty",
volume = "32",
number = "1",
pages = "57--76",
month = jan,
year = "2006",
CODEN = "JRUNEN",
DOI = "http://dx.doi.org/10.1007/s10797-006-6666-3",
ISSN = "0895-5646 (print), 1573-0476 (electronic)",
bibdate = "Fri Nov 25 11:25:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Maslov:2006:BGA,
author = "V. P. Maslov",
title = "{Bose} gas of anharmonic oscillators and a refinement
of {Zipf}'s law",
journal = j-TEORET-MATH-FIZ,
volume = "148",
number = "3",
pages = "495--496",
year = "2006",
CODEN = "TMFZAL",
DOI = "http://dx.doi.org/10.1007/s11232-006-0117-2",
ISSN = "0564-6162",
MRclass = "82B10",
MRnumber = "2283664",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
}
@Article{Maslov:2006:NAD,
author = "V. P. Maslov",
title = "Negative asymptotic dimension, a new condensate, and
their relation to the quantized {Zipf} law",
journal = j-MAT-ZAMETKI,
volume = "80",
number = "6",
pages = "856--863",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11006-006-0203-7",
ISSN = "0025-567X",
MRclass = "82B10 (20F69 53C23 81S10 91F20)",
MRnumber = "2311613 (2008e:82005)",
MRreviewer = "Artur E. Ruuge",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
}
@Article{Maslov:2006:RZM,
author = "V. P. Maslov",
title = "A refinement of the {Zipf--Mandelbrot} law and
lacunarity in an ideal gas",
journal = j-TEORET-MATH-FIZ,
volume = "147",
number = "3",
pages = "511--512",
year = "2006",
CODEN = "TMFZAL",
DOI = "http://dx.doi.org/10.1007/s11232-006-0083-8",
ISSN = "0564-6162",
MRclass = "82B10",
MRnumber = "2254729 (2007d:82007)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
}
@Article{Maslov:2006:ZLR,
author = "V. P. Maslov and T. V. Maslova",
title = "On {Zipf}'s law and rank distributions in linguistics
and semiotics",
journal = j-MAT-ZAMETKI,
volume = "80",
number = "5",
pages = "718--732",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11006-006-0189-1",
ISSN = "0025-567X",
MRclass = "60C05 (62-07 62P99)",
MRnumber = "2311586 (2008g:60027)",
MRreviewer = "Konstantin E. Feldman",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
Zametki",
ZMnumber = "Zbl 1134.62086",
}
@Article{Maslova:2006:ZLM,
author = "T. V. Maslova",
title = "{Zipf}'s law and {Maslov}'s formula as applied to
semiotic systems",
journal = j-DOKL-MATH,
volume = "74",
number = "3",
pages = "917--920",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1134/S1064562406060330",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Sat Nov 12 11:13:35 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
classmath = "62E20 (Asymptotic distribution theory in statistics)
82B03 (Foundations of equilibrium statistical
mechanics)",
fjournal = "Doklady Mathematics",
language = "English. Russian original",
ZMnumber = "pre05824774",
}
@Article{Maslova:2006:ZLV,
author = "T. V. Maslova",
title = "On the {Zipf} law and the {V. P. Maslov} formula for
semiotic systems",
journal = j-DOKL-AKAD-NAUK,
volume = "411",
number = "6",
pages = "754--757",
year = "2006",
CODEN = "DANKAS",
ISSN = "0869-5652",
MRclass = "62E20 (82B03)",
MRnumber = "2451374",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
Nauk",
}
@Article{Metwally:2006:IES,
author = "Ahmed Metwally and Divyakant Agrawal and Amr {El
Abbadi}",
title = "An integrated efficient solution for computing
frequent and top-$k$ elements in data streams",
journal = j-TODS,
volume = "31",
number = "3",
pages = "1095--1133",
month = sep,
year = "2006",
CODEN = "ATDSD3",
DOI = "http://doi.acm.org/10.1145/1166074.1166084",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Tue Oct 17 05:41:01 MDT 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/tods/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See comments in \cite{Liu:2010:CIE}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Database Systems",
}
@Article{Miller:2006:MCL,
author = "S. J. Miller and M. J. Nigrini",
title = "The {Modulo 1 Central Limit Theorem} and {Benford's
Law} for Products",
journal = "International Journal of Algebra",
volume = "3",
number = "3",
pages = "119--130",
month = jul,
year = "2006",
CODEN = "????",
ISSN = "1312-8868",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......7686M;
http://arxiv.org/abs/math/0607686",
abstract = "We derive a necessary and sufficient condition for the
sum of $M$ independent continuous random variables
modulo $1$ to converge to the uniform distribution in
$L^1([0,1])$, and discuss generalizations to discrete
random variables. A consequence is that if $X_1,
\ldots{}, X_M$ are independent continuous random
variables with densities $f_1, \ldots{}, f_M$, for any
base $B$ as $M \to \infty$ for many choices of the
densities the distribution of the digits of $X_1 *
\cdots{} * X_M$ converges to Benford's law base $B$.
The rate of convergence can be quantified in terms of
the Fourier coefficients of the densities, and provides
an explanation for the prevalence of Benford behavior
in many diverse systems.",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0607686",
keywords = "Mathematics - Probability, Mathematics - Classical
Analysis and ODEs, 60F05, 60F25, 11K06 (Primary),
42A10, 42A61, 62E15 (Secondary)",
}
@Article{Miller:2006:OSB,
author = "S. J. Miller and M. J. Nigrini",
title = "Order Statistics and {Benford's Law}",
journal = "ArXiv Mathematics e-prints",
month = jan,
year = "2006",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006math......1344M",
acknowledgement = ack-nhfb,
eprint = "arXiv:math/0601344",
keywords = "Mathematics - Probability, Mathematics - Number
Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16
(Secondary)",
}
@Article{Moret:2006:NBL,
author = "M. A. Moret and V. de Senna and M. G. Pereira and G.
F. Zebende",
title = "{Newcomb--Benford} Law in Astrophysical Sources",
journal = j-INT-J-MOD-PHYS-C,
volume = "17",
number = "11",
pages = "1597--1604",
month = "????",
year = "2006",
CODEN = "IJMPEO",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
bibdate = "Mon Nov 14 17:37:59 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
}
@TechReport{Morrow:2006:BLF,
author = "John Morrow",
title = "{Benford's Law}, Families of Distributions and a Test
Basis",
type = "Report",
institution = "University of Wisconsin--Madison",
address = "Madison, WI, USA",
month = "",
year = "2006",
bibdate = "Tue Nov 22 20:44:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Revised draft of 9 October 2010.",
URL = "http://www.johnmorrow.info/projects/benford/benfordMain.pdf",
acknowledgement = ack-nhfb,
lastaccess = "22 November 2011",
}
@Article{Posch:2006:ADP,
author = "Peter N. Posch and Welf A. Kreiner",
title = "Analysing digits for portfolio formation and index
tracking",
journal = j-J-ASSET-MANAGE,
volume = "7",
number = "1",
pages = "69--80",
month = may,
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1057/palgrave.jam.2240203",
ISSN = "1470-8272 (print), 1479-179X (electronic)",
ISSN-L = "1470-8272",
bibdate = "Fri Nov 25 11:19:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A general methodology is proposed for using digit
distributions as an approach to examining arbitrary
datasets. With the Newcomb--Benford law as a starting
point, a more general framework for digital analysis is
developed. A new measure is proposed based on this
framework, namely the Digital-Fit Factor (DFF). The use
of index comparison on the S\&P500 and the Dow Jones
Industrial Average is demonstrated. The DFF is then
used to construct portfolios and measure their
performance compared with that of the index. The
average returns using the measure exceed the index
composition by 6--14 percentage points per year by
being more stable at the same time. Furthermore, these
measures require only a very small proportion of the
available information and are thus very efficient.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Asset Management",
keywords = "Benford's Law",
}
@InProceedings{Sanches:2006:IRU,
author = "Jo{\~a}o M. Sanches and Jorge S. Marques",
booktitle = "{2006 IEEE International Conference on Image
Processing, Atlanta, Georgia, 8--11 October 2006}",
title = "Image Reconstruction using the {Benford Law}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2029--2032",
year = "2006",
DOI = "http://dx.doi.org/10.1109/ICIP.2006.312845",
ISBN = "1-4244-0480-0",
ISBN-13 = "978-1-4244-0480-3",
ISSN = "1522-4880",
bibdate = "Tue Nov 15 09:03:24 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/conf/icip/icip2006.html#SanchesM06;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Tt has been claimed that the first digit of real
signals follows a logarithmic distribution, called
Benford law. This paper shows that this distribution is
a natural prior for the gradient of several types of
medical images (MRI, CT, ultrasound) and proposes a
reconstruction algorithm based on the Benford law which
does not require any parameter tuning. Experimental
results are presented to illustrate the performance of
the reconstruction algorithm",
acknowledgement = ack-nhfb,
}
@Article{Schneider:2006:RAS,
author = "Reto U. Schneider",
title = "{Das R{\"a}tsel der abgegriffenen Seiten: Vor {\"u}ber
hundert Jahren stiess ein Astronom auf ein
merkw{\"u}rdiges statistisches Gesetz, das heute
Steuerbetr{\"u}ger entlarven soll}. ({German}) [{The}
puzzle of the worn pages: More than a hundred years ago
an astronomer came across a strange statistical law
that will now expose tax cheats]",
journal = "{NZZ Folio: Die Zeitschrift der Neuen Z{\"u}rcher
Zeitung}",
number = "1/06",
month = "????",
year = "2006",
bibdate = "Fri Nov 18 12:18:17 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www-x.nzz.ch/folio/curr/articles/schneider_2.html;
http://www.nzzfolio.ch/www/d80bd71b-b264-4db4-afd0-277884b93470/showarticle/4c9a5444-883e-4e6b-8a4c-6c31f32c02f3.aspx",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Schuette:2006:TFZ,
author = "Paul Schuette and Marcus C. Spruill",
title = "Tail fit and the {Zipf--Pareto} law",
journal = "Extremes",
volume = "9",
number = "3-4",
pages = "243--261",
year = "2006",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s10687-007-0030-6",
ISSN = "1386-1999",
MRnumber = "2367837",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Extremes. Statistical Theory and Applications in
Science, Engineering and Economics",
xxyear = "2007",
}
@Article{Sugimoto:2006:AFP,
author = "Toyoaki Sugimoto and Naoto Miyoshi",
title = "On the asymptotics of fault probability in
least-recently-used caching with {Zipf}-type request
distribution",
journal = j-RAND-STRUCT,
volume = "29",
number = "3",
pages = "296--323",
year = "2006",
CODEN = "RSALFD",
DOI = "http://dx.doi.org/10.1002/rsa.20098",
ISSN = "1042-9832",
ISSN-L = "1042-9832",
MRclass = "68N25 (60C05 62E20 62P30 68P05 68U35)",
MRnumber = "2254493 (2008h:68028)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Random Structures and Algorithms",
}
@Article{Wilkinson:2006:RPC,
author = "Leland Wilkinson",
title = "Revising the {Pareto} Chart",
journal = j-AMER-STAT,
volume = "60",
number = "4",
pages = "332--334",
month = nov,
year = "2006",
CODEN = "ASTAAJ",
DOI = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313006X152243",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
bibdate = "Thu Aug 26 21:48:27 MDT 2010",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Ackermann:2007:DMB,
author = "Heiner Ackermann and Alantha Newman and Heiko
R{\"o}glin and Berthold V{\"o}cking",
title = "Decision-making based on approximate and smoothed
{Pareto} curves",
journal = j-THEOR-COMP-SCI,
volume = "378",
number = "3",
pages = "253--270",
day = "9",
month = jun,
year = "2007",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Mar 29 08:55:49 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/03043975",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
}
@Article{Amin:2007:TVA,
author = "Zeinab H. Amin",
title = "Tests for the Validity of the Assumption that the
Underlying Distribution of Life is {Pareto}",
journal = j-J-APPL-STAT,
volume = "34",
number = "2",
pages = "195--201",
year = "2007",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
}
@Article{Bakulina:2007:AZL,
author = "M. P. Bakulina",
title = "Application of {Zipf}'s law for text compression",
journal = "Diskretn. Anal. Issled. Oper. Ser. 2",
volume = "14",
number = "2",
pages = "3--13",
year = "2007",
CODEN = "????",
ISSN = "1560-9901",
MRclass = "94A15",
MRnumber = "2542308 (2010i:94076)",
MRreviewer = "I. Vajda",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}.
Seriya 2",
}
@Article{Berger:2007:NMO,
author = "Arno Berger and Theodore P. Hill",
title = "{Newton}'s Method Obeys {Benford}'s Law",
journal = j-AMER-MATH-MONTHLY,
volume = "114",
number = "7",
pages = "588--601",
month = aug # "\slash " # sep,
year = "2007",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65G50 (37N30)",
MRnumber = "2341322 (2008h:65016)",
MRreviewer = "Uwe Sch{\"a}fer",
bibdate = "Mon Jan 30 12:00:29 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/i27642270;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/27642274",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
}
@Article{Bernik:2007:BLA,
author = "V. I. Bernik and N. I. Kalosha",
title = "{Benford}'s law and the approximation of logarithms of
natural numbers by rational numbers",
journal = "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser.
F{\=\i}z.-Mat. Navuk",
volume = "??",
number = "3",
pages = "68--73, 127",
year = "2007",
CODEN = "????",
ISSN = "0002-3574",
MRclass = "11J83 (11A63 11K36)",
MRnumber = "2398318 (2008j:11084)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Vests{\=\i} Natsyyanal\cprime na{\u\i}
Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya
F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya
Natsional\cprime no{\u\i} Akademii Nauk Belarusi.
Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the
National Academy of Sciences of Belarus. Physics and
Mathematics Series",
}
@Article{Brown:2007:UZL,
author = "R. J. C. Brown",
title = "The use of {Zipf}'s law in the screening of analytical
data: a step beyond {Benford}",
journal = j-ANALYST,
volume = "132",
number = "4",
pages = "344",
year = "2007",
CODEN = "ANALAO",
DOI = "http://dx.doi.org/10.1039/b618255k",
ISSN = "0003-2654 (print), 1364-5528 (electronic)",
ISSN-L = "0003-2654",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007Ana...132..344B",
abstract = "This study shows for the first time the effectiveness
of Zipf's law in screening analytical data sets for
outliers, data formatting and data transcription
errors, particularly when the data sets are small. In
the case of pollutant concentrations in ambient air,
the multivariate nature of the measurement, and the
relationship between the measured values of these
multivariant quantities are the characteristics that
allow a Zipf's law approach to data screening to be
successful. Furthermore, it has been shown that Zipf's
law has advantages over other novel data screening
techniques, such as Benford's law, in terms of
sensitivity and scope",
acknowledgement = ack-nhfb,
fjournal = "The Analyst",
}
@Article{Chacko:2007:EPB,
author = "Manoj Chacko and P. Yageen Thomas",
title = "Estimation of a Parameter of Bivariate {Pareto}
Distribution by Ranked Set Sampling",
journal = j-J-APPL-STAT,
volume = "34",
number = "6",
pages = "703--714",
year = "2007",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
acknowledgement = ack-nhfb,
}
@Article{Cho:2007:BBL,
author = "Wendy K. Tam Cho and Brian J. Gaines",
title = "Breaking the ({Benford}) law: statistical fraud
detection in campaign finance",
journal = j-AMER-STAT,
volume = "61",
number = "3",
pages = "218--223",
month = aug,
year = "2007",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/000313007X223496",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2393725",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496;
http://www.tandfonline.com/doi/abs/10.1198/000313007X223496",
abstract = "Benford's law is seeing increasing use as a diagnostic
tool for isolating pockets of large datasets with
irregularities that deserve closer inspection. Popular
and academic accounts of campaign finance are rife with
tales of corruption, but the complete dataset of
transactions for federal campaigns is enormous.
Performing a systematic sweep is extremely arduous;
hence, these data are a natural candidate for initial
screening by comparison to Benford's distributions.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@Article{Clauset:2007:FST,
author = "Aaron Clauset and Maxwell Young and Kristian Skrede
Gleditsch",
title = "On the Frequency of Severe Terrorist Events",
journal = j-J-CONFL-RESOLUT,
volume = "51",
number = "1",
pages = "58--87",
month = feb,
year = "2007",
CODEN = "JCFRAL",
DOI = "http://dx.doi.org/10.1177/0022002706296157",
ISSN = "0022-0027 (print), 1552-8766 (electronic)",
ISSN-L = "0022-0027",
bibdate = "Thu Nov 24 14:07:17 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jcr.sagepub.com/content/51/1/58.abstract;
http://jcr.sagepub.com;
http://www.jstor.org/journals/00220027.html",
abstract = "In the spirit of Lewis Richardson's original study of
the statistics of deadly conflicts, we study the
frequency and severity of terrorist attacks worldwide
since 1968. We show that these events are uniformly
characterized by the phenomenon of ``scale
invariance,'' that is, the frequency scales as an
inverse power of the severity, $P(x) \approx
x{-\alpha}$. We find that this property is a robust
feature of terrorism, persisting when we control for
economic development of the target country, the type of
weapon used, and even for short time scales. Further,
we show that the center of the distribution oscillates
slightly with a period of roughly 13 years, that there
exist significant temporal correlations in the
frequency of severe events, and that current models of
event incidence cannot account for these variations or
the scale invariance property of global terrorism.
Finally, we describe a simple toy model for the
generation of these statistics and briefly discuss its
implications.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Conflict Resolution",
}
@Article{Diekmann:2007:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! {Using} {Benford's Law} to Detect
Fraudulent Scientific Data",
journal = j-J-APPL-STAT,
volume = "34",
number = "3--4",
pages = "321--329",
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/02664760601004940",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRnumber = "2380543",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.tandf.co.uk/journals/routledge/02664763.html",
URL = "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by `Benford's law'. Recently, a test against
this distribution was used to identify fraudulent
accounting data. This test is based on the supposition
that first, second, third, and other digits in real
data follow the Benford distribution while the digits
in fabricated data do not. Is it possible to apply
Benford tests to detect fabricated or falsified
scientific data as well as fraudulent financial data?
We approached this question in two ways. First, we
examined the use of the Benford distribution as a
standard by checking the frequencies of the nine
possible first and ten possible second digits in
published statistical estimates. Second, we conducted
experiments in which subjects were asked to fabricate
statistical estimates (regression coefficients). The
digits in these experimental data were scrutinized for
possible deviations from the Benford distribution.
There were two main findings. First, both digits of the
published regression coefficients were approximately
Benford distributed or at least followed a pattern of
monotonic decline. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. Surprisingly, first digits of faked
data also exhibited a pattern of monotonic decline,
while second, third, and fourth digits were distributed
less in accordance with Benford's law. At least in the
case of regression coefficients, there were indications
that checks for digit-preference anomalies should focus
less on the first (i.e., leftmost) and more on later
digits.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
keywords = "Benford's Law; data fabrication; digital analysis;
distribution of digits from regression coefficients;
first digit law; Zipf's Law",
}
@Article{Dumbgen:2007:EBA,
author = "L. D{\"u}mbgen and C. Leuenberger",
title = "Explicit bounds for the approximation error in
{Benford}'s law",
journal = "ArXiv e-prints",
month = may,
year = "2007",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0705.4488",
keywords = "Mathematics - Probability, 60E15, 60F99",
primaryclass = "math.PR",
}
@InProceedings{Fu:2007:GBL,
author = "D. Fu and Y. Q. Shi and W. Su",
editor = "Edward J. {Delp III} and Ping Wah Wong",
booktitle = "{Society of Photo-Optical Instrumentation Engineers
(SPIE)} Conference Series",
title = "A generalized {Benford}'s law for {JPEG} coefficients
and its applications in image forensics",
volume = "6505",
publisher = pub-SPIE,
address = pub-SPIE:adr,
month = feb,
year = "2007",
DOI = "http://dx.doi.org/10.1117/12.704723",
ISSN = "0277-786X (print), 1996-756X (electronic)",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series",
URL = "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F",
acknowledgement = ack-nhfb,
}
@Article{Giles:2007:BLN,
author = "D. E. Giles",
title = "{Benford's Law} and naturally occurring prices in
certain {eBay} auctions",
journal = "Applied Economics Letters",
volume = "14",
number = "3",
pages = "157--161",
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/13504850500425667",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Wed Nov 16 09:49:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/toc/rael20/current",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Fibonacci sequences; Lucas sequences",
}
@Article{Grendar:2007:ENP,
author = "Marian Grendar and George Judge and Laura Schechter",
title = "An empirical non-parametric likelihood family of
data-based {Benford}-like distributions",
journal = j-PHYSICA-A,
volume = "380",
number = "??",
pages = "429--438",
month = jul,
year = "2007",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2007.02.062",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://adsabs.harvard.edu/abs/2007PhyA..380..429G;
http://www.sciencedirect.com/science/article/pii/S0378437107001963",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
keywords = "Benford's Law",
}
@Article{Guo:2007:DIM,
author = "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao
and Xiaodong Zhang",
title = "Does {Internet} media traffic really follow
{Zipf}-like distribution?",
journal = j-SIGMETRICS,
volume = "35",
number = "1",
pages = "359--360",
month = jun,
year = "2007",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1254882.1254929",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Fri Jun 27 09:42:48 MDT 2008",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "It is commonly agreed that Web traffic follows the
Zipf-like distribution, which is an analytical
foundation for improving Web access performance by
client-server based proxy caching systems on the
Internet. However, some recent studies have observed
non-Zipf-like distributions of Internet media traffic
in different content delivery systems. Due to the
variety of media delivery systems and the diversity of
media content, existing studies on media traffic are
largely workload specific, and the observed access
patterns are often different from or even conflict with
each other. For Web media systems, study [3] reports
that the access pattern of streaming media is Zipf-like
in a university campus network, while study [2] finds
that it is not Zipf-like in an enterprise media
server.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
keywords = "media; stretched exponential; Zipf-like",
}
@Article{Gupta:2007:IMS,
author = "Arjun K. Gupta and Saralees Nadarajah",
title = "Information matrices for some bivariate {Pareto}
distributions",
journal = j-APPL-MATH-COMP,
volume = "184",
number = "2",
pages = "1069--1079",
day = "15",
month = jan,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
bibdate = "Sat Jul 12 09:03:01 MDT 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
}
@Article{Hand:2007:DDD,
author = "D. Hand",
title = "Deception and Dishonesty with Data: Fraud in Science",
journal = "Significance",
volume = "4",
number = "??",
pages = "22--25",
month = "????",
year = "2007",
CODEN = "????",
ISSN = "1740-9705",
bibdate = "Thu Nov 17 19:17:58 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Hungerbuhler:2007:BGF,
author = "Norbert H{\"u}ngerb{\"u}hler",
title = "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie
die Mathematik Steuers{\"u}ndern das F{\"u}rchten
lehrt} [{Benford's Law} on leading digits. Mathematics
teaches tax evaders to fear]",
type = "Report",
institution = "EducETH",
address = "Z{\"u}rich, Switzerland",
pages = "24",
day = "2",
month = mar,
year = "2007",
bibdate = "Fri Nov 18 12:02:21 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf",
acknowledgement = ack-nhfb,
language = "German",
lastaccess = "18 November 2011",
remark = "This report has several nice figures, including
photographs of Newcomb, Benford, and worn pages of log
tables, and an amazing plot of the agreement of
200,125,088 mathematical constants with Benford's
Law.",
}
@Article{Kumar:2007:DDD,
author = "Kuldeep Kumar and Sukanto Bhattacharya",
title = "Detecting the dubious digits: {Benford}'s law in
forensic accounting",
journal = "Significance [Magazine of the Royal Statistical
Society]",
volume = "4",
number = "2",
pages = "81--83",
month = jun,
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1740-9713.2007.00234.x",
ISSN = "1740-9705",
MRnumber = "2380610",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Significance. Statistics Making Sense",
onlinedate = "7 Jun 2007",
}
@Article{Mansury:2007:EZL,
author = "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s",
title = "The emergence of {Zipf}'s law in a system of cities:
an agent-based simulation approach",
journal = j-J-ECON-DYN-CONTROL,
volume = "31",
number = "7",
pages = "2438--2460",
year = "2007",
CODEN = "JEDCDH",
DOI = "http://dx.doi.org/10.1016/j.jedc.2006.08.002",
ISSN = "0165-1889 (print), 1879-1743 (electronic)",
ISSN-L = "0165-1889",
bibdate = "Sat Nov 12 11:17:04 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "This paper develops a spatial agent-based model to
generate a system of cities that exhibits the
statistical properties of the Zipf's Law. The numerical
results suggest that the combination of bounded
rationality and maximum heterogeneity of agents can
produce a generic power-law relationship in the size
distribution of cities, but does not always generate
the Zipf's Law. We found sufficient conditions on the
probability distribution of spatial reach to generate
the Zipf's Law associated with unit power coefficient.
Our model also indicates that the Zipf's Law breaks
down unless the extent of agglomeration economies
overwhelms the negative disagglomerating forces.",
acknowledgement = ack-nhfb,
classmath = "91B72 (Spatial models)",
fjournal = "Journal of Economic Dynamics and Control",
keywords = "complex systems; power laws; spatial agent based
models",
ZMnumber = "1163.91504",
}
@Article{Maslov:2007:PTZ,
author = "V. P. Maslov",
title = "Phase transitions of the zeroth kind and the
quantization of the {Zipf} law",
journal = j-TEORET-MATH-FIZ,
volume = "150",
number = "1",
pages = "118--142",
year = "2007",
CODEN = "TMFZAL",
DOI = "http://dx.doi.org/10.1007/s11232-007-0008-1",
ISSN = "0564-6162",
MRclass = "82B26 (82B03)",
MRnumber = "2325869 (2008g:82037)",
MRreviewer = "N. N. Ganikhodjaev",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
Matematicheskaya Fizika",
}
@Article{Nadarajah:2007:CPG,
author = "Saralees Nadarajah and Samuel Kotz",
title = "On the convolution of {Pareto} and gamma
distributions",
journal = j-COMP-NET-AMSTERDAM,
volume = "51",
number = "12",
pages = "3650--3654",
day = "22",
month = aug,
year = "2007",
CODEN = "????",
ISSN = "1389-1286",
bibdate = "Sat Apr 2 08:42:20 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/13891286",
acknowledgement = ack-nhfb,
fjournal = "Computer Networks",
}
@Article{Nicolaisen:2007:PPB,
author = "Jeppe Nicolaisen and Birger Hj{\o}rland",
title = "Practical potentials of {Bradford}'s law: {A} critical
examination of the received view",
journal = j-J-DOC,
volume = "63",
number = "3",
pages = "359--377",
month = "????",
year = "2007",
CODEN = "JDOCAS",
DOI = "http://dx.doi.org/10.1108/00220410710743298",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 11:58:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Nigrini:2007:BLA,
author = "Mark J. Nigrini and Steven J. Miller",
title = "{Benford's Law} Applied to Hydrology Data --- Results
and Relevance to Other Geophysical Data",
journal = j-MATH-GEOL,
volume = "39",
number = "5",
pages = "469--490",
month = "????",
year = "2007",
CODEN = "MATGED",
DOI = "http://dx.doi.org/10.1007/s11004-007-9109-5",
ISSN = "0882-8121 (print), 1573-8868 (electronic)",
ISSN-L = "0882-8121",
bibdate = "Mon Nov 21 22:05:26 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/m2274ng70435u3x6/",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Geology",
}
@Article{Nye:2007:PEN,
author = "J. Nye and C. Moul",
title = "The Political Economy of Numbers: On the Application
of {Benford's Law} to International Macroeconomic
Statistics",
journal = "{B. E.} Journal of Macroeconomics",
volume = "7",
number = "1",
pages = "??--??",
month = "????",
year = "2007",
CODEN = "????",
DOI = "http://dx.doi.org/10.2202/1935-1690.1449",
ISSN = "1935-1690",
bibdate = "Tue Nov 22 20:48:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.bepress.com/bejm/vol7/iss1/art17",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "Berkeley Electronic Press Journal of Macroeconomics",
}
@Article{Simons:2007:SIP,
author = "John L. Simons",
title = "A simple (inductive) proof for the non-existence of
2-cycles of the $3 x + 1$ problem",
journal = j-J-NUMBER-THEORY,
volume = "123",
number = "1",
pages = "10--17",
month = mar,
year = "2007",
CODEN = "JNUTA9",
ISSN = "0022-314X (print), 1096-1658 (electronic)",
ISSN-L = "0022-314X",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0022314X06001223",
acknowledgement = ack-nhfb,
fjournal = "Journal of Number Theory",
keywords = "Benford's Law",
}
@Article{Wells:2007:QPV,
author = "K. Wells and J. Chiverton and M. Partridge and M.
Barry and H. Kadhem and B. Ott",
title = "Quantifying the Partial Volume Effect in {PET} Using
{Benford's Law}",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "54",
number = "5",
pages = "1616--1625",
month = oct,
year = "2007",
CODEN = "IRNSAM",
DOI = "http://dx.doi.org/10.1109/TNS.2007.903182",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2007ITNS...54.1616W",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
}
@Article{Yeh:2007:SMD,
author = "Hsiaw-Chan Yeh",
title = "Some multivariate discrete time series models for
dependent multivariate {Zipf} counts",
journal = "Bull. Inst. Math. Acad. Sin. (N.S.)",
volume = "2",
number = "1",
pages = "29--53",
year = "2007",
CODEN = "????",
ISSN = "0304-9825",
MRclass = "62M10 (62H20)",
MRnumber = "2294107",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica. New Series",
}
@Article{Aono:2008:ISO,
author = "June Y. Aono and Liming Guan",
title = "The impact of {Sarbanes--Oxley} act on cosmetic
earnings management",
journal = "Research in Accounting Regulation",
volume = "20",
number = "??",
pages = "205--215",
month = oct,
year = "2008",
CODEN = "????",
ISSN = "1052-0457",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S1052045707002123",
acknowledgement = ack-nhfb,
fjournal = "Research in Accounting Regulation",
keywords = "Benford's Law",
}
@Article{Bhattacharya:2008:FAB,
author = "S. Bhattacharya and K. Kumar",
title = "Forensic Accounting and {Benford's Law} [In the
Spotlight]",
journal = j-IEEE-SIGNAL-PROCESS-MAG,
volume = "25",
number = "2",
pages = "152--150",
month = mar,
year = "2008",
CODEN = "ISPRE6",
DOI = "http://dx.doi.org/10.1109/MSP.2007.914724",
ISSN = "1053-5888 (print), 1558-0792 (electronic)",
ISSN-L = "1053-5888",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008ISPM...25..152B",
acknowledgement = ack-nhfb,
fjournal = "IEEE signal processing magazine",
}
@Article{Chakravorty:2008:TAE,
author = "S. Chakravorty and Samia M. Siha",
title = "Testing the accuracy of employee-reported data: An
inexpensive alternative approach to traditional
methods",
journal = j-EUR-J-OPER-RES,
volume = "189",
number = "3",
pages = "583--593",
day = "16",
month = sep,
year = "2008",
CODEN = "EJORDT",
ISSN = "0377-2217 (print), 1872-6860 (electronic)",
ISSN-L = "0377-2217",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
acknowledgement = ack-nhfb,
fjournal = "European Journal of Operational Research",
keywords = "Benford's Law",
}
@Article{Costas:2008:NCC,
author = "Eduardo Costas and Victoria L{\'o}pez-Rodas and F.
Javier Toro and Antonio Flores-Moya",
title = "The number of cells in colonies of the cyanobacterium
{{\em Microcystis aeruginosa\/}} satisfies {Benford}'s
law",
journal = j-AQUAT-BOT,
volume = "89",
number = "3",
pages = "341--343",
month = oct,
year = "2008",
CODEN = "AQBODS",
ISSN = "0304-3770 (print), 1879-1522 (electronic)",
ISSN-L = "0304-3770",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0304377008000533",
acknowledgement = ack-nhfb,
fjournal = "Aquatic Botany",
keywords = "Benford's Law",
}
@Article{Depken:2008:BZB,
author = "Craig A. {Depken II}",
title = "{Benford}, {Zipf} and the blogosphere",
journal = j-APPL-ECON-LETT,
volume = "15",
number = "9",
pages = "689--692",
month = "????",
year = "2008",
DOI = "http://dx.doi.org/10.1080/13504850600735270",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Jan 07 09:18:33 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
onlinedate = "04 Jul 2008",
}
@Article{Dumbgen:2008:EBA,
author = "Lutz D{\"u}mbgen and Christoph Leuenberger",
title = "Explicit bounds for the approximation error in
{Benford}'s law",
journal = j-ELECTRON-COMMUN-PROBAB,
volume = "13",
pages = "99--112",
year = "2008",
CODEN = "????",
ISSN = "1083-589X",
MRclass = "60E15 (60F99)",
MRnumber = "2386066 (2009b:60056)",
MRreviewer = "Pieter C. Allaart",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0705.4488;
http://weber.math.washington.edu/~ejpecp/ECP/index.php",
abstract = "Benford's law states that for many random variables $X
> 0$ its leading digit $D = D(X)$ satisfies
approximately the equation $P(D = d) = log_{10}(1 +
1/d)$ for $d = 1, 2, \ldots{}, 9$. This phenomenon
follows from another, maybe more intuitive fact,
applied to $Y:= log_{10}(X)$: For many real random
variables $Y$, the remainder $U:= Y - floor(Y)$ is
approximately uniformly distributed on $[0,1)$. The
present paper provides new explicit bounds for the
latter approximation in terms of the total variation of
the density of $Y$ or some derivative of it. These
bounds are an interesting alternative to traditional
Fourier methods which yield mostly qualitative results.
As a by-product we obtain explicit bounds for the
approximation error in Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Communications in Probability",
}
@Article{Gauvrit:2008:PLB,
author = "Nicolas Gauvrit and Jean-Paul Delahaye",
title = "Pourquoi la loi de {Benford} n'est pas
myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is
not mysterious]",
journal = "Math. Sci. Hum. Math. Soc. Sci.",
volume = "??",
number = "182",
pages = "7--15",
year = "2008",
CODEN = "????",
ISSN = "0987-6936",
MRclass = "62A01 (91E10)",
MRnumber = "2433183 (2009f:62008)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Math{\'e}matiques et Sciences Humaines. Mathematics
and Social Sciences",
language = "French",
}
@Article{Hefeeda:2008:TMP,
author = "Mohamed Hefeeda and Osama Saleh",
title = "Traffic modeling and proportional partial caching for
peer-to-peer systems",
journal = j-IEEE-TRANS-NETWORKING,
volume = "16",
number = "6",
pages = "1447--1460",
month = dec,
year = "2008",
CODEN = "IEANEP",
DOI = "http://dx.doi.org/10.1109/TNET.2008.918081",
ISSN = "1063-6692",
ISSN-L = "1063-6692",
bibdate = "Fri Mar 6 16:31:04 MST 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
abstract = "Peer-to-peer (P2P) file sharing systems generate a
major portion of the Internet traffic, and this portion
is expected to increase in the future. We explore the
potential of deploying proxy caches in different
Autonomous Systems (ASes) with the goal of reducing the
cost incurred by Internet service providers and
alleviating the load on the Internet backbone. We
conduct an eight-month measurement study to analyze the
P2P traffic characteristics that are relevant to
caching, such as object popularity, popularity
dynamics, and object size. Our study shows that the
popularity of P2P objects can be modeled by a
Mandelbrot-Zipf distribution, and that several
workloads exist in P2P traffic. Guided by our findings,
we develop a novel caching algorithm for P2P traffic
that is based on object segmentation, and proportional
partial admission and eviction of objects. Our
trace-based simulations show that with a relatively
small cache size, a byte hit rate of up to 35\% can be
achieved by our algorithm, which is close to the byte
hit rate achieved by an off-line optimal algorithm with
complete knowledge of future requests. Our results also
show that our algorithm achieves a byte hit rate that
is at least 40\% more, and at most triple, the byte hit
rate of the common web caching algorithms. Furthermore,
our algorithm is robust in face of aborted downloads,
which is a common case in P2P systems.",
acknowledgement = ack-nhfb,
fjournal = "IEEE\slash ACM Transactions on Networking",
keywords = "internet measurement; network protocols; peer-to-peer
systems; traffic analysis; traffic modeling",
}
@Article{Huang:2008:IZL,
author = "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and
Jing-Shiuan Hua",
title = "An investigation of {Zipf's Law} for fraud detection",
journal = j-DEC-SUPP-SYS,
volume = "46",
number = "1",
pages = "70--83",
month = dec,
year = "2008",
CODEN = "DSSYDK",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923608001073",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law",
}
@Article{Humenberger:2008:EBB,
author = "H. Humenberger",
title = "{Eine elementarmathematische Begr{\"u}ndung des
Benford-Gesetzes}. ({German}) [{An} elementary
mathematical derivation of the {Benford Law}]",
journal = "Der Mathematikunterricht",
volume = "54",
number = "??",
pages = "24--34",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "0025-5807",
bibdate = "Fri Nov 18 11:59:44 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Ipeirotis:2008:CAH,
author = "Panagiotis G. Ipeirotis and Luis Gravano",
title = "Classification-aware hidden-web text database
selection",
journal = j-TOIS,
volume = "26",
number = "2",
pages = "6:1--6:??",
month = mar,
year = "2008",
CODEN = "ATISET",
DOI = "http://doi.acm.org/10.1145/1344411.1344412",
ISSN = "1046-8188",
ISSN-L = "0734-2047",
bibdate = "Thu Jun 12 16:52:34 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/tois/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Many valuable text databases on the web have
noncrawlable contents that are ``hidden'' behind search
interfaces. Metasearchers are helpful tools for
searching over multiple such ``hidden-web'' text
databases at once through a unified query interface. An
important step in the metasearching process is database
selection, or determining which databases are the most
relevant for a given user query. The state-of-the-art
database selection techniques rely on statistical
summaries of the database contents, generally including
the database vocabulary and associated word
frequencies. Unfortunately, hidden-web text databases
typically do not export such summaries, so previous
research has developed algorithms for constructing
approximate content summaries from document samples
extracted from the databases via querying. We present a
novel ``focused-probing'' sampling algorithm that
detects the topics covered in a database and adaptively
extracts documents that are representative of the topic
coverage of the database. Our algorithm is the first to
construct content summaries that include the
frequencies of the words in the database.
Unfortunately, Zipf's law practically guarantees that
for any relatively large database, content summaries
built from moderately sized document samples will fail
to cover many low-frequency words; in turn, incomplete
content summaries might negatively affect the database
selection process, especially for short queries with
infrequent words. To enhance the sparse document
samples and improve the database selection decisions,
we exploit the fact that topically similar databases
tend to have similar vocabularies, so samples extracted
from databases with a similar topical focus can
complement each other. We have developed two database
selection algorithms that exploit this observation. The
first algorithm proceeds hierarchically and selects the
best categories for a query, and then sends the query
to the appropriate databases in the chosen categories.
The second algorithm uses ``shrinkage,'' a statistical
technique for improving parameter estimation in the
face of sparse data, to enhance the database content
summaries with category-specific words. We describe how
to modify existing database selection algorithms to
adaptively decide (at runtime) whether shrinkage is
beneficial for a query. A thorough evaluation over a
variety of databases, including 315 real web databases
as well as TREC data, suggests that the proposed
sampling methods generate high-quality content
summaries and that the database selection algorithms
produce significantly more relevant database selection
decisions and overall search results than existing
algorithms.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Information Systems (TOIS)",
keywords = "database selection; Distributed information retrieval;
web search",
}
@Article{Jager:2008:DAD,
author = "Hendrik Jager and Pierre Liardet",
title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs
de convergents de fractions continues. ({French})
[Arithmetic distributions of the denominators of
continued fractions]",
journal = "Proceedings of the Koninklijke Nederlandse Akademie
van Wetenschappen, Series A, Indagationes
mathematicae",
volume = "91",
number = "2",
pages = "181--197",
day = "20",
month = jun,
year = "2008",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/S1385-7258(88)80026-X",
ISSN = "1385-7258 (print), 1878-5972 (electronic)",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
acknowledgement = ack-nhfb,
fjournal = "Indagationes Mathematicae (Proceedings)",
keywords = "Benford's Law",
language = "French",
xxjournal = "Indagationes Mathematicae (Proceedings)",
}
@Article{Jang:2008:CDH,
author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
S. J. Miller",
title = "Chains of distributions, hierarchical {Bayesian}
models and {Benford's Law}",
journal = "ArXiv e-prints",
month = may,
year = "2008",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J;
http://arxiv.org/abs/0805.4226",
abstract = "Kossovsky recently conjectured that the distribution
of leading digits of a chain of probability
distributions converges to Benford's law as the length
of the chain grows. We prove his conjecture in many
cases, and provide an interpretation in terms of
products of independent random variables and a central
limit theorem. An interesting consequence is that in
hierarchical Bayesian models priors tend to satisfy
Benford's Law as the number of levels of the hierarchy
increases, which allows us to develop some simple tests
(based on Benford's law) to test proposed models. We
give explicit formulas for the error terms as sums of
Mellin transforms, which converges extremely rapidly as
the number of terms in the chain grows. We may
interpret our results as showing that certain Markov
chain Monte Carlo processes are rapidly mixing to
Benford's law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0805.4226",
keywords = "Mathematics - Probability, Mathematics - Statistics
Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
pagecount = "15",
primaryclass = "math.PR",
}
@Article{Jelenkovic:2008:CMS,
author = "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang",
title = "Characterizing the miss sequence of the {LRU} cache",
journal = j-SIGMETRICS,
volume = "36",
number = "2",
pages = "119--121",
month = sep,
year = "2008",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1453175.1453203",
ISSN = "0163-5999 (print), 1557-9484 (electronic)",
ISSN-L = "0163-5999",
bibdate = "Wed Aug 25 07:31:09 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
abstract = "Renewed interest in caching systems stems from their
wide-spread use for reducing the document download
latency over the Internet. Since caches are usually
organized in a hierarchical manner, it is important to
study the performance properties of tandem caches. The
first step in understanding this problem is to
characterize the miss stream from one single cache
since it represents the input to the next level cache.
In this regard, we discover that the miss stream from
one single cache is approximated well by the
superposition of a number of asymptotically independent
renewal processes. Interestingly, when this weakly
correlated miss sequence is fed into another cache,
this barely observable correlation can lead to
measurably different caching performance when compared
to the independent reference model. This result is
likely to enable the development of a rigorous analysis
of the tandem cache performance.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMETRICS Performance Evaluation Review",
keywords = "average-case analysis; cache fault probability;
hierarchical caching; least-recently-used caching; web
caching; Zipf's law",
}
@Article{Kafri:2008:SIS,
author = "Oded Kafri",
title = "Sociological Inequality and the {Second Law}",
journal = "ArXiv e-prints",
year = "2008",
bibdate = "Mon Nov 21 06:41:29 2011",
bibsource = "http://dblp.uni-trier.de;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0805.3206",
abstract = "There are two fair ways to distribute particles in
boxes. The first way is to divide the particles equally
between the boxes. The second way, which is calculated
here, is to score fairly the particles between the
boxes. The obtained power law distribution function
yields an uneven distribution of particles in boxes. It
is shown that the obtained distribution fits well to
sociological phenomena, such as the distribution of
votes in polls and the distribution of wealth and
Benford's law.",
acknowledgement = ack-nhfb,
}
@InProceedings{Krakar:2008:ABL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
editor = "Boris Aurer and Miroslav Ba{\'c}a",
booktitle = "Proceedings of the 19th Central European Conference on
Information and Intelligent Systems (CECIS 2008)",
title = "Application of {Benford's Law} in Payment System
Auditing",
publisher = "Fakultet organizacije i informatike",
address = "Vara{\v{z}}din, Croatia",
pages = "187--193",
year = "2008",
bibdate = "Sun Nov 13 11:14:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Krakar:2008:EBL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
editor = "Mario Plenkovi{\'c}",
booktitle = "Society and Technology 2008",
title = "Evaluation of {Benford's Law}: application in stock
prices and stock turnover",
publisher = "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo",
address = "Zagreb, Croatia",
pages = "57--71",
year = "2008",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Nov 13 11:18:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
remark = "International Federation of Communication Studies,
Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u
Zagrebu.",
}
@Article{Liu:2008:MNS,
author = "Cheng-Shi Liu",
title = "Maximal non-symmetric entropy leads naturally to
{Zipf}'s law",
journal = j-FRACTALS,
volume = "16",
number = "1",
pages = "99--101",
year = "2008",
CODEN = "FRACEG",
DOI = "http://dx.doi.org/10.1142/S0218348X08003788",
ISSN = "0218-348X",
MRclass = "94A17 (94A15)",
MRnumber = "2399875 (2009c:94027)",
MRreviewer = "Yasuichi Horibe",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Fractals. Complex Geometry, Patterns, and Scaling in
Nature and Society",
}
@Article{Lolbert:2008:NEG,
author = "Tam{\'a}s Lolbert",
title = "On the non-existence of a general {Benford}'s law",
journal = "Math. Social Sci.",
volume = "55",
number = "2",
pages = "103--106",
month = mar,
year = "2008",
CODEN = "MSOSDD",
DOI = "http://dx.doi.org/10.1016/j.mathsocsci.2007.09.001",
ISSN = "0165-4896 (print), 1879-3118 (electronic)",
MRclass = "60A10 (60E10)",
MRnumber = "2391902",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0165489607000935",
abstract = "Benford's law states that in randomly collected
numbers certain digits are more often leading digits
than others. More formally: the general law states that
the mantissae follow the logarithmic distribution in
any base. Benford's law was recognized by many
mathematicians so that several possible explanations
have been derived, but several questions are still
open. Applications are widespread, for example an
auditing technique (the so-called digital analysis),
which is employed around the world by internal revenue
services to detect tax fraud, is based on this
phenomenon.\par
In this paper it will be shown that there exists no
probability measure that would obey Benford's law for
any base, but if the set of possible bases does not
exceed a given upper limit, most real-life
distributions obey, or can be transformed to obey
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Social Sciences",
}
@Article{Luque:2008:FDF,
author = "Bartolo Luque and Lucas Lacasa",
title = "The first digit frequencies of primes and {Riemann}
zeta zeros tend to uniformity following a
size-dependent generalized {Benford}'s law",
journal = "ArXiv e-prints",
month = nov,
year = "2008",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L;
http://arxiv.org/abs/0811.3302",
abstract = "Prime numbers seem to distribute among the natural
numbers with no other law than that of chance, however
its global distribution presents a quite remarkable
smoothness. Such interplay between randomness and
regularity has motivated scientists of all ages to
search for local and global patterns in this
distribution that eventually could shed light into the
ultimate nature of primes. In this work we show that a
generalization of the well known first-digit Benford's
law, which addresses the rate of appearance of a given
leading digit $d$ in data sets, describes with
astonishing precision the statistical distribution of
leading digits in the prime numbers sequence. Moreover,
a reciprocal version of this pattern also takes place
in the sequence of the nontrivial Riemann zeta zeros.
We prove that the prime number theorem is, in the last
analysis, the responsible of these patterns. Some new
relations concerning the prime numbers distribution are
also deduced, including a new approximation to the
counting function $\pi(n)$. Furthermore, some relations
concerning the statistical conformance to this
generalized Benford's law are derived. Some
applications are finally discussed.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0811.3302",
keywords = "Mathematics - Number Theory, Mathematics -
Probability, Mathematics - Statistics",
pagecount = "20",
primaryclass = "math.NT",
}
@Article{Miller:2008:MCL,
author = "Steven J. Miller and Mark J. Nigrini",
title = "The modulo $1$ central limit theorem and {Benford}'s
law for products",
journal = "Int. J. Algebra",
volume = "2",
number = "1--4",
pages = "119--130",
year = "2008",
CODEN = "????",
ISSN = "1312-8868",
MRclass = "60F05 (11K06 42A10)",
MRnumber = "2417189 (2009e:60053)",
MRreviewer = "Gutti J. Babu",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Algebra",
}
@Article{Miller:2008:OSB,
author = "Steven J. Miller and Mark J. Nigrini",
title = "Order statistics and {Benford}'s law",
journal = j-INT-J-MATH-MATH-SCI,
year = "2008",
CODEN = "????",
ISSN = "0161-1712",
ISSN-L = "0161-1712",
MRclass = "62G30 (62E10)",
MRnumber = "2461421 (2010c:62168)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Article ID 382948.",
URL = "http://arxiv.org/abs/math/0601344",
abstract = "Fix a base $B$ and let zeta have the standard
exponential distribution; the distribution of digits of
zeta base $B$ is known to be very close to Benford's
Law. If there exists a $C$ such that the distribution
of digits of $C$ times the elements of some set is the
same as that of zeta, we say that set exhibits shifted
exponential behavior base $B$ (with a shift of $\log_B
C \bmod 1$). Let $X_1, \ldots{}, X_N$ be independent
identically distributed random variables. If the
$X_i$'s are drawn from the uniform distribution on
$[0,L]$, then as $N \to \infty$ the distribution of the
digits of the differences between adjacent order
statistics converges to shifted exponential behavior
(with a shift of $\log_B L / N \bmod 1$). By
differentiating the cumulative distribution function of
the logarithms modulo 1, applying Poisson Summation and
then integrating the resulting expression, we derive
rapidly converging explicit formulas measuring the
deviations from Benford's Law. Fix a delta in $(0,1)$
and choose $N$ independent random variables from any
compactly supported distribution with uniformly bounded
first and second derivatives and a second order Taylor
series expansion at each point. The distribution of
digits of any $N^\delta$ consecutive differences {\em
and\/} all $N - 1$ normalized differences of the order
statistics exhibit shifted exponential behavior. We
derive conditions on the probability density which
determine whether or not the distribution of the digits
of all the un-normalized differences converges to
Benford's Law, shifted exponential behavior, or
oscillates between the two, and show that the Pareto
distribution leads to oscillating behavior.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
pagecount = "19",
}
@Article{Ni:2008:BLH,
author = "D. Ni and Z. Ren",
title = "{Benford}'s law and half-lives of unstable nuclei",
journal = j-EUR-PHYS-J-A,
volume = "38",
pages = "251--255",
month = dec,
year = "2008",
CODEN = "EPJAFV",
DOI = "http://dx.doi.org/10.1140/epja/i2008-10680-8",
ISSN = "1434-6001 (print), 1434-601X (electronic)",
ISSN-L = "1434-6001",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008EPJA...38..251N",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal A: Hadrons and Nuclei",
}
@Article{Pain:2008:BLC,
author = "Jean-Christophe Pain",
title = "{Benford}'s law and complex atomic spectra",
journal = j-PHYS-REV-E,
volume = "77",
number = "1",
pages = "012102",
month = jan,
year = "2008",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.77.012102",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008PhRvE..77a2102P;
http://pre.aps.org/abstract/PRE/v77/i1/e012102",
abstract = "We found that in transition arrays of complex atomic
spectra, the strengths of electric-dipolar lines obey
Benford's law, which means that their significant
digits follow a logarithmic distribution favoring the
smallest values. This indicates that atomic processes
result from the superposition of uncorrelated
probability laws and that the occurrence of digits
reflects the constraints induced by the selection
rules. Furthermore, Benford's law can be a useful test
of theoretical spectroscopic models. Its applicability
to the statistics of electric-dipolar lines can be
understood in the framework of random matrix theory and
is consistent with the Porter-Thomas law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eid = "012102",
eprint = "0801.0946",
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
keywords = "Probability theory, Oscillator strengths, lifetimes,
transition moments, Other topics in the theory of the
electronic structure of atoms and molecules",
pagecount = "3",
primaryclass = "quant-ph",
}
@Article{Ravikumar:2008:BND,
author = "Bala Ravikumar",
title = "The {Benford--Newcomb} Distribution and Unambiguous
Context-Free Languages",
journal = j-INT-J-FOUND-COMP-SCI,
volume = "19",
number = "3",
pages = "717--727",
month = jun,
year = "2008",
CODEN = "IFCSEN",
DOI = "http://dx.doi.org/10.1142/S0129054108005905",
ISSN = "0129-0541",
MRclass = "68Q42 (68Q25 68Q45)",
MRnumber = "2417964 (2009h:68068)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Foundations of Computer
Science (IJFCS)",
}
@Article{Schurger:2008:EBS,
author = "Klaus Sch{\"u}rger",
title = "Extensions of {Black--Scholes} processes and
{Benford}'s law",
journal = j-STOCH-PROC-APPL,
volume = "118",
number = "7",
pages = "1219--1243",
month = jul,
year = "2008",
CODEN = "STOPB7",
DOI = "http://dx.doi.org/10.1016/j.spa.2007.07.017",
ISSN = "0304-4149 (print), 1879-209X (electronic)",
ISSN-L = "0304-4149",
MRclass = "60F10 (60G44 91B02 91B28)",
MRnumber = "2428715 (2009g:60037)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304414907001391",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Processes and Their Applications",
}
@Article{Semboloni:2008:HCS,
author = "F. Semboloni",
title = "Hierarchy, cities size distribution and {Zipf}'s law",
journal = j-EUR-PHYS-J-B,
volume = "63",
number = "3",
pages = "295--301",
year = "2008",
CODEN = "EPJBFY",
DOI = "http://dx.doi.org/10.1140/epjb/e2008-00203-1",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
MRclass = "91D10 (82B99 91D25)",
MRnumber = "2421552 (2009f:91111)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "The European Physical Journal B. Condensed Matter and
Complex Systems",
ZMnumber = "Zbl 1189.91174",
}
@Article{Shaki:2008:RSN,
author = "Samuel Shaki and Martin H. Fischer",
title = "Reading space into numbers --- a cross-linguistic
comparison of the {SNARC} effect",
journal = j-COGNITION,
volume = "108",
number = "2",
pages = "590--599",
month = aug,
year = "2008",
CODEN = "CGTNAU",
ISSN = "0010-0277 (print), 1873-7838 (electronic)",
ISSN-L = "0010-0277",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0010027708000978",
acknowledgement = ack-nhfb,
fjournal = "Cognition",
keywords = "Benford's Law; Spatial Numerical Association of
Response Codes (SNARC)",
}
@Article{Vuko:2008:UBL,
author = "Tina Vuko",
title = "Using {Benford's Law} to Detect Earnings Management
Practice: the Case of Listed Companies in {Croatia}",
journal = "Global Business \& Economics Anthology",
volume = "1",
number = "??",
pages = "69--74",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "1553-1333",
bibdate = "Sun Nov 13 11:10:55 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Watrin:2008:BLI,
author = "C. Watrin and R. Struffert and R. Ullmann",
title = "{Benford's Law}: An Instrument for Selecting Tax Audit
Targets?",
journal = "Review of Managerial Science",
volume = "2",
number = "3",
pages = "219--237",
month = nov,
year = "2008",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s11846-008-0019-9",
ISSN = "1863-6691",
bibdate = "Tue Nov 22 20:58:51 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Book{Ziliak:2008:CSS,
author = "Stephen Thomas Ziliak and Deirdre N. McCloskey",
title = "The Cult of Statistical Significance: How the Standard
Error Costs Us Jobs, Justice, and Lives",
publisher = "University of Michigan Press",
address = "Ann Arbor, MI, USA",
pages = "xxiii + 321",
year = "2008",
ISBN = "0-472-07007-X (cloth), 0-472-05007-9 (paperback)",
ISBN-13 = "978-0-472-07007-7 (cloth), 978-0-472-05007-9
(paperback)",
LCCN = "HB137 .Z55 2008",
bibdate = "Tue Dec 9 15:55:11 MST 2008",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
series = "Economics, cognition, and society",
URL = "http://www.loc.gov/catdir/enhancements/fy0809/2007035401-d.html",
acknowledgement = ack-nhfb,
remark = "This book has important comments on the battles among
Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
Pearson, supplementing the discussion of those
conflicts in \cite{McGrayne:2011:TWH}.",
subject = "economics; statistical methods; statistics; social
aspects; statistical hypothesis testing",
}
@InProceedings{Altamirano:2009:GTU,
author = "C. Altamirano and A. Robledo",
editor = "J. Zhou",
booktitle = "Complex Sciences",
title = "Generalized Thermodynamics Underlying the Laws of
{Zipf} and {Benford}",
volume = "5",
publisher = pub-SV,
address = pub-SV:adr,
pages = "2232--??",
year = "2009",
DOI = "http://dx.doi.org/10.1007/978-3-642-02469-6_100",
ISBN = "3-642-02468-8",
ISBN-13 = "978-3-642-02468-9",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A",
acknowledgement = ack-nhfb,
}
@Article{Anderson:2009:CRC,
author = "Thomas Anderson",
title = "Conference reviewing considered harmful",
journal = j-OPER-SYS-REV,
volume = "43",
number = "2",
pages = "108--116",
month = apr,
year = "2009",
CODEN = "OSRED8",
DOI = "http://doi.acm.org/10.1145/1531793.1531815",
ISSN = "0163-5980",
ISSN-L = "0163-5980",
bibdate = "Thu Apr 23 19:43:22 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "This paper develops a model of computer systems
research to help prospective authors understand the
often obscure workings of conference program
committees. We present data to show that the
variability between reviewers is often the dominant
factor as to whether a paper is accepted. We argue that
paper merit is likely to be Zipf distributed, making it
inherently difficult for program committees to
distinguish between most papers. We use game theory to
show that with noisy reviews and Zipf merit, authors
have an incentive to submit papers too early and too
often. These factors make conference reviewing, and
systems research as a whole, less efficient and less
effective. We describe some recent changes in
conference design to address these issues, and we
suggest some further potential improvements.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGOPS Operating Systems Review",
}
@Article{Battersby:2009:SAH,
author = "Stephen Battersby",
title = "Statistical analyses hint at fraud in {Iranian}
election",
journal = j-NEW-SCIENTIST,
volume = "202",
number = "2714",
pages = "10--??",
day = "24",
month = jun,
year = "2009",
CODEN = "NWSCAL",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407909616821",
acknowledgement = ack-nhfb,
fjournal = "The New Scientist",
keywords = "Benford's Law",
xxISSN = "0262-4079, 0028-6664",
}
@TechReport{Bauer:2009:DDF,
author = "J. Bauer and J. Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford's
Law} on Regression Tables",
type = "Report",
number = "??",
institution = "Institute of Sociology, LMU Munich",
address = "Munich, Germany",
month = "????",
year = "2009",
bibdate = "Fri Nov 18 11:46:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Berger:2009:BOB,
author = "A. Berger and T. P. Hill",
title = "{Benford} Online Bibliography",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
year = "2009",
bibdate = "Sat Nov 12 16:48:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.benfordonline.net",
acknowledgement = ack-nhfb,
remark = "According to \cite{Berger:2011:BLS}, the authors'
online bibliography contains more than 600
references.",
}
@InProceedings{Berinde:2009:SOH,
author = "Radu Berinde and Graham Cormode and Piotr Indyk and
Martin J. Strauss",
title = "Space-optimal heavy hitters with strong error bounds",
crossref = "Paredaens:2009:PTE",
pages = "157--166",
year = "2009",
DOI = "http://doi.acm.org/10.1145/1559795.1559819",
bibdate = "Thu Jul 2 14:05:34 MDT 2009",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "The problem of finding heavy hitters and approximating
the frequencies of items is at the heart of many
problems in data stream analysis. It has been observed
that several proposed solutions to this problem can
outperform their worst-case guarantees on real data.
This leads to the question of whether some stronger
bounds can be guaranteed. We answer this in the
positive by showing that a class of `counter-based
algorithms' (including the popular and very
space-efficient FREQUENT and SPACESAVING algorithms)
provide much stronger approximation guarantees than
previously known. Specifically, we show that errors in
the approximation of individual elements do not depend
on the frequencies of the most frequent elements, but
only on the frequency of the remaining `tail.' This
shows that counter-based methods are the most
space-efficient (in fact, space-optimal) algorithms
having this strong error bound.\par
This tail guarantee allows these algorithms to solve
the `sparse recovery' problem. Here, the goal is to
recover a faithful representation of the vector of
frequencies, $f$. We prove that using space $O(k)$, the
algorithms construct an approximation $f*$ to the
frequency vector $f$ so that the L1 error $||f -
f*||_1$ is close to the best possible error
$\hbox{min}_{f_2} || f_2 - f ||_1$, where $f$ 2 ranges
over all vectors with at most $k$ non-zero entries.
This improves the previously best known space bound of
about $O(k \log n)$ for streams without element
deletions (where $n$ is the size of the domain from
which stream elements are drawn). Other consequences of
the tail guarantees are results for skewed (Zipfian)
data, and guarantees for accuracy of merging multiple
summarized streams.",
acknowledgement = ack-nhfb,
keywords = "frequency estimation; heavy hitters; streaming
algorithms",
}
@Article{Bradley:2009:WBL,
author = "Jonathan R. Bradley and David L. Farnsworth",
title = "What Is {Benford's Law}?",
journal = "Teaching Statistics",
volume = "31",
number = "1",
pages = "2--6",
month = jan,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1467-9639.2009.00347.x",
ISSN = "0141-982X (print), 1467-9639 (electronic)",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
onlinedate = "6 Jan 2009",
}
@InProceedings{Burns:2009:SSR,
author = "B. D. Burns",
editor = "N. Taatgen and H. van Rijn",
booktitle = "{Proceedings of the Thirty-First Annual Conference of
the Cognitive Science Society, Cognitive Science
Society, Austin, TX}",
title = "Sensitivity to Statistical Regularities: People
(Largely) Follow {Benford's Law}",
publisher = "????",
address = "????",
pages = "2872--2877",
year = "2009",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 18 11:57:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Chakravorty:2009:TBL,
author = "S. Chakravorty and V. Sridharan",
title = "Testing {Benford's Law} for improving supply chain
decision-making: a field experiment",
journal = j-DRUG-DISCOVERY-TODAY,
volume = "122",
number = "2",
pages = "606--618",
month = dec,
year = "2009",
CODEN = "DDTOFS",
ISSN = "1359-6446 (print), 1878-5832 (electronic)",
ISSN-L = "1359-6446",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
acknowledgement = ack-nhfb,
fjournal = "Drug Discovery Today",
keywords = "Benford's Law",
}
@Article{Chuang:2009:FPS,
author = "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen",
title = "Feature-preserved sampling over streaming data",
journal = j-TKDD,
volume = "2",
number = "4",
pages = "15:1--15:??",
month = jan,
year = "2009",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1460797.1460798",
ISSN = "1556-4681",
ISSN-L = "1556-4681",
bibdate = "Fri Apr 24 17:59:51 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/tkdd/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "In this article, we explore a novel sampling model,
called {\em feature preserved sampling\/} ({\em FPS\/})
that sequentially generates a high-quality sample over
sliding windows. The sampling quality we consider
refers to the degree of consistency between the sample
proportion and the population proportion of each
attribute value in a window. Due to the time-variant
nature of real-world datasets, users are more likely to
be interested in the most recent data. However,
previous works have not been able to generate a
high-quality sample over sliding windows that precisely
preserves up-to-date population characteristics.
Motivated by this shortcoming, we have developed the
{\em FPS\/} algorithm, which has several advantages:
(1) it sequentially generates a sample from a
time-variant data source over sliding windows; (2) the
execution time of {\em FPS\/} is linear with respect to
the database size; (3) the {\em relative\/}
proportional differences between the sample proportions
and population proportions of most distinct attribute
values are guaranteed to be below a specified error
threshold, $\epsilon$, while the {\em relative\/}
proportion differences of the remaining attribute
values are as close to $\epsilon$ as possible, which
ensures that the generated sample is of high quality;
(4) the sample rate is close to the user specified rate
so that a high quality sampling result can be obtained
without increasing the sample size; (5) by a thorough
analytical and empirical study, we prove that {\em
FPS\/} has acceptable space overheads, especially when
the attribute values have Zipfian distributions, and
{\em FPS\/} can also excellently preserve the
population proportion of multivariate features in the
sample; and (6) {\em FPS\/} can be applied to infinite
streams and finite datasets equally, and the generated
samples can be used for various applications. Our
experiments on both real and synthetic data validate
that {\em FPS\/} can effectively obtain a high quality
sample of the desired size. In addition, while using
the sample generated by {\em FPS\/} in various mining
applications, a significant improvement in efficiency
can be achieved without compromising the model's
precision.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Knowledge Discovery from Data
(TKDD)",
keywords = "sampling; Streaming mining",
}
@Article{Clauset:2009:PLD,
author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
Newman",
title = "Power-Law Distributions in Empirical Data",
journal = j-SIAM-REVIEW,
volume = "51",
number = "4",
pages = "661--703",
month = "????",
year = "2009",
CODEN = "SIREAD",
DOI = "http://dx.doi.org/10.1137/070710111",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Mon May 17 17:56:49 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
}
@Article{Docampo:2009:BLA,
author = "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and
Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio
Flores-Moya",
title = "{Benford}'s law applied to aerobiological data and its
potential as a quality control tool",
journal = "Aerobiologia",
volume = "25",
number = "4",
pages = "275--283",
month = dec,
year = "2009",
CODEN = "AROBFT",
DOI = "http://dx.doi.org/10.1007/s10453-009-9132-8",
ISSN = "0393-5965 (print), 1573-3025 (electronic)",
bibdate = "Fri Nov 25 10:47:33 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132",
acknowledgement = ack-nhfb,
}
@Article{Dorfleitner:2009:PBE,
author = "Gregor Dorfleitner and Christian Klein",
title = "Psychological barriers in {European} stock markets:
Where are they?",
journal = "Global Finance Journal",
volume = "19",
number = "3",
pages = "268--285",
month = oct,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.gfj.2008.09.001",
ISSN = "1044-0283 (print), 1873-5665 (electronic)",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S1044028308000549",
acknowledgement = ack-nhfb,
fjournal = "Global Finance Journal",
keywords = "Benford's Law",
}
@Article{Fewster:2009:SEB,
author = "R. M. Fewster",
title = "A Simple Explanation of {Benford's Law}",
journal = j-AMER-STAT,
volume = "63",
number = "1",
pages = "26--32",
month = feb,
year = "2009",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/tast.2009.0005",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2655700",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@Article{Gauvrit:2009:LBG,
author = "Nicolas Gauvrit and Jean-Paul Delahaye",
title = "Loi de {Benford} g{\'e}n{\'e}rale. ({French})
[{General} {Benford}'s law]",
journal = "Math. Sci. Hum. Math. Soc. Sci.",
volume = "??",
number = "186",
pages = "5--15",
year = "2009",
CODEN = "????",
ISSN = "0987-6936",
MRclass = "62E10 (11A63 37A45)",
MRnumber = "2562062 (2010i:62029)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://msh.revues.org/document11034.html",
acknowledgement = ack-nhfb,
fjournal = "Math{\'e}matiques et Sciences Humaines. Mathematics
and Social Sciences",
language = "French",
}
@Article{Gauvrit:2009:SRI,
author = "N. Gauvrit and J.-P. Delahaye",
title = "Scatter and regularity imply {Benford}'s law \ldots{}
and more",
journal = "ArXiv e-prints",
month = oct,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G;
http://arxiv.org/abs/0910.1359",
abstract = "A random variable (r.v.) $X$ is said to follow
Benford's law if $\log(X)$ is uniform $\bmod 1$. Many
experimental data sets prove to follow an approximate
version of it, and so do many mathematical series and
continuous random variables. This phenomenon received
some interest, and several explanations have been put
forward. Most of them focus on specific data, depending
on strong assumptions, often linked with the log
function. Some authors hinted --- implicitly --- that
the two most important characteristics of a random
variable when it comes to Benford are regularity and
scatter. In a first part, we prove two theorems, making
up a formal version of this intuition: scattered and
regular r.v.'s do approximately follow Benford's law.
The proofs only need simple mathematical tools, making
the analysis easy. Previous explanations thus become
corollaries of a more general and simpler one. These
results suggest that Benford's law does not depend on
properties linked with the log function. We thus
propose and test a general version of the Benford's
law. The success of these tests may be viewed as an a
posteriori validation of the analysis formulated in the
first part.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0910.1359",
keywords = "Mathematics - Probability, Statistics - Methodology,
G.3",
primaryclass = "math.PR",
}
@Article{Gisin:2009:EEV,
author = "Vladimir Gisin and Andrey Markov and Igor Vinukov",
title = "Estimation of extreme values of returns using the
{Zipf--Mandelbrot} flow",
journal = j-INT-J-PURE-APPL-MATH,
volume = "50",
number = "2",
pages = "245--250",
year = "2009",
CODEN = "????",
ISSN = "1311-8080",
ISSN-L = "1314-3395",
MRclass = "60G70 (91B28 91B84)",
MRnumber = "2488836",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Pure and Applied
Mathematics",
}
@TechReport{Gonzales-Garcia:2009:BLM,
author = "J. Gonzales-Garcia and G. Pastor",
title = "{Benford's Law} and Macroeconomic Data Quality",
type = "Working Paper",
institution = "International Monetary Fund",
address = "????",
year = "2009",
bibdate = "Tue Nov 22 18:53:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437",
acknowledgement = ack-nhfb,
}
@Article{Gunnel:2009:DBL,
author = "S. G{\"u}nnel and K.-H. T{\"o}dter",
title = "Does {Benford's Law} Hold in Economic Research and
Forecasting?",
journal = j-EMPIRICA,
volume = "36",
number = "3",
pages = "273--292",
month = aug,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1007/s10663-008-9084-1",
ISSN = "0340-8744 (print), 1573-6911 (electronic)",
ISSN-L = "0340-8744",
bibdate = "Thu Nov 17 19:16:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/content/100261/",
abstract = "First and higher order digits in data sets of natural
and socio-economic processes often follow a
distribution called Benford's law. This phenomenon has
been used in business and scientific applications,
especially in fraud detection for financial data. In
this paper, we analyse whether Benford's law holds in
economic research and forecasting. First, we examine
the distribution of regression coefficients and
standard errors in research papers, published in
Empirica and Applied Economics Letters. Second, we
analyse forecasts of GDP growth and CPI inflation in
Germany, published in Consensus Forecasts. There are
two main findings: The relative frequencies of the
first and second digits in economic research are
broadly consistent with Benford's law. In sharp
contrast, the second digits of Consensus Forecasts
exhibit a massive excess of zeros and fives, raising
doubts on their information content.",
acknowledgement = ack-nhfb,
fjournal = "Empirica",
}
@Article{Hales:2009:TBL,
author = "Douglas N. Hales and Satya S. Chakravorty and V.
Sridharan",
title = "Testing {Benford's Law} for improving supply chain
decision-making: {A} field experiment",
journal = j-INT-J-PROD-ECON,
volume = "122",
number = "2",
pages = "606--618",
month = dec,
year = "2009",
CODEN = "JPCEYE",
DOI = "http://dx.doi.org/10.1016/j.ijpe.2009.06.017",
ISSN = "0925-5273 (print), 1873-7579 (electronic)",
ISSN-L = "0925-5273",
bibdate = "Wed Nov 23 18:41:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
acknowledgement = ack-nhfb,
ajournal = "Int. j. prod. econ.",
fjournal = "International Journal of Production Economics",
}
@Article{Hartshorn:2009:BRB,
author = "Kevin Hartshorn",
title = "Book Review: {{\booktitle{The fabulous Fibonacci
numbers}} by Alfred Posamentier and Ingmar Lehmann}",
journal = "Journal of Mathematics and the Arts",
volume = "3",
number = "2",
pages = "113--116",
month = "????",
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/17513470902897569",
ISSN = "1751-3472 (print), 1751-3480 (electronic)",
ISSN-L = "1751-3472",
bibdate = "Sat Jan 07 09:43:47 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569",
acknowledgement = ack-nhfb,
onlinedate = "05 Jun 2009",
}
@Article{Hurlimann:2009:GBL,
author = "Werner H{\"u}rlimann",
title = "Generalizing {Benford}'s law using power laws:
application to integer sequences",
journal = j-INT-J-MATH-MATH-SCI,
pages = "10",
year = "2009",
CODEN = "????",
ISSN = "0161-1712",
ISSN-L = "0161-1712",
MRclass = "60E05 (11B83 62E15)",
MRnumber = "2533550 (2010h:60043)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Article ID 970284.",
URL = "http://arxiv.org/abs/math/0607166",
abstract = "A simple method to derive parametric analytical
extensions of Benford's law for first digits of
numerical data is proposed. Two generalized Benford
distributions are considered, namely the two-sided
power Benford distribution and the new Pareto Benford
distribution. The fitting capabilities of these
generalized Benford distributions are illustrated and
compared at some interesting and important integer
sequences.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematics and Mathematical
Sciences",
}
@Article{Jang:2009:CDH,
author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
S. J. Miller",
title = "Chains of distributions, hierarchical {Bayesian}
models and {Benford's Law}",
journal = "Journal of Algebra, Number Theory: Advances and
Applications",
volume = "1",
number = "1",
pages = "37--60",
month = mar,
year = "2009",
CODEN = "????",
ISSN = "0972-5555",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0805.4226",
keywords = "Mathematics - Probability, Mathematics - Statistics
Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
primaryclass = "math.PR",
}
@Article{Janvresse:2009:BL,
author = "Elise Janvresse and Thierry de la Rue",
title = "{Benford}'s law",
journal = "Butl. Soc. Catalana Mat.",
volume = "24",
number = "1",
pages = "5--12",
year = "2009",
CODEN = "????",
ISSN = "0214-316X",
MRclass = "62-01",
MRnumber = "2567485",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Translated by Frederic Utzet",
acknowledgement = ack-nhfb,
fjournal = "Butllet{\'\i}n de la Societat Catalana de
Matem{\`a}tiques",
}
@Article{Jolissaint:2009:LBR,
author = "Paul Jolissaint",
title = "Loi de {Benford}, relations de r{\'e}currence et
suites {\'e}quidistribu{\'e}es. {II}. ({French})
[{Benford}'s Law, recurrence relations, and
equidistributed sequences. {II}]",
journal = j-ELEM-MATH,
volume = "64",
number = "1",
pages = "21--36",
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.4171/EM/112",
ISSN = "0013-6018 (print), 1420-8962 (electronic)",
ISSN-L = "0013-6018",
MRclass = "62E10 (11A63 37A45)",
MRnumber = "2471593 (2010f:62032)",
MRreviewer = "Denys Pommeret",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Elemente der Mathematik",
language = "French",
}
@Article{Judge:2009:DPS,
author = "G. Judge and L. Schechter",
title = "Detecting Problems in Survey Data using {Benford's
Law}",
journal = j-J-HUM-RESOUR,
volume = "44",
number = "1",
pages = "1--24",
month = "Winter",
year = "2009",
CODEN = "JHREA9",
DOI = "http://dx.doi.org/10.3368/jhr.44.1.1",
ISSN = "0022-166X (print), 1548-8004 (electronic)",
ISSN-L = "0022-166X",
bibdate = "Tue Nov 22 18:55:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://jhr.uwpress.org/content/44/1/1.abstract;
http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm",
acknowledgement = ack-nhfb,
fjournal = "Journal of Human Resources",
}
@Article{Kafri:2009:DNE,
author = "Oded Kafri",
title = "The Distributions in Nature and Entropy Principle",
journal = "ArXiv e-prints",
day = "28",
month = jul,
year = "2009",
bibdate = "Mon Nov 21 07:26:11 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/0907.4852",
abstract = "The derivation of the maximum entropy distribution of
particles in boxes yields two kinds of distributions: a
``bell-like'' distribution and a long-tail
distribution. The first one is obtained when the ratio
between particles and boxes is low, and the second one
when the ratio is high. The obtained long tail
distribution yields correctly the empirical Zipf law,
Pareto's 20:80 rule and Benford's law. Therefore, it is
concluded that the long tail and the ``bell-like''
distributions are outcomes of the tendency of
statistical systems to maximize entropy.",
acknowledgement = ack-nhfb,
pagecount = "19",
}
@Article{Kafri:2009:EPD,
author = "Oded Kafri",
title = "Entropy Principle in Direct Derivation of {Benford's
Law}",
journal = "ArXiv e-prints",
month = jan,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K;
http://arxiv.org/abs/0901.3047",
abstract = "The uneven distribution of digits in numerical data,
known as Benford's law, was discovered in 1881. Since
then, this law has been shown to be correct in copious
numerical data relating to economics, physics and even
prime numbers. Although it attracts considerable
attention, there is no a priori probabilistic criterion
when a data set should or should not obey the law. Here
a general criterion is suggested, namely that any file
of digits in the Shannon limit (namely, having maximum
entropy) has a Benford's law distribution of digits.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0901.3047",
keywords = "Computer Science - Discrete Mathematics, Physics -
Data Analysis, Statistics and Probability",
primaryclass = "cs.DM",
}
@Article{Krakar:2009:ABL,
author = "Zdravko Krakar and Mario {\v{Z}}gela",
title = "Application of {Benford's Law} in Payment System
Auditing",
journal = "Journal of Information Ethics and Organisational
Science",
volume = "33",
number = "1",
pages = "39--51",
month = "????",
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Nov 13 11:12:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf",
acknowledgement = ack-nhfb,
xxjournal = "Journal of Informational and Organizational Sciences",
}
@Article{Lansey:2009:ISR,
author = "Jonathan C. Lansey and Bruce Bukiet",
title = "{Internet} Search Result Probabilities: {Heaps' Law}
and Word Associativity",
journal = j-J-QUANT-LINGUISTICS,
volume = "16",
number = "1",
pages = "40--66",
month = "????",
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/09296170802514153",
ISSN = "1744-5035",
bibdate = "Sat Jan 07 09:36:17 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153",
abstract = "We study the number of internet search results
returned from multi-word queries based on the number of
results returned when each word is searched for
individually. We derive a model to describe search
result values for multi-word queries using the total
number of pages indexed by Google and by applying the
Zipf power law to the words per page distribution on
the internet and Heaps' law for unique word counts.
Based on data from 351 word pairs each with exactly one
hit when searched for together, and a Zipf law
coefficient determined in other studies, we approximate
the Heaps' law coefficient for the indexed worldwide
web (about 8 billion pages) to be $\beta = 0.52$.
Previous studies used under 20,000 pages. We
demonstrate through examples how the model can be used
to analyse automatically the relatedness of word pairs
assigning each a value we call ``strength of
associativity''. We demonstrate the validity of our
method with word triplets and through two experiments
conducted 8 months apart. We then use our model to
compare the index sizes of competing search giants
Yahoo and Google.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Linguistics",
keywords = "Benford's Law; Heaps' Law; Zipf's Law",
onlinedate = "25 Feb 2009",
remark = "From page 65: ``We mention that tests we have
conducted show that internet searches for random
numbers return approximately log-normally distributed
results and sorting by first digits yields results that
follow Benford's law (1938).''",
}
@Article{Lipovetsky:2009:PLD,
author = "Stan Lipovetsky",
title = "{Pareto} $80/20$ law: derivation via random
partitioning",
journal = j-INT-J-MATH-EDU-SCI-TECH,
volume = "40",
number = "2",
pages = "271--277",
month = "????",
year = "2009",
CODEN = "IJMEBM",
DOI = "http://dx.doi.org/10.1080/00207390802213609",
ISSN = "0020-739X (print), 1464-5211 (electronic)",
ISSN-L = "0020-739X",
bibdate = "Sat Jan 07 09:22:31 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609",
abstract = "The Pareto 80/20 Rule, also known as the Pareto
principle or law, states that a small number of causes
(20\%) is responsible for a large percentage (80\%) of
the effect. Although widely recognized as a heuristic
rule, this proportion has not been theoretically based.
The article considers derivation of this 80/20 rule and
some other standard quotients from the mean and its
interval estimation for the total value defined by the
product of two variables in the random partitioning
model.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Mathematical Education in
Science and Technology",
onlinedate = "19 Feb 2009",
}
@TechReport{Moller:2009:MQA,
author = "M. M{\"o}ller",
title = "Measuring the Quality of Auditing Services with the
Help of {Benford's Law} -- An Empirical Analysis and
Discussion of this Methodical Approach",
type = "Report",
number = "",
institution = "Institute for Accounting and Control, University of
Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "25",
day = "24",
month = apr,
year = "2009",
bibdate = "Tue Nov 22 20:40:12 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://ssrn.com/abstract=1529307",
abstract = "The so-called Benford's Law describes regularity in
the distribution of digits of randomly selected
numbers, which states that the relative frequency of
the leading digits reduces in a systematic manner from
the digit 1 to the digit 9. This distribution
hypothesis is being discussed in recent times as an
audit instrument in order to gain insights into
possible conscious and inadvertent errors in data
records. The present paper analyses the closing
accounts of 1,373 annual financial statements of
companies listed on the German DAX and compares these
with the Benford's distribution hypothesis. It can be
seen in the process that data pertaining to financial
accounts, which have not been audited by the so-called
``Big 4'' audit firms, but by smaller external
auditors, deviate to a significant extent from the
regularity of Benford's Law, which appears to make the
use of Benford's Law suitable as a benchmark to assess
the quality of the audit.",
acknowledgement = ack-nhfb,
}
@Article{Moret:2009:GSA,
author = "M. A. Moret and V. de Senna and M. C. Santana and G.
F. Zebende",
title = "Geometric Structural Aspects of Proteins and
{Newcomb--Benford Law}",
journal = j-INT-J-MOD-PHYS-C,
volume = "20",
number = "12",
pages = "1981--1988",
month = "????",
year = "2009",
CODEN = "IJMPEO",
DOI = "http://dx.doi.org/10.1142/S0129183109014874",
ISSN = "0129-1831 (print), 1793-6586 (electronic)",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Modern Physics C [Physics and
Computers]",
keywords = "Hydrophobicity, protein packing, complex systems, Time
series analysis, Systems obeying scaling laws, Binary
and multiple stars",
}
@Article{Ni:2009:BLD,
author = "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren",
title = "{Benford's Law} and $\beta$-Decay Half-Lives",
journal = j-COMM-THEOR-PHYS,
volume = "51",
number = "4",
pages = "713--716",
month = apr,
year = "2009",
CODEN = "CTPHDI",
DOI = "http://dx.doi.org/10.1088/0253-6102/51/4/25",
ISSN = "0253-6102",
ISSN-L = "0253-6102",
bibdate = "Sun Nov 13 11:01:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N;
http://stacks.iop.org/0253-6102/51/i=4/a=25",
abstract = "The experimental values of 2059 $\beta$-decay
half-lives are systematically analyzed and
investigated. We have found that they are in
satisfactory agreement with Benford's law, which states
that the frequency of occurrence of each figure, 1--9,
as the first significant digit in a surprisingly large
number of different data sets follows a logarithmic
distribution favoring the smaller ones. Benford's
logarithmic distribution of $\beta$-decay half-lives
can be explained in terms of Newcomb's justification of
Benford's law and empirical exponential law of
$\beta$-decay half-lives. Moreover, we test the
calculated values of 6721 $\beta$-decay half-lives with
the aid of Benford's law. This indicates that Benford's
law is useful for theoretical physicists to test their
methods for calculating $\beta$-decay half-lives.",
acknowledgement = ack-nhfb,
fjournal = "Communications in theoretical physics",
}
@Article{Nigrini:2009:DDU,
author = "Mark J. Nigrini and Steven J. Miller",
title = "Data Diagnostics Using Second-Order Tests of
{Benford's Law}",
journal = j-AUDITING,
volume = "28",
number = "2",
pages = "305--324",
month = nov,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.2308/aud.2009.28.2.305",
ISSN = "0278-0380 (print), 1558-7991 (electronic)",
ISSN-L = "0278-0380",
bibdate = "Tue Nov 15 09:11:56 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://aaapubs.org/loi/ajpt;
http://link.aip.org/link/AJPTXX/v28/i2/p305/s1",
abstract = "Auditors are required to use analytical procedures to
identify the existence of unusual transactions, events,
and trends. Benford's Law gives the expected patterns
of the digits in numerical data, and has been advocated
as a test for the authenticity and reliability of
transaction level accounting data. This paper describes
a new second-order test that calculates the digit
frequencies of the differences between the ordered
(ranked) values in a data set. These digit frequencies
approximate the frequencies of Benford's Law for most
data sets. The second-order test is applied to four
sets of transactional data. The second-order test
detected errors in data downloads, rounded data, data
generated by statistical procedures, and the inaccurate
ordering of data. The test can be applied to any data
set and nonconformity usually signals an unusual issue
related to data integrity that might not have been
easily detectable using traditional analytical
procedures",
acknowledgement = ack-nhfb,
fjournal = "Auditing: A Journal of Practice \& Theory",
}
@Article{Romero-Rochin:2009:DBL,
author = "V. Romero-Rochin",
title = "A derivation of {Benford's Law} \ldots{} and a
vindication of {Newcomb}",
journal = "ArXiv e-prints",
month = sep,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0909.3822R;
http://arxiv.org/abs/0909.3822",
abstract = "We show how Benford's Law (BL) for first, second,
\ldots{}, digits, emerges from the distribution of
digits of numbers of the type $a^{R}$, with $a$ any
real positive number and $R$ a set of real numbers
uniformly distributed in an interval $[P\log_a(10), (P
+ 1) \log_a(10))$ for any integer $P$. The result is
shown to be number base and scale invariant. A rule
based on the mantissas of the logarithms allows for a
determination of whether a set of numbers obeys BL or
not. We show that BL applies to numbers obtained from
the {\it multiplication\/} or {\it division\/} of
numbers drawn from any distribution. We also argue that
(most of) the real-life sets that obey BL are because
they are obtained from such basic arithmetic
operations. We exhibit that all these arguments were
discussed in the original paper by Simon Newcomb in
1881, where he presented Benford's Law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0909.3822",
keywords = "Mathematics - Probability, Mathematics - History and
Overview",
pagecount = "12",
primaryclass = "math.PR",
}
@Article{Roukema:2009:BLA,
author = "B. F. Roukema",
title = "{Benford's Law} anomalies in the 2009 {Iranian}
presidential election",
journal = "ArXiv e-prints",
month = jun,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009arXiv0906.2789R;
http://arxiv.org/abs/0906.2789",
abstract = "The vote count first digit frequencies of the 2009
Iranian presidential election are analysed assuming
proportionality of candidates' votes to the total vote
per voting area. This method is closely related to
Benford's Law. A highly significant ($p \approx
0.0007$) excess of vote counts for candidate $K$ that
start with the digit 7 is found (41 observed, 21.2--22
expected). Using this property as a selection criterion
leads to the following coincidences. (i) Among the six
most populous voting areas, this criterion selects
those three that have greater proportions of votes for
A than the other three. The probability that the two
sub-groups are drawn from the same distribution is $p
\approx 0.1$. (ii) $K$'s vote counts for these same
three voting areas all have the same second digit. The
probability of this is $p \approx 0.01$. (iii) Most
(75\%) of the vote counts for $K$ in voting areas with
70 to 79 votes for $K$ are odd, and every even number
occurs exactly once. The probability of the latter is
$p \approx 0.0005$. Interpreting the big city effect
(i) +( ii) as an overestimate of the true vote, assumed
to be roughly 50\% to match other data, while retaining
constant total vote numbers and increasing votes for
the other three candidates in proportion to their
average voting percentages, would imply that the
difference between A's and M's vote totals would drop
by about one million votes. These results do not
exclude other anomalies.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "0906.2789",
keywords = "Statistics - Applications",
primaryclass = "stat.AP",
}
@Article{Sambridge:2009:ABL,
author = "M. Sambridge and H. Tkalcic and A. Jackson",
title = "On the applicability of {Benford's Law} in the
Geosciences",
journal = "AGU Fall Meeting Abstracts",
pages = "A1756--??",
month = dec,
year = "2009",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 15 06:32:38 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2009AGUFM.S33A1756S",
acknowledgement = ack-nhfb,
keywords = "[1294] GEODESY AND GRAVITY / Instruments and
techniques, [1594] GEOMAGNETISM AND PALEOMAGNETISM /
Instruments and techniques, [3294] MATHEMATICAL
GEOPHYSICS / Instruments and techniques, [7299]
SEISMOLOGY / General or miscellaneous",
}
@Article{Shao:2009:FDD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First digit distribution of hadron full width",
journal = j-MOD-PHYS-LETT-A,
volume = "24",
number = "40",
pages = "3275--3282",
month = "????",
year = "2009",
CODEN = "MPLAEQ",
DOI = "http://dx.doi.org/10.1142/S0217732309031223",
ISSN = "0217-7323 (print), 1793-6632 (electronic)",
bibdate = "Mon Nov 14 16:26:06 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "A phenomenological law, called Benford's law, states
that the occurrence of the first digit, i.e.,
$1,2,\ldots{},9$, of numbers from many real world
sources is not uniformly distributed, but instead
favors smaller ones according to a logarithmic
distribution. We investigate, for the first time, the
first digit distribution of the full widths of mesons
and baryons in the well defined science domain of
particle physics systematically, and find that they
agree excellently with the Benford distribution. We
also discuss several general properties of Benford's
law, i.e., the law is scale-invariant, base-invariant,
and power-invariant. This means that the lifetimes of
hadrons follow also Benford's law.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1004.3077",
fjournal = "Modern Physics Letters A (MPLA)",
primaryclass = "hep-ph",
}
@Article{Speed:2009:YWP,
author = "T. Speed",
title = "You want proof?",
journal = j-BULL-INST-MATH-STAT,
volume = "38",
number = "??",
pages = "11--??",
month = "????",
year = "2009",
CODEN = "SMBCVA",
ISSN = "0146-3942",
bibdate = "Wed Nov 16 07:00:01 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://bulletin.imstat.org/archive/",
acknowledgement = ack-nhfb,
fjournal = "Bulletin --- Institute of Mathematical Statistics",
keywords = "Benford's Law",
remark = "As of 16 November 2011, volume 38 is not yet online at
the publisher Web site, although there are (broken)
links for volumes 31 (2002) to date.",
}
@Misc{Tao:2009:BLZ,
author = "Terrence Tao",
title = "{Benford}'s law, {Zipf}'s law, and the {Pareto}
distribution",
howpublished = "Web document.",
year = "2009",
bibdate = "Mon Nov 14 16:59:19 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/",
acknowledgement = ack-nhfb,
}
@Article{Todter:2009:BLI,
author = "Karl-Heinz T{\"o}dter",
title = "{Benford's Law} as an Indicator of Fraud in
Economics",
journal = j-GER-ECON-REV,
volume = "10",
number = "3",
pages = "339--351",
month = aug,
year = "2009",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1468-0475.2009.00475.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
onlinedate = "16 Jun 2009",
}
@Article{Xie:2009:FAS,
author = "Tao Xie and Yao Sun",
title = "A file assignment strategy independent of workload
characteristic assumptions",
journal = j-TOS,
volume = "5",
number = "3",
pages = "10:1--10:??",
month = nov,
year = "2009",
CODEN = "????",
DOI = "http://doi.acm.org/10.1145/1629075.1629079",
ISSN = "1553-3077 (print), 1553-3093 (electronic)",
ISSN-L = "1553-3077",
bibdate = "Tue Mar 16 15:33:57 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tos/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/tos.bib",
abstract = "The problem of statically assigning nonpartitioned
files in a parallel I/O system has been extensively
investigated. A basic workload characteristic
assumption of most existing solutions to the problem is
that there exists a strong inverse correlation between
file access frequency and file size. In other words,
the most popular files are typically small in size,
while the large files are relatively unpopular. Recent
studies on the characteristics of Web proxy traces
suggested, however, the correlation, if any, is so weak
that it can be ignored. Hence, the following two
questions arise naturally. First, can existing
algorithms still perform well when the workload
assumption does not hold? Second, if not, can one
develop a new file assignment strategy that is immune
to the workload assumption? To answer these questions,
we first evaluate the performance of three well-known
file assignment algorithms with and without the
workload assumption, respectively. Next, we develop a
novel static nonpartitioned file assignment strategy
for parallel I/O systems, called static round-robin
(SOR), which is immune to the workload assumption.
Comprehensive experimental results show that SOR
consistently improves the performance in terms of mean
response time over the existing schemes.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Storage",
keywords = "File assignment; load balancing; parallel I/O;
workload characteristics; Zipfian distribution",
}
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When Can One Test an Explanation? {Compare} and
Contrast {Benford's Law} and the Fuzzy {CLT}",
journal = j-AMER-STAT,
volume = "64",
number = "3",
pages = "221--227",
month = aug,
year = "2010",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/tast.2010.09098",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2757166",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@Article{Altamirano:2010:PTS,
author = "Carlo Altamirano and Alberto Robledo",
title = "Possible thermodynamic structure underlying the laws
of {Zipf} and {Benford}",
journal = "ArXiv e-prints",
day = "10",
month = aug,
year = "2010",
bibdate = "Mon Nov 21 07:12:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1008.1614",
abstract = "We show that the laws of Zipf and Benford, obeyed by
scores of numerical data generated by many and diverse
kinds of natural phenomena and human activity are
related to the focal expression of a generalized
thermodynamic structure. This structure is obtained
from a deformed type of statistical mechanics that
arises when configurational phase space is incompletely
visited in a severe way. Specifically, the restriction
is that the accessible fraction of this space has
fractal properties. The focal expression is an
(incomplete) Legendre transform between two entropy (or
Massieu) potentials that when particularized to first
digits leads to a previously existing generalization of
Benford's law. The inverse functional of this
expression leads to Zipf's law; but it naturally
includes the bends or tails observed in real data for
small and large rank. Remarkably, we find that the
entire problem is analogous to the transition to chaos
via intermittency exhibited by low-dimensional
nonlinear maps. Our results also explain the generic
form of the degree distribution of scale-free
networks.",
acknowledgement = ack-nhfb,
remark = "To be published in European Physical Journal B.",
}
@Article{Anderson:2010:BLC,
author = "Theresa Anderson and Larry Rolen and Ruth Stoehr",
title = "{Benford's} Law For Coefficients of Modular Forms and
Partition Functions",
journal = "ArXiv e-prints",
day = "3",
month = sep,
year = "2010",
bibdate = "Mon Nov 21 07:10:51 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1009.0780",
abstract = "Here we prove that Benford's law holds for
coefficients of an infinite class of modular forms.
Expanding the work of Bringmann and Ono on exact
formulas for harmonic Maass forms, we derive the
necessary asymptotics. This implies that the
unrestricted partition function $p(n)$, as well as
other natural partition functions, satisfy Benford's
law.",
acknowledgement = ack-nhfb,
pagecount = "10",
}
@Article{Bachmann:2010:APC,
author = "Val{\'e}rie Bachmann and Martin H. Fischer and
Hans-Peter Landolt and Peter Brugger",
title = "Asymmetric prefrontal cortex functions predict
asymmetries in number space",
journal = j-BRAIN-COGN,
volume = "74",
number = "3",
pages = "306--311",
month = dec,
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.bandc.2010.08.011",
ISSN = "0278-2626 (print), 1090-2147 (electronic)",
ISSN-L = "0278-2626",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0278262610001272",
acknowledgement = ack-nhfb,
fjournal = "Brain and Cognition",
keywords = "Benford's Law; small-number bias (SNB); Spatial
Numerical Association of Response Codes (SNARC)
effect",
}
@Article{Balanzario:2010:SCB,
author = "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz",
title = "Sufficient conditions for {Benford}'s law",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "23--24",
pages = "1713--1719",
day = "1--15",
month = dec,
year = "2010",
CODEN = "SPLTDC",
DOI = "http://dx.doi.org/10.1016/j.spl.2010.07.014",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "62E10 (62E17)",
MRnumber = "2734233 (2011i:62019)",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
keywords = "Benford's Law",
}
@Article{Balaz:2010:BLD,
author = "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch",
title = "{Benford}'s law and distribution functions of
sequences in $(0, 1)$",
journal = "Mathematical Notes",
volume = "88",
number = "3--4",
pages = "449--463",
month = oct,
year = "2010",
CODEN = "????",
ISSN = "0001-4346 (print), 1573-8876 (electronic)",
bibdate = "Fri Nov 25 10:52:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Bauer:2010:DDF,
author = "J. Bauer and J. Gross",
title = "Difficulties Detecting Fraud? {The} Use of {Benford's
Law} on Regression Tables",
type = "Report",
institution = "Institute of Sociology,
Ludwig-Maximilians-Universit{\"a}t",
address = "M{\"u}nchen, Germany",
pages = "????",
year = "2010",
bibdate = "Tue Nov 22 21:15:18 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Berger:2010:FFF,
author = "Arno Berger and Theodore P. Hill",
title = "Fundamental Flaws in {Feller}'s Classical Derivation
of {Benford's Law}",
journal = "ArXiv e-prints",
month = may,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:23:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B;
http://arxiv.org/abs/1005.2598",
abstract = "Feller's classic text ``An Introduction to Probability
Theory and its Applications'' contains a derivation of
the well known significant-digit law called Benford's
law. More specifically, Feller gives a sufficient
condition (`large spread') for a random variable $X$ to
be approximately Benford distributed, that is, for
$\log_{10}X$ to be approximately uniformly distributed
modulo one. This note shows that the large-spread
derivation, which continues to be widely cited and
used, contains serious basic errors. Concrete examples
and a new inequality clearly demonstrate that large
spread (or large spread on a logarithmic scale) does
not imply that a random variable is approximately
Benford distributed, for any reasonable definition of
`spread' or measure of dispersion",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1005.2598",
keywords = "Mathematics - Probability, Mathematics - Statistics,
62Axx",
primaryclass = "math.PR",
}
@TechReport{Berger:2010:LSD,
author = "A. Berger",
title = "Large Spread Does Not Imply {Benford's Law}",
type = "Preprint",
institution = "Department of Mathematical and Statistical Sciences,
University of Alberta",
address = "Edmonton, AB, Canada",
year = "2010",
bibdate = "Sat Nov 12 16:46:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.math.ualberta.ca/~aberger/Publications.html",
acknowledgement = ack-nhfb,
}
@Article{Block:2010:GEB,
author = "Henry W. Block and Thomas H. Savits",
title = "A General Example for {Benford} Data",
journal = j-AMER-STAT,
volume = "64",
number = "4",
pages = "335--339",
month = nov,
year = "2010",
CODEN = "ASTAAJ",
DOI = "http://dx.doi.org/10.1198/tast.2010.09169",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRnumber = "2758565",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.amstat.org/publications/tas/;
http://www.math.utah.edu/pub/tex/bib/amstat.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
abstract = "Benford's Law deals, among other things, with the
proportion of numbers whose first significant digit is
a $1$ (e.g., $0.00131$ and $19668$ both have first
significant digit $1$) in a variety of datasets. In
these datasets, which arise in various compendiums or
as mixtures of various sets of numbers, the proportion
of numbers with first significant digit one is $0.3010$
which is much higher than the commonsense value of $1 /
9$. The reasons for this occurrence have been elusive.
Mathematical attempts to explain this phenomenon have
been relatively fruitless. Methods involving
probability have been somewhat more successful. In this
article we give some simple reasons for this occurrence
and also give an example of a general mixture of
distributions which exactly satisfies this Law. Various
other examples and counterexamples are also given.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
}
@InCollection{Corazza:2010:CFM,
author = "Marco Corazza and Andrea Ellero and Alberto Zorzi",
booktitle = "Mathematical and statistical methods for actuarial
sciences and finance",
title = "Checking financial markets via {Benford}'s law: the
{S\&P 500} case",
publisher = "Springer Italia",
address = "Milan, Italy",
pages = "93--102",
year = "2010",
MRclass = "62P05",
MRnumber = "2676191",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Corominas-Murtra:2010:UZL,
author = "Bernat Corominas-Murtra and Ricard V. Sol{\'e}",
title = "Universality of {Zipf}'s law",
journal = j-PHYS-REV-E,
volume = "82",
number = "1",
pages = "011102",
year = "2010",
CODEN = "PLEEE8",
DOI = "http://dx.doi.org/10.1103/PhysRevE.82.011102",
ISSN = "1539-3755 (print), 1550-2376 (electronic)",
ISSN-L = "1539-3755",
MRclass = "82B03 (62B10)",
MRnumber = "2736361 (2011j:82002)",
MRreviewer = "N. N. Ganikhodjaev",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review E (Statistical physics, plasmas,
fluids, and related interdisciplinary topics)",
pagecount = "9",
}
@Article{Courtland:2010:CML,
author = "Rachel Courtland",
title = "Curious mathematical law is rife in nature",
journal = j-NEW-SCIENTIST,
volume = "208",
number = "2782",
pages = "10--??",
day = "16",
month = oct,
year = "2010",
CODEN = "NWSCAL",
DOI = "http://dx.doi.org/10.1016/S0262-4079(10)62497-9",
ISSN = "0262-4079 (print), 1364-8500 (electronic)",
ISSN-L = "0262-4079",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0262407910624979",
acknowledgement = ack-nhfb,
fjournal = "The New Scientist",
keywords = "Benford's Law; earthquake detection",
xxISSN = "0262-4079, 0028-6664",
}
@Article{Debreceny:2010:DMJ,
author = "S. Debreceny and Glen L. Gray",
title = "Data mining journal entries for fraud detection: An
exploratory study",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "157--181",
month = sep,
year = "2010",
CODEN = "IJAIA7",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See discussion
\cite{Grabski:2010:DDM,Kriel:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/journal/14670895;
http://www.sciencedirect.com/science/article/pii/S1467089510000540",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
}
@Article{Deligny:2010:RRL,
author = "H. Deligny and P. Jolissaint",
title = "Relations de r{\'e}currence lin{\'e}aires,
primitivit{\'e} et loi de {Benford}. ({French})
[{Linear} recurrence relations, primitivity, and
{Benford's Law}]",
journal = "ArXiv e-prints",
day = "23",
month = jul,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:14:51 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D;
http://arxiv.org/abs/1007.5349",
abstract = "We prove that many sequences of positive numbers
$(a_n)$ defined by finite linear difference equations
$a_{n+k} = c_{k-1} a_{n+k-1} + \ldots{} + c_0 a_n$ with
suitable nonnegative reals coefficients $c_i$ satisfy
Benford's Law on the first digit in many bases $b > 2$.
Our techniques rely on Perron--Frobenius theory via the
companion matrix of the characteristic polynomial of
the defining equation.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1007.5349",
keywords = "Mathematics - Dynamical Systems, Mathematics - Rings
and Algebras, 11A99",
language = "French",
primaryclass = "math.DS",
}
@Article{Diekmann:2010:BLF,
author = "Andreas Diekmann and Ben Jann",
title = "{Benford's Law} and Fraud Detection: Facts and
Legends",
journal = j-GER-ECON-REV,
volume = "11",
number = "3",
pages = "397--401",
month = aug,
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1111/j.1468-0475.2010.00510.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Mon Nov 14 17:09:33 MST 2011",
bibsource = "http://onlinelibrary.wiley.com/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
onlinedate = "6 Apr 2010",
}
@Article{Farkas:2010:SUN,
author = "Janos Farkas and Gy{\"o}rgy Gyurky",
title = "The significance of using the {Newcomb--Benford} law
as a test of nuclear half-life calculations",
journal = "Acta Physica Polonica, B",
volume = "41",
pages = "1213--1221",
year = "2010",
CODEN = "APOBBB",
ISSN = "0587-4254 (print), 1509-5770 (electronic)",
bibdate = "Mon Nov 14 16:21:42 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F;
http://arxiv.org/abs/1006.3615",
abstract = "Half-life number sequences collected from nuclear data
charts are found to obey the Newcomb--Benford law.
Based on this fact, it has been suggested recently,
that this law should be used to test the quality of
nuclear decay models. In this paper we briefly recall
how, when and why the Newcomb--Benford law can be
observed in a set of numbers with a given probability
distribution. We investigate the special case of
nuclear half-lives, and show that the law provides no
additional clue in understanding decay half-lives.
Thus, it can play no significant role in testing
nuclear decay theories.",
acknowledgement = ack-nhfb,
ajournal = "Acta Phys. Pol. B",
ajournal-2 = "Acta Phys. Polon. B",
archiveprefix = "arXiv",
eprint = "1006.3615",
primaryclass = "math-ph",
}
@Article{Fischer:2010:HCS,
author = "Martin H. Fischer and Richard A. Mills and Samuel
Shaki",
title = "How to cook a {SNARC}: Number placement in text
rapidly changes spatial-numerical associations",
journal = j-BRAIN-COGN,
volume = "72",
number = "3",
pages = "333--336",
month = apr,
year = "2010",
CODEN = "????",
ISSN = "0278-2626 (print), 1090-2147 (electronic)",
ISSN-L = "0278-2626",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0278262609002024",
acknowledgement = ack-nhfb,
fjournal = "Brain and Cognition",
keywords = "Benford's Law; Spatial Numerical Association of
Response Codes (SNARC)",
}
@Article{Formann:2010:NBL,
author = "A. K. Formann and R. J. Morris",
title = "The {Newcomb--Benford Law} in Its Relation to Some
Common Distributions",
journal = j-PLOS-ONE,
volume = "51",
month = may,
year = "2010",
CODEN = "POLNCL",
DOI = "http://dx.doi.org/10.1371/journal.pone.0010541",
ISSN = "1932-6203",
bibdate = "Mon Nov 14 18:19:09 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010PLoSO...510541F",
acknowledgement = ack-nhfb,
ages = "10541",
fjournal = "PLoS One",
}
@Article{Giuliano:2010:UPI,
author = "Rita Giuliano and {\'E}lise Janvresse",
title = "A unifying probabilistic interpretation of {Benford}'s
law",
journal = "Unif. Distrib. Theory",
volume = "5",
number = "2",
pages = "169--182",
year = "2010",
CODEN = "????",
ISSN = "1336-913X",
MRclass = "60J10 (11K99 60A99)",
MRnumber = "2781415",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Uniform Distribution Theory",
}
@Article{Grabski:2010:DDM,
author = "Severin Grabski",
title = "Discussion of {``Data mining journal entries for fraud
detection: An exploratory study''}",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "182--185",
month = sep,
year = "2010",
CODEN = "IJAIA7",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000394",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
}
@Article{Hickman:2010:DAC,
author = "Matthew Hickman and Stephen Rice",
title = "Digital Analysis of Crime Statistics: Does Crime
Conform to {Benford's Law}?",
journal = j-J-QUANT-CRIMINOL,
volume = "26",
number = "3",
pages = "333--349",
month = sep,
year = "2010",
CODEN = "JQCRE6",
DOI = "http://dx.doi.org/10.1007/s10940-010-9094-6",
ISSN = "0748-4518 (print), 1573-7799 (electronic)",
ISSN-L = "0748-4518",
bibdate = "Fri Nov 25 10:30:30 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Quantitative Criminology",
keywords = "Benford distribution; Benford's law; Crime data; Crime
statistics; Data errors; Digital analysis; Fabricated
data; First digit; Fraud detection; Uniform crime
reports",
}
@Article{Kaynar:2010:FSM,
author = "B. Kaynar and A. Berger and T. P. Hill and A. Ridder",
title = "Finite-state {Markov} Chains obey {Benford's Law}",
journal = "ArXiv e-prints",
month = mar,
year = "2010",
CODEN = "????",
ISSN = "????",
MRclass = "60J22, 11K06, 15B51",
bibdate = "Tue Nov 15 06:30:53 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K;
http://arxiv.org/abs/1003.0562",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1003.0562",
keywords = "Mathematics - Probability",
primaryclass = "math.PR",
}
@Article{Klar:2010:ZLL,
author = "B. Klar and P. R. Parthasarathy and N. Henze",
title = "{Zipf} and {Lerch} limit of birth and death
processes",
journal = "Probab. Engrg. Inform. Sci.",
volume = "24",
number = "1",
pages = "129--144",
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1017/S0269964809990179",
ISSN = "0269-9648",
MRclass = "60J27 (91F20)",
MRnumber = "2575846 (2010m:60254)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Probability in the Engineering and Informational
Sciences",
}
@Article{Kriel:2010:DDM,
author = "Eckhardt Kriel",
title = "Discussion of {``Data mining journal entries for fraud
detection: An exploratory study''}",
journal = j-INT-J-ACCOUNT-INFO-SYS,
volume = "11",
number = "3",
pages = "186--188",
month = sep,
year = "2010",
CODEN = "IJAIA7",
ISSN = "1467-0895 (print), 1873-4723 (electronic)",
ISSN-L = "1467-0895",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
note = "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.",
URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000400",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Accounting Information
Systems",
keywords = "Benford's Law",
}
@Article{Lee:2010:SAR,
author = "Joanne Lee and Wendy K. Tam Cho and George G. Judge",
title = "{Stigler}'s approach to recovering the distribution of
first significant digits in natural data sets",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "2",
pages = "82--88",
day = "15",
month = jan,
year = "2010",
CODEN = "SPLTDC",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715209003563",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
keywords = "Benford's Law",
}
@Article{Liu:2010:CIE,
author = "Hongyan Liu and Xiaoyu Wang and Yinghui Yang",
title = "Comments on {``An integrated efficient solution for
computing frequent and top-$k$ elements in data
streams''}",
journal = j-TODS,
volume = "35",
number = "2",
pages = "15:1--15:??",
month = apr,
year = "2010",
CODEN = "ATDSD3",
DOI = "http://doi.acm.org/10.1145/1735886.1735894",
ISSN = "0362-5915 (print), 1557-4644 (electronic)",
ISSN-L = "0362-5915",
bibdate = "Wed Apr 28 13:44:08 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/tods/;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Metwally:2006:IES}.",
abstract = "We investigate a well-known algorithm, {\em
Space-Saving\/} [Metwally et al. 2006], which has been
proven efficient and effective at mining frequent
elements in data streams. We discovered an error in one
of the theorems in Metwally et al. [2006]. Experiments
are conducted to illustrate the error.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Database Systems",
keywords = "approximate queries; data streams; frequent elements;
top-$k$ elements; Zipfian distributions",
}
@Article{Lu:2010:BLP,
author = "Ocean Fan Lu and David E. Giles",
title = "{Benford's Law} and psychological barriers in certain
{eBay} auctions",
journal = j-APPL-ECON-LETT,
volume = "17",
number = "10",
pages = "1005--1008",
month = "????",
year = "2010",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/13504850802631814",
ISSN = "1350-4851 (print), 1466-4291 (electronic)",
ISSN-L = "1350-4851",
bibdate = "Sat Jan 07 09:10:23 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814",
abstract = "Using generalizations of Benford's Law we test for the
absence of psychological barriers at various price
levels in eBay auctions for professional football
tickets. Our empirical results indicate that this
hypothesis cannot be rejected.",
acknowledgement = ack-nhfb,
fjournal = "Applied Economics Letters",
onlinedate = "16 Jun 2009",
}
@Article{Mahdian:2010:BBM,
author = "Babak Mahdian and Stanislav Saic",
title = "A bibliography on blind methods for identifying image
forgery",
journal = j-SIGNAL-PROCESS-IMAGE-COMMUN,
volume = "25",
number = "6",
pages = "389--399",
month = jul,
year = "2010",
CODEN = "SPICEF",
ISSN = "0923-5965 (print), 1879-2677 (electronic)",
ISSN-L = "0923-5965",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0923596510000536",
acknowledgement = ack-nhfb,
fjournal = "Signal Processing: Image Communication",
keywords = "Benford's Law",
}
@Article{Manoochehrnia:2010:BLA,
author = "P. Manoochehrnia and F. Rachidi and M. Rubinstein and
W. Schulz and G. Diendorfer",
title = "{Benford's Law} and Its Application to Lightning
Data",
journal = j-IEEE-TRANS-ELECTROMAGN-COMPAT,
volume = "52",
number = "4",
pages = "956--961",
month = nov,
year = "2010",
CODEN = "IEMCAE",
DOI = "http://dx.doi.org/10.1109/TEMC.2010.2067218",
ISSN = "0018-9375 (print), 1558-187X (electronic)",
ISSN-L = "0018-9375",
bibdate = "Mon Nov 21 22:24:43 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electromagnetic Compatibility",
}
@Article{Novikov:2010:APB,
author = "V. P. Novikov",
title = "Aspectual Principle, {Benford's Law} and {Russell's
Paradox}",
journal = "ArXiv e-prints",
month = dec,
year = "2010",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 18:11:57 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1012.5537N;
http://arxiv.org/abs/1012.5537",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1012.5537",
keywords = "Mathematics - Classical Analysis and ODEs",
pagecount = "5",
primaryclass = "math.CA",
}
@Article{Orita:2010:UBL,
author = "Masaya Orita and Ayako Moritomo and Tatsuya Niimi and
Kazuki Ohno",
title = "Use of {Benford}'s law in drug discovery data",
journal = j-DRUG-DISCOVERY-TODAY,
volume = "15",
number = "9--10",
pages = "328--331",
month = may,
year = "2010",
CODEN = "DDTOFS",
DOI = "http://dx.doi.org/10.1016/j.drudis.2010.03.003",
ISSN = "1359-6446 (print), 1878-5832 (electronic)",
ISSN-L = "1359-6446",
bibdate = "Wed Nov 23 18:48:37 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1359644610000796",
acknowledgement = ack-nhfb,
fjournal = "Drug Discovery Today",
}
@InProceedings{Qadir:2010:EJC,
author = "G. Qadir and X. Zhao and A. T. S. Ho",
booktitle = "{Society of Photo-Optical Instrumentation Engineers
(SPIE)} Conference Series",
title = "Estimating {JPEG2000} compression for image forensics
using {Benford's Law}",
volume = "7723",
publisher = pub-SPIE,
address = pub-SPIE:adr,
month = apr,
year = "2010",
DOI = "http://dx.doi.org/10.1117/12.855085",
bibdate = "Mon Nov 14 18:25:16 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Society of Photo-Optical Instrumentation Engineers
(SPIE) Conference Series",
URL = "http://adsabs.harvard.edu/abs/2010SPIE.7723E..14Q",
acknowledgement = ack-nhfb,
}
@Book{Saichev:2010:TZL,
author = "Alexander Saichev and Yannick Malevergne and Didier
Sornette",
title = "Theory of {Zipf}'s law and beyond",
volume = "632",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 171",
year = "2010",
DOI = "http://dx.doi.org/10.1007/978-3-642-02946-2",
ISBN = "3-642-02945-0",
ISBN-13 = "978-3-642-02945-5",
MRclass = "91-02 (91B70 91B82)",
MRnumber = "2569206 (2011b:91008)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Lecture Notes in Economics and Mathematical Systems",
acknowledgement = ack-nhfb,
ZMnumber = "Zbl 1189.91009",
}
@Article{Sambridge:2010:BLN,
author = "M. Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and A.
Jackson",
title = "{Benford}'s law in the natural sciences",
journal = "Geophysical Research Letters",
volume = "37",
number = "22",
pages = "L22301--L22306",
month = "????",
year = "2010",
CODEN = "GPRLAJ",
DOI = "http://dx.doi.org/10.1029/2010GL044830",
ISSN = "0094-8276",
bibdate = "Sun Nov 13 11:03:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010GeoRL..3722301S;
http://www.agu.org/pubs/crossref/2010/2010GL044830.shtml",
abstract = "More than 100 years ago it was predicted that the
distribution of first digits of real world observations
would not be uniform, but instead follow a trend where
measurements with lower first digit (1, 2, \ldots{})
occur more frequently than those with higher first
digits (\ldots{}, 8, 9). This result has long been
known but regarded largely as a mathematical curiosity
and received little attention in the natural sciences.
Here we show that the first digit rule is likely to be
a widespread phenomenon and may provide new ways to
detect anomalous signals in data. We test 15 sets of
modern observations drawn from the fields of physics,
astronomy, geophysics, chemistry, engineering and
mathematics, and show that Benford's law holds for them
all. These include geophysical observables such as the
length of time between geomagnetic reversals, depths of
earthquakes, models of Earth's gravity, geomagnetic and
seismic structure. In addition we find it also holds
for other natural science observables such as the
rotation frequencies of pulsars; green-house gas
emissions, the masses of exoplanets as well as numbers
of infectious diseases reported to the World Health
Organization. The wide range of areas where it is
manifested opens up new possibilities for exploitation.
An illustration is given of how seismic energy from an
earthquake can be detected from just the first digit
distribution of displacement counts on a seismometer,
i.e., without actually looking at the details of a
seismogram at all. This led to the first ever detection
of an earthquake using first digit information alone.",
acknowledgement = ack-nhfb,
ajournal = "Geophys. Res. Lett.",
fjournal = "Geophysical research letters",
}
@Article{Shao:2010:EMD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "Empirical Mantissa Distributions of Pulsars",
journal = j-ASTROPART-PHYS,
volume = "33",
number = "4",
pages = "255--262",
month = may,
year = "2010",
CODEN = "APHYEE",
DOI = "http://dx.doi.org/10.1016/j.astropartphys.2010.02.003",
ISSN = "0927-6505 (print), 1873-2852 (electronic)",
ISSN-L = "0927-6505",
bibdate = "Mon Nov 14 16:24:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1005.1702;
http://www.sciencedirect.com/science/article/pii/S0927650510000447",
abstract = "The occurrence of digits one through nine as the
leftmost nonzero digit of numbers from real world
sources is often not uniformly distributed, but
instead, is distributed according to a logarithmic law,
known as Benford's law. Here, we investigate
systematically the mantissa distributions of some
pulsar quantities, and find that for most quantities
their first digits conform to this law. However, the
barycentric period shows significant deviation from the
usual distribution, but satisfies a generalized
Benford's law roughly. Therefore pulsars can serve as
an ideal assemblage to study the first digit
distributions of real world data, and the observations
can be used to constrain theoretical models of pulsar
behavior.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1005.1702",
fjournal = "Astroparticle Physics",
primaryclass = "astro-ph.IM",
}
@Article{Shao:2010:FDD,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First Digit Distribution of Hadron Full Width",
journal = "ArXiv e-prints",
day = "19",
month = apr,
year = "2010",
bibdate = "Mon Nov 21 07:21:00 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1004.3077",
abstract = "A phenomenological law, called Benford's law, states
that the occurrence of the first digit, i.e., $1, 2,
\ldots{}, 9$, of numbers from many real world sources
is not uniformly distributed, but instead favors
smaller ones according to a logarithmic distribution.
We investigate, for the first time, the first digit
distribution of the full widths of mesons and baryons
in the well defined science domain of particle physics
systematically, and find that they agree excellently
with the Benford distribution. We also discuss several
general properties of Benford's law, i.e., the law is
scale-invariant, base-invariant, and power-invariant.
This means that the lifetimes of hadrons follow also
Benford's law.",
acknowledgement = ack-nhfb,
pagecount = "8",
}
@Article{Shao:2010:FDL,
author = "Lijing Shao and Bo-Qiang Ma",
title = "First-Digit Law in Nonextensive Statistics",
journal = "ArXiv e-prints",
year = "2010",
bibdate = "Mon Nov 21 07:09:52 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1010.2699",
abstract = "Nonextensive statistics, characterized by a
nonextensive parameter $q$, is a promising and
practically useful generalization of the Boltzmann
statistics to describe power-law behaviors from
physical and social observations. We here explore the
unevenness of the first digit distribution of
nonextensive statistics analytically and numerically.
We find that the first-digit distribution follows
Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the
temperature. The fluctuation decreases when $q$
increases, and the result converges to Benford's law
exactly as $q$ approaches 2. The relevant regularities
between nonextensive statistics and Benford's law are
also presented and discussed.",
acknowledgement = ack-nhfb,
}
@Article{Shao:2010:SDL,
author = "Lijing Shao and Bo-Qiang Ma",
title = "The significant digit law in statistical physics",
journal = j-PHYSICA-A,
volume = "389",
number = "16",
pages = "3109--3116",
month = may,
year = "2010",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2010.04.021",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
MRclass = "82B03",
MRnumber = "2652860 (2011d:82007)",
bibdate = "Sat Nov 12 10:09:22 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1005.0660;
http://inspirehep.net/record/855898;
http://inspirehep.net/record/873155;
http://www.sciencedirect.com/science/article/pii/S0378437110003596",
abstract = "The occurrence of the nonzero leftmost digit, i.e.,
$1, 2, \ldots{}, 9$, of numbers from many real world
sources is not uniformly distributed as one might
naively expect, but instead, the nature favors smaller
ones according to a logarithmic distribution, named
Benford's law. We investigate three kinds of widely
used physical statistics, i.e., the Boltzmann--Gibbs
(BG) distribution, the Fermi--Dirac (FD) distribution,
and the Bose--Einstein (BE) distribution, and find that
the BG and FD distributions both fluctuate slightly in
a periodic manner around the Benford distribution with
respect to the temperature of the system, while the BE
distribution conforms to it exactly whatever the
temperature is. Thus the Benford's law seems to present
a general pattern for physical statistics and might be
even more fundamental and profound in nature.
Furthermore, various elegant properties of Benford's
law, especially the mantissa distribution of data sets,
are discussed.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
}
@Book{Singleton:2010:FAF,
author = "Tommie Singleton and Aaron J. Singleton",
title = "Fraud auditing and forensic accounting",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Fourth",
pages = "xiv + 317",
year = "2010",
ISBN = "0-470-56413-X",
ISBN-13 = "978-0-470-56413-4",
LCCN = "HV8079.W47 B65 2010",
bibdate = "Tue Nov 22 10:31:33 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = "Wiley corporate F and A",
URL = "http://catalogimages.wiley.com/images/db/jimages/9780470564134.jpg;
http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-t.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010013504-b.html",
abstract = "Completely revised and updated, Fraud Auditing and
Forensic Accounting, Fourth Edition reveals how to
develop an investigative eye toward both internal and
external fraud and provides crucial information on how
to deal with it when discovered. With new chapters on
the physiological aspects of the fraudster and on fraud
response, as well as new material on non-financial
aspects of fraud investigation, body language,
discourse analysis, and interviewing techniques, this
authoritative, timely book equips auditors,
investigators, corporate attorneys, and accountants to
identify the signs of financial fraud and successfully
investigate it",
acknowledgement = ack-nhfb,
remark = "Derived from third edition (2006). 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",
tableofcontents = "Background of Fraud Auditing and Forensic
Accounting \\
Fraud Principles \\
Fraud Schemes \\
Red Flags \\
Fraud Risk Assessment \\
Fraud Prevention \\
Fraud Detection \\
Fraud Response \\
Computer Crime \\
Fraud and the Accounting Information System \\
Gathering Evidence \\
Cyber Forensics \\
Obtaining and Evaluating Nonfinancial Evidence in a
Fraud Examination \\
General Criteria and Standards for Establishing an
Expert Witness's Qualifications \\
The Legal Role and Qualifications of an Expert Witness
\\
Effective Tactics and Procedures for the Expert Witness
in Court \\
Fraud and the Public Accounting Profession",
}
@Article{Strzalka:2010:SPB,
author = "Dominik Strza{\l}ka",
title = "On some properties of {Benford}'s law",
journal = "J. Korean Math. Soc.",
volume = "47",
number = "5",
pages = "1055--1075",
year = "2010",
CODEN = "JKMSDG",
DOI = "http://dx.doi.org/10.4134/JKMS.2010.47.5.1055",
ISSN = "0304-9914",
MRclass = "11A63",
MRnumber = "2723008",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Korean Mathematical Society",
}
@Article{Szewczak:2010:LTR,
author = "S. Szewczak",
title = "A limit theorem for random sums modulo $1$",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "9--10",
pages = "747--751",
month = may,
year = "2010",
CODEN = "SPLTDC",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715210000106",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
keywords = "Benford's Law",
}
@Misc{Wagon:2010:BLD,
author = "S. Wagon",
title = "{Benford's Law} and Data Spread",
year = "2010",
bibdate = "Sat Nov 12 16:59:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "Web site.",
URL = "http://demonstrations.wolfram.com/BenfordsLawAndDataSpread",
acknowledgement = ack-nhfb,
}
@Article{Adamic:2011:CSU,
author = "Lada Adamic",
title = "Complex systems: Unzipping {Zipf}'s law",
journal = j-NATURE,
volume = "474",
number = "7350",
pages = "164--165",
month = jun,
year = "2011",
CODEN = "NATUAS",
DOI = "http://dx.doi.org/10.1038/474164a",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Tue Nov 15 09:29:15 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html",
acknowledgement = ack-nhfb,
fjournal = "Nature",
onlinedate = "09 June 2011",
}
@Article{Altamirano:2011:PTS,
author = "C. Altamirano and A. Robledo",
title = "Possible thermodynamic structure underlying the laws
of {Zipf} and {Benford}",
journal = j-EUR-PHYS-J-B,
volume = "81",
number = "3",
pages = "345--351",
month = jun,
year = "2011",
CODEN = "EPJBFY",
DOI = "http://dx.doi.org/10.1140/epjb/e2011-10968-5",
ISSN = "1434-6028 (print), 1434-6036 (electronic)",
ISSN-L = "1434-6028",
bibdate = "Mon Nov 14 17:53:47 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011EPJB...81..345A",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1008.1614",
fjournal = "European Physical Journal B: Condensed Matter and
Complex Systems",
primaryclass = "cond-mat.stat-mech",
}
@Article{Anderson:2011:BLC,
author = "Theresa C. Anderson and Larry Rolen and Ruth Stoehr",
title = "{Benford}'s law for coefficients of modular forms and
partition functions",
journal = j-PROC-AM-MATH-SOC,
volume = "139",
number = "5",
pages = "1533--1541",
year = "2011",
CODEN = "PAMYAR",
DOI = "http://dx.doi.org/10.1090/S0002-9939-2010-10577-4",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "11F12 (11F20 11P83)",
MRnumber = "2763743",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
}
@Article{Andrew:2011:OBM,
author = "Alex M. Andrew",
title = "Obituary: {Beno{\^\i}t Mandelbrot: 20 November
1924--14 October 2010}",
journal = "Kybernetes",
volume = "40",
number = "1--2",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "KBNTA3",
ISSN = "0368-492X (print), 1758-7883 (electronic)",
bibdate = "Fri Nov 25 07:32:54 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://en.wikipedia.org/wiki/ernst_von_glasersfeld;
http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf;
http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825;
http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary;
http://www.math.yale.edu/mandelbrot/;
http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html",
acknowledgement = ack-nhfb,
}
@Article{Baek:2011:ZLU,
author = "Seung Ki Baek and Sebastian Bernhardsson and Petter
Minnhagen",
title = "{Zipf}'s law unzipped",
journal = j-NEW-J-PHYS,
volume = "13",
number = "4",
pages = "043004",
month = "????",
year = "2011",
CODEN = "NJOPFM",
DOI = "http://dx.doi.org/10.1088/1367-2630/13/4/043004",
ISSN = "1367-2630",
bibdate = "Tue Nov 15 09:32:45 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://iopscience.iop.org/1367-2630/13/4/043004",
abstract = "Why does Zipf's law give a good description of data
from seemingly completely unrelated phenomena? Here it
is argued that the reason is that they can all be
described as outcomes of a ubiquitous random group
division: the elements can be citizens of a country and
the groups family names, or the elements can be all the
words making up a novel and the groups the unique
words, or the elements could be inhabitants and the
groups the cities in a country and so on. A random
group formation (RGF) is presented from which a
Bayesian estimate is obtained based on minimal
information: it provides the best prediction for the
number of groups with $k$ elements, given the total
number of elements, groups and the number of elements
in the largest group. For each specification of these
three values, the RGF predicts a unique group
distribution $N(k) \propto \exp(-b k) / k^\gamma$,
where the power-law index $\gamma$ is a unique function
of the same three values. The universality of the
result is made possible by the fact that no
system-specific assumptions are made about the
mechanism responsible for the group division. The
direct relation between $\gamma$ and the total number
of elements, groups and the number of elements in the
largest group is calculated. The predictive power of
the RGF model is demonstrated by direct comparison with
data from a variety of systems. It is shown that
$\gamma$ usually takes values in the interval $1 \leq
\gamma \leq 2$ and that the value for a given
phenomenon depends in a systematic way on the total
size of the dataset. The results are put in the context
of earlier discussions on Zipf's and Gibrat's laws,
$N(k) \propto k^{-2}$ and the connection between growth
models and RGF is elucidated.",
acknowledgement = ack-nhfb,
fjournal = "New Journal of Physics",
pagecount = "21",
}
@Article{Bawden:2011:BMS,
author = "David Bawden",
title = "{Beno{\^\i}t Mandelbrot} and the self-similarity of
information",
journal = j-J-DOC,
volume = "67",
number = "2",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "JDOCAS",
ISSN = "0022-0418 (print), 1758-7379 (electronic)",
ISSN-L = "0022-0418",
bibdate = "Fri Nov 25 07:40:34 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717",
acknowledgement = ack-nhfb,
fjournal = "Journal of Documentation",
}
@Article{Becker:2011:BLC,
author = "T. Becker and A. Greaves-Tunnell and S. J. Miller and
R. Ronan and F. W. Strauch",
title = "{Benford's Law} and Continuous Dependent Random
Variables",
journal = "ArXiv e-prints",
month = nov,
year = "2011",
CODEN = "????",
ISSN = "????",
bibdate = "Mon Nov 14 17:50:20 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B;
http://arxiv.org/abs/1111.0568",
abstract = "Many systems exhibit a digit bias. For example, the
first digit base 10 of the Fibonacci numbers, or of
$2^n$, equals 1 not 10\% or 11\% of the time, as one
would expect if all digits were equally likely, but
about 30\% of the time. This phenomenon, known as
Benford's Law, has many applications, ranging from
detecting tax fraud for the IRS to analyzing round-off
errors in computer science.\par
The central question is determining which data sets
follow Benford's law. Inspired by natural processes
such as particle decay, our work examines models for
the decomposition of conserved quantities. We prove
that in many instances the distribution of lengths of
the resulting pieces converges to Benford behavior as
the number of divisions grow. The main difficulty is
that the resulting random variables are dependent,
which we handle by a careful analysis of the
dependencies and tools from Fourier analysis to obtain
quantified convergence rates.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1111.0568",
keywords = "Mathematics - Probability, 11K06, 60A10 (primary),
60E10 (secondary)",
primaryclass = "math.PR",
}
@Article{Berger:2011:BLS,
author = "Arno Berger and Theodore P. Hill",
title = "{Benford}'s law strikes back: no simple explanation in
sight for mathematical gem",
journal = j-MATH-INTEL,
volume = "33",
number = "1",
pages = "85--91",
month = mar,
year = "2011",
CODEN = "MAINDC",
DOI = "http://dx.doi.org/10.1007/s00283-010-9182-3",
ISSN = "0343-6993",
ISSN-L = "0343-6993",
MRclass = "62A99 (60E05)",
MRnumber = "2774458",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematical Intelligencer",
}
@Article{Berger:2011:BTB,
author = "Arno Berger and Theodore P. Hill",
title = "A basic theory of {Benford's Law}",
journal = j-PROBAB-SURV,
volume = "8",
pages = "1--126",
year = "2011",
CODEN = "????",
DOI = "http://dx.doi.org/10.1214/11-PS175",
ISSN = "1549-5787",
bibdate = "Tue Nov 15 11:07:49 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://projecteuclid.org/euclid.ps/1311860830",
abstract = "Drawing from a large, diverse body of work, this
survey presents a comprehensive and unified
introduction to the mathematics underlying the
prevalent logarithmic distribution of significant
digits and significands, often referred to as {\em
Benford's Law\/} (BL) or, in a special case, as the
{\em First Digit Law}. The invariance properties that
characterize BL are developed in detail. Special
attention is given to the emergence of BL in a wide
variety of deterministic and random processes. Though
mainly expository in nature, the article also provides
strengthened versions of, and simplified proofs for,
many key results in the literature. Numerous intriguing
problems for future research arise naturally.",
acknowledgement = ack-nhfb,
fjournal = "Probabability Surveys",
keywords = "base-invariance; Benford's Law; difference equation;
mixture of distributions; random probability measure;
scale-invariance; shadowing; significant digits;
sum-invariance; uniform distribution mod 1",
}
@Article{Berger:2011:FSM,
author = "Arno Berger and Theodore P. Hill and Bahar Kaynar and
Ad Ridder",
title = "Finite-state {Markov} Chains Obey {Benford's Law}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "32",
number = "3",
pages = "665--684",
month = "????",
year = "2011",
CODEN = "SJMAEL",
DOI = "http://dx.doi.org/10.1137/100789890",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Aug 24 11:18:18 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
URL = "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
onlinedate = "July 21, 2011",
}
@Article{Berger:2011:SDP,
author = "Arno Berger",
title = "Some dynamical properties of {Benford} sequences",
journal = j-J-DIFFERENCE-EQU-APPL,
volume = "17",
number = "2",
pages = "137--159",
year = "2011",
CODEN = "????",
DOI = "http://dx.doi.org/10.1080/10236198.2010.549012",
ISSN = "1023-6198",
ISSN-L = "1023-6198",
MRclass = "37A45 (11K06 37Bxx)",
MRnumber = "2783341",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012",
acknowledgement = ack-nhfb,
ajournal = "J. Difference Equ. Appl.",
fjournal = "Journal of Difference Equations and Applications",
}
@Article{Bernhardsson:2011:PPM,
author = "Sebastian Bernhardsson and Seung Ki Baek and Petter
Minnhagen",
title = "A paradoxical property of the monkey book",
journal = j-J-STAT-MECH-THEORY-EXP,
volume = "2011",
number = "??",
pages = "P07013",
month = jul,
year = "2011",
CODEN = "JSMTC6",
DOI = "http://dx.doi.org/10.1088/1742-5468/2011/07/P07013",
ISSN = "1742-5468",
bibdate = "Mon Nov 21 21:57:13 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://iopscience.iop.org/1742-5468/2011/07/P07013/;
http://arxiv.org/abs/1103.2681",
abstract = "A `monkey book' is a book consisting of a random
sequence of letters and blanks, where a group of
letters surrounded by two blanks is defined as a word.
We compare the statistics of the word distribution for
a monkey book to real books. It is shown that the word
distribution statistics for the monkey book is
different and quite distinct from a typical real book.
In particular, the monkey book obeys Heaps' power law
to an extraordinarily good approximation, in contrast
to the word distributions for real books, which deviate
from Heaps' law in a characteristic way. This
discrepancy is traced to the different properties of a
`spiked' distribution and its smooth envelope. The
somewhat counter-intuitive conclusion is that a `monkey
book' obeys Heaps' power law precisely because its
word-frequency distribution is not a smooth power law,
contrary to the expectation based on simple
mathematical arguments that if one is a power law, so
is the other.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Mechanics: Theory and
Experiment",
keywords = "Heaps' Law",
}
@Article{Bhattacharya:2011:ABA,
author = "Sukanto Bhattacharya and Dongming Xu and Kuldeep
Kumar",
title = "An {ANN}-based auditor decision support system using
{Benford}'s law",
journal = j-DEC-SUPP-SYS,
volume = "50",
number = "3",
pages = "576--584",
month = feb,
year = "2011",
CODEN = "DSSYDK",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001351",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law",
}
@Article{Bose:2011:QMD,
author = "Indranil Bose and Selwyn Piramuthu and Michael J.
Shaw",
title = "Quantitative methods for Detection of Financial
Fraud",
journal = j-DEC-SUPP-SYS,
volume = "50",
number = "3",
pages = "557--558",
month = feb,
year = "2011",
CODEN = "DSSYDK",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001296",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law",
}
@Article{Breunig:2011:SEI,
author = "Christian Breunig and Achim Goerres",
title = "Searching for electoral irregularities in an
established democracy: Applying {Benford's Law} tests
to {Bundestag} elections in {Unified Germany}",
journal = j-ELECT-STUDIES,
volume = "30",
number = "3",
pages = "534--545",
month = sep,
year = "2011",
CODEN = "????",
DOI = "http://dx.doi.org/10.1016/j.electstud.2011.03.005",
ISSN = "0261-3794 (print), 1873-6890 (electronic)",
ISSN-L = "0261-3794",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0261379411000370",
acknowledgement = ack-nhfb,
fjournal = "Electoral Studies",
keywords = "Benford's Law",
}
@Article{Campanario:2011:BLC,
author = "Juan Campanario and Mar{\'\i}a Coslado",
title = "{Benford}'s law and citations, articles and impact
factors of scientific journals",
journal = j-SCIENTOMETRICS,
volume = "88",
number = "2",
pages = "421--432",
month = aug,
year = "2011",
CODEN = "SCNTDX",
DOI = "http://dx.doi.org/10.1007/s11192-011-0387-9",
ISSN = "0138-9130 (print), 1588-2861 (electronic)",
ISSN-L = "0138-9130",
bibdate = "Fri Nov 25 10:43:36 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientometrics",
}
@Article{Chang:2011:CGR,
author = "Harry M. Chang",
title = "Constructing $n$-gram rules for natural language
models through exploring the limitation of the
{Zipf--Mandelbrot} law",
journal = j-COMPUTING,
volume = "91",
number = "3",
pages = "241--264",
month = mar,
year = "2011",
CODEN = "CMPTA2",
DOI = "http://dx.doi.org/10.1007/s00607-010-0116-x",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68T50",
MRnumber = "2776088",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
acknowledgement = ack-nhfb,
fjournal = "Computing. Archives for Scientific Computing",
}
@Article{Doyle:2011:ITA,
author = "Laurance R. Doyle and Brenda McCowan and Simon
Johnston and Sean F. Hanser",
title = "Information theory, animal communication, and the
search for extraterrestrial intelligence",
journal = "Acta Astronautica",
volume = "68",
number = "3--4",
pages = "406--417",
month = feb # "\slash " # mar,
year = "2011",
CODEN = "????",
ISSN = "????",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0094576509005682",
acknowledgement = ack-nhfb,
fjournal = "Acta Astronautica",
keywords = "Benford's Law; Zipf's Law",
}
@Article{Eliazar:2011:LLZ,
author = "Iddo Eliazar",
title = "Limit laws for {Zipf}'s law",
journal = j-J-PHYS-A,
volume = "44",
number = "2",
pages = "022001",
year = "2011",
CODEN = "JPHAC5",
DOI = "http://dx.doi.org/10.1088/1751-8113/44/2/022001",
ISSN = "1751-8113",
ISSN-L = "0305-4470",
MRclass = "62G30 (91D20)",
MRnumber = "2749082 (2011i:62083)",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics. A. Mathematical and Theoretical",
pagecount = "6",
ZMnumber = "Zbl 1204.62196",
}
@Misc{Farbaniec:2011:AFD,
author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
title = "Application of the first digit law in credibility
evaluation of the financial accounting data based on
particular cases",
howpublished = "Lecture slides for 10th International Congress on
Internal Control, Internal Audit, Fraud and
Anti-Corruption Issues, Krak{\'o}w, September 14--16,
2011.",
pages = "27",
year = "2011",
bibdate = "Thu Dec 01 21:27:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://benford.pl/documents/benford_pikw.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Farbaniec:2011:UBL,
author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
editor = "????",
booktitle = "10th International Congress on Internal Control,
Internal Audit, Fraud and Anti-Corruption Issues,
Krak{\'o}w, September 14--16, 2011",
title = "Using {Benford}'s law to detect irregularities in the
collection of data",
publisher = "????",
address = "????",
pages = "??--??",
year = "2011",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Dec 01 21:32:03 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}
@Article{Garcia:2011:FPA,
author = "Juan Manuel Garcia Garcia",
title = "A fixed-point algorithm to estimate the {Yule-Simon}
distribution parameter",
journal = j-APPL-MATH-COMP,
volume = "217",
number = "21",
pages = "8560--8566",
day = "1",
month = jul,
year = "2011",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 25 12:05:30 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/science/journal/00963003",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300311004607",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
}
@Article{Hui:2011:BLN,
author = "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min",
title = "{Benford's Law} in Nuclear Structure Physics",
journal = j-CHIN-PHYS-LETT,
volume = "28",
number = "3",
pages = "32101--32104",
month = mar,
year = "2011",
CODEN = "CPLEEU",
DOI = "http://dx.doi.org/10.1088/0256-307X/28/3/032101",
ISSN = "0256-307X (print), 1741-3540 (electronic)",
ISSN-L = "0256-307X",
bibdate = "Fri Nov 25 10:37:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Chinese Physics Letters",
}
@Article{Janvresse:2011:AAU,
author = "{\'E}lise Janvresse and Thierry {De La Rue}",
title = "Averaging along Uniform Random Integers",
journal = "ArXiv e-prints",
year = "2011",
bibdate = "Mon Nov 21 07:06:41 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1103.1719",
abstract = "Motivated by giving a meaning to ``The probability
that a random integer has initial digit d'', we define
a URI-set as a random set E of natural integers such
that each n>0 belongs to E with probability 1/n,
independently of other integers. This enables us to
introduce two notions of densities on natural numbers:
The URI-density, obtained by averaging along the
elements of $E$, and the local URI-density, which we
get by considering the $k$-th element of $E$ and
letting $k$ go to infinity. We prove that the elements
of $E$ satisfy Benford's law, both in the sense of
URI-density and in the sense of local URI-density.
Moreover, if $b_1$ and $b_2$ are two multiplicatively
independent integers, then the mantissae of a natural
number in base $b_1$ and in base $b_2$ are independent.
Connections of URI-density and local URI-density with
other well-known notions of densities are established:
Both are stronger than the natural density, and
URI-density is equivalent to log-density. We also give
a stochastic interpretation, in terms of URI-set, of
the $H_\infty$-density.",
acknowledgement = ack-nhfb,
}
@Article{Jiang:2011:BLN,
author = "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao",
title = "{Benford}'s law in nuclear structure physics",
journal = j-CHIN-PHYS-LETT,
volume = "28",
number = "3",
pages = "032101",
month = "????",
year = "2011",
CODEN = "CPLEEU",
DOI = "http://dx.doi.org/10.1088/0256-307X/28/3/032101",
ISSN = "0256-307X (print), 1741-3540 (electronic)",
ISSN-L = "0256-307X",
bibdate = "Mon Nov 14 16:16:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
ajournal = "Chin. Phys. Lett.",
fjournal = "Chinese Physics Letters",
pagecount = "4",
}
@Article{Kim:2011:ZAS,
author = "SeongKi Kim and HaYoon Song and SangYong Han",
title = "{ZipfAllocation}: an algorithm for static allocation
of movies in a cluster of video servers",
journal = j-SPE,
volume = "41",
number = "6",
pages = "695--716",
month = may,
year = "2011",
CODEN = "SPEXBL",
DOI = "http://dx.doi.org/10.1002/spe.1027",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Tue Jun 21 17:09:57 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Soft{\-}ware\emdash Prac{\-}tice and Experience",
onlinedate = "25 Nov 2010",
}
@Misc{Li:2011:ZLB,
author = "Wentian Li",
title = "{Zipf's Law} bibliography",
howpublished = "Web site.",
month = aug,
year = "2011",
bibdate = "Fri Nov 25 08:58:21 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "The site holds 870 references (in untagged
reference-list form) up to 11 August 2011.",
URL = "http://www.nslij-genetics.org/wli/zipf/",
acknowledgement = ack-nhfb,
lastaccess = "25 November 2011",
}
@Article{Liu:2011:BLC,
author = "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren",
title = "{Benford}'s law and cross-sections of {$A(n, \alpha)
B$} reactions",
journal = j-EUR-PHYS-J-A,
volume = "47",
pages = "78",
month = jun,
year = "2011",
CODEN = "EPJAFV",
DOI = "http://dx.doi.org/10.1140/epja/i2011-11078-3",
ISSN = "1434-6001 (print), 1434-601X (electronic)",
ISSN-L = "1434-6001",
bibdate = "Mon Nov 14 18:00:32 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011EPJA...47...78L",
acknowledgement = ack-nhfb,
fjournal = "European Physical Journal A: Hadrons and Nuclei",
}
@InProceedings{Lyons:2011:NSF,
author = "M. Lyons and E. Carl-Ludwig Siegel",
booktitle = "APS March Meeting Abstracts",
title = "{NON-Shor} Factorization via {BEQS BEC}: {Watkins}
Number-Theory ``Pure''-Mathematics $\cup$ with
Statistical-Physics: {Benford} Log-Law Inversion to
{ONLY} {BEQS} digit $d = 0$ {BEC}!!!",
publisher = "American Physical Society",
address = "????",
pages = "K1142",
month = mar,
year = "2011",
bibdate = "Mon Nov 14 18:08:39 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L",
acknowledgement = ack-nhfb,
}
@Book{McGrayne:2011:TWH,
author = "Sharon Bertsch McGrayne",
title = "The theory that would not die: how {Bayes}' rule
cracked the {Enigma} code, hunted down {Russian}
submarines, and emerged triumphant from two centuries
of controversy",
publisher = pub-YALE,
address = pub-YALE:adr,
pages = "xiii + 320",
year = "2011",
ISBN = "0-300-16969-8",
ISBN-13 = "978-0-300-16969-0",
LCCN = "QA279.5 .M415 2011",
bibdate = "Wed May 11 14:42:54 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
abstract = "Bayes' rule appears to be a straightforward, one-line
theorem: by updating our initial beliefs with objective
new information, we get a new and improved belief. To
its adherents, it is an elegant statement about
learning from experience. To its opponents, it is
subjectivity run amok. In the first-ever account of
Bayes' rule for general readers, Sharon Bertsch
McGrayne explores this controversial theorem and the
human obsessions surrounding it. She traces its
discovery by an amateur mathematician in the 1740s
through its development into roughly its modern form by
French scientist Pierre Simon Laplace. She reveals why
respected statisticians rendered it professionally
taboo for 150 years --- at the same time that
practitioners relied on it to solve crises involving
great uncertainty and scanty information, even breaking
Germany's Enigma code during World War II, and explains
how the advent of off-the-shelf computer technology in
the 1980s proved to be a game-changer. Today, Bayes'
rule is used everywhere from DNA de-coding to Homeland
Security. Drawing on primary source material and
interviews with statisticians and other scientists, The
Theory That Would Not Die is the riveting account of
how a seemingly simple theorem ignited one of the
greatest controversies of all time.",
acknowledgement = ack-nhfb,
remark = "This book has important comments on the battles among
Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
Pearson, supplementing the extensive discussion of
those conflicts in \cite{Ziliak:2008:CSS}.",
subject = "Bayesian statistical decision theory; history; science
/ history; mathematics / history and philosophy",
}
@Article{Mebane:2011:CBL,
author = "Walter R. Mebane",
title = "Comment on {Benford's Law} and the Detection of
Election Fraud",
journal = "Political Analysis",
volume = "19",
number = "3",
pages = "269--272",
day = "18",
month = jul,
year = "2011",
CODEN = "????",
DOI = "http://dx.doi.org/10.1093/pan/mpr024",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
bibdate = "Fri Nov 25 11:00:46 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See \cite{Myagkov:2011:BLD}.",
acknowledgement = ack-nhfb,
}
@Article{Michel:2011:QAC,
author = "Jean-Baptiste Michel and Yuan Kui Shen and Aviva
Presser Aiden and Adrian Veres and Matthew K. Gray and
{The Google Books Team} and Joseph P. Pickett and Dale
Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant
and Steven Pinker and Martin A. Nowak and Erez
Lieberman Aiden",
title = "Quantitative Analysis of Culture Using Millions of
Digitized Books",
journal = j-SCIENCE,
volume = "331",
number = "6014",
pages = "176--182",
day = "14",
month = jan,
year = "2011",
CODEN = "SCIEAS",
DOI = "http://dx.doi.org/10.1126/science.1199644",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Fri Dec 09 11:06:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.sciencemag.org/content/331/6014/176.abstract",
acknowledgement = ack-nhfb,
fjournal = "Science",
keywords = "Zipf's law",
remark = "This papers reports results from a large study of
cultural phenomena, fame, and word usage from 4\% of
all books ever printed. Among the findings is this
quote from the first page: ``we estimated the number of
words in the English lexicon as 544,000 in 1900,
597,000 in 1950, and 1,022,000 in 2000. The lexicon is
enjoying a period of enormous growth: The addition of
$\approx 8500$ words/year has increased the size of the
language by over 70\% during the past 50 years.'' From
page 177: ``Consistent with Zipf's famous law, a large
fraction of the words in our lexicon (63\%) were in
this lowest-frequency bin. As a result, we estimated
that 52\% of the English lexicon --- the majority of
the words used in English books --- consists of lexical
`dark matter' undocumented in standard references
(12).''",
}
@Article{Mir:2011:LLD,
author = "Tariq Ahmad Mir",
title = "Law of the leading digits and the ideological struggle
for numbers",
journal = "ArXiv e-prints",
pages = "11",
year = "2011",
bibdate = "Mon Nov 21 07:02:48 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1104.3948",
abstract = "Benford's law states that the occurrence of
significant digits in many data sets is not uniform but
tends to follow a logarithmic distribution such that
the smaller digits appear as first significant digits
more frequently than the larger ones. We investigate
here numerical data on the country-wise adherent
distribution of seven major world religions i.e.,
Christianity, Islam, Buddhism, Hinduism, Sikhism,
Judaism and Baha'ism to see if the proportion of the
leading digits occurring in the distribution conforms
to Benford's law. We find that the adherent data of all
the religions, except Christianity, excellently does
conform to Benford's law. Furthermore, unlike the
adherent data on Christianity, the significant digit
distribution of the three major Christian denominations
i.e. Catholicism, Protestantism and Orthodoxy obeys the
law. Thus in spite of their complexity general laws can
be established for the evolution of the religious
groups.",
acknowledgement = ack-nhfb,
}
@Article{Muller:2011:HAS,
author = "Hans Christian M{\"u}ller",
title = "How an arcane statistical law could have prevented the
{Greek} disaster",
journal = "Economics Intelligence",
volume = "??",
number = "??",
pages = "??",
day = "28",
month = jul,
year = "2011",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Nov 20 10:04:08 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/",
abstract = "If we had known what we know today, Greece would not
have been able to enter the Euro area. The
macroeconomic data the country reported to Eurostat in
Luxembourg were heavily tweaked. Unfortunately,
however, this only became clear years after it was too
late.",
acknowledgement = ack-nhfb,
}
@Article{Myagkov:2011:BLD,
author = "Mikhail Myagkov and Peter C. Ordeshook",
title = "{Benford's Law} and the Detection of Election Fraud",
journal = "Political Analysis",
volume = "19",
number = "3",
pages = "245--268",
month = jul,
year = "2011",
CODEN = "????",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
bibdate = "Fri Nov 25 10:57:31 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "See comment in \cite{Mebane:2011:CBL}.",
acknowledgement = ack-nhfb,
}
@Article{Rauch:2011:FFE,
author = "Bernhard Rauch and Max G{\"o}ttsche and Gernot
Br{\"a}hler and Stefan Engel",
title = "Fact and Fiction in {EU}-Governmental Economic Data",
journal = j-GER-ECON-REV,
volume = "12",
number = "3",
pages = "243--255",
month = aug,
year = "2011",
DOI = "http://dx.doi.org/10.1111/j.1468-0475.2011.00542.x",
ISSN = "1465-6485 (print), 1468-0475 (electronic)",
ISSN-L = "1465-6485",
bibdate = "Sun Nov 20 09:58:25 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract",
abstract = "To detect manipulations or fraud in accounting data,
auditors have successfully used Benford's law as part
of their fraud detection processes. Benford's law
proposes a distribution for first digits of numbers in
naturally occurring data. Government accounting and
statistics are similar in nature to financial
accounting. In the European Union (EU), there is
pressure to comply with the Stability and Growth Pact
criteria. Therefore, like firms, governments might try
to make their economic situation seem better. In this
paper, we use a Benford test to investigate the quality
of macroeconomic data relevant to the deficit criteria
reported to Eurostat by the EU member states. We find
that the data reported by Greece shows the greatest
deviation from Benford's law among all euro states.",
acknowledgement = ack-nhfb,
fjournal = "German Economic Review",
keywords = "Benford's law; government statistics; fraud detection;
auditing",
onlinedate = "28 April 2011",
}
@Article{Ravisankar:2011:DFS,
author = "P. Ravisankar and V. Ravi and G. Raghava Rao and I.
Bose",
title = "Detection of financial statement fraud and feature
selection using data mining techniques",
journal = j-DEC-SUPP-SYS,
volume = "50",
number = "2",
pages = "491--500",
month = jan,
year = "2011",
CODEN = "DSSYDK",
ISSN = "0167-9236 (print), 1873-5797 (electronic)",
ISSN-L = "0167-9236",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001879",
acknowledgement = ack-nhfb,
fjournal = "Decision Support Systems",
keywords = "Benford's Law",
}
@Article{Romano:2011:NLR,
author = "Paul K. Romano and Harry McLaughlin",
title = "On Non-Linear Recursive Sequences and {Benford's
Law}",
journal = j-FIB-QUART,
volume = "49",
number = "2",
pages = "134--138",
month = may,
year = "2011",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
MRclass = "11K31 (11B37)",
MRnumber = "2801800",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.fq.math.ca/49-2.html;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
URL = "http://www.fq.math.ca/Abstracts/49-2/romano.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
}
@Article{Ross:2011:BLG,
author = "Kenneth A. Ross",
title = "{Benford's Law}, a Growth Industry",
journal = j-AMER-MATH-MONTHLY,
volume = "118",
number = "7",
pages = "571--583",
month = aug # "\slash " # sep,
year = "2011",
CODEN = "AMMYAE",
DOI = "http://dx.doi.org/10.4169/amer.math.monthly.118.07.571",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jan 30 08:58:20 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.118.issue-7;
http://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.jstor.org/stable/10.4169;
http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.07.571.pdf;
http://www.maa.org/history/presidents/ross.html",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
remark = "The author was President of the Mathematical
Association of America (1995--1996).",
}
@Article{SenDe:2011:BLD,
author = "Aditi {Sen De} and Ujjwal Sen",
title = "{Benford}'s law detects quantum phase transitions
similarly as earthquakes",
journal = j-EUROPHYS-LETT,
volume = "95",
number = "5",
pages = "50008",
month = sep,
year = "2011",
CODEN = "EULEEJ",
DOI = "http://dx.doi.org/10.1209/0295-5075/95/50008",
ISSN = "0295-5075 (print), 1286-4854 (electronic)",
ISSN-L = "0295-5075",
bibdate = "Mon Nov 14 17:52:09 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://arxiv.org/abs/1103.5398",
abstract = "A century ago, it was predicted that the first
significant digit appearing in a data would be
nonuniformly distributed, with the number one appearing
with the highest frequency. This law goes by the name
of Benford's law. It holds for data ranging from
infectious disease cases to national greenhouse gas
emissions. Quantum phase transitions are cooperative
phenomena where qualitative changes occur in many-body
systems at zero temperature. We show that the
century-old Benford's law can detect quantum phase
transitions, much like it detects earthquakes.
Therefore, being certainly of very different physical
origins, seismic activity and quantum cooperative
phenomena may be detected by similar methods. The
result has immediate implications in precise
measurements in experiments in general, and for
realizable quantum computers in particular. It shows
that estimation of the first significant digit of
measured physical observables is enough to detect the
presence of quantum phase transitions in macroscopic
systems.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1103.5398",
fjournal = "Europhysics Letters",
primaryclass = "quant-ph",
}
@Article{Tang:2011:ESP,
author = "Lian Tang and Da Hui Wang",
title = "An explanation of the shift parameter {$\rho$} in the
{Zipf--Mandelbrot} law",
journal = "Beijing Shifan Daxue Xuebao",
volume = "47",
number = "1",
pages = "97--100",
year = "2011",
CODEN = "BSDKDH",
ISSN = "0476-0301",
MRclass = "94A17",
MRnumber = "2807603",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
fjournal = "Beijing Shifan Daxue Xuebao. Ziran Kexue Ban. Journal
of Beijing Normal University (Natural Science)",
}
@Article{Vallee:2011:BMF,
author = "Robert Vall{\'e}e",
title = "{Beno{\^\i}t Mandelbrot} --- further notes",
journal = "Kybernetes",
volume = "40",
number = "9--10",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "KBNTA3",
ISSN = "0368-492X (print), 1758-7883 (electronic)",
bibdate = "Fri Nov 25 07:38:10 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=9/10&articleid=17003220",
acknowledgement = ack-nhfb,
}
@Misc{Weisstein:2011:BL,
author = "Eric W. Weisstein",
title = "{Benford's Law}",
howpublished = "MathWorld---A Wolfram Web Resource",
year = "2011",
bibdate = "Tue Nov 15 08:40:40 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
URL = "http://mathworld.wolfram.com/BenfordsLaw.html",
acknowledgement = ack-nhfb,
}
@Article{Mir:2012:LLD,
author = "Tariq Ahmad Mir",
title = "The law of the leading digits and the world
religions",
journal = j-PHYSICA-A,
volume = "391",
number = "3",
pages = "792--798",
day = "1",
month = feb,
year = "2012",
CODEN = "PHYADX",
DOI = "http://dx.doi.org/10.1016/j.physa.2011.09.001",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Mon Nov 21 07:04:12 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.sciencedirect.com/",
URL = "http://www.sciencedirect.com/science/article/pii/S0378437111007175",
acknowledgement = ack-nhfb,
fjournal = "Physica A: Statistical Mechanics and its
Applications",
}
@Article{Ross:2012:FDS,
author = "Kenneth A. Ross",
title = "First digits of squares and cubes",
journal = j-MATH-MAG,
volume = "??",
number = "??",
pages = "??--??",
month = "????",
year = "2012",
CODEN = "MAMGA8",
ISSN = "0025-570X",
bibdate = "Fri Nov 25 14:11:28 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
note = "To appear (cited in \cite{Ross:2011:BLG}).",
URL = "http://www.maa.org/history/presidents/ross.html",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
keywords = "Benford's Law",
remark = "The author was President of the Mathematical
Association of America (1995--1996).",
}
%%% ====================================================================
%%% Cross-referenced entries must come last:
@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;
http://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib
http://www.math.utah.edu/pub/tex/bib/fparith.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",
}
@Proceedings{Apers:1989:VLD,
editor = "P. M. G. (Petrus Maria Gerardus) Apers and Gio
Wiederhold",
booktitle = "Very large data bases: proceedings: proceedings of the
Fifteenth International Conference on Very Large Data
Bases, August 22--25, 1989, Amsterdam, The
Netherlands",
title = "Very large data bases: proceedings: proceedings of the
Fifteenth International Conference on Very Large Data
Bases, August 22--25, 1989, Amsterdam, The
Netherlands",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xii + 467",
year = "1989",
ISBN = "1-55860-101-5",
ISBN-13 = "978-1-55860-101-7",
LCCN = "QA 76.9 D3 I61 1989",
bibdate = "Sat Dec 7 13:05:35 MST 1996",
bibsource = "DBLP; http://dblp.uni-trier.de;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
keywords = "database management -- congresses",
}
@Book{Warren:2003:HD,
author = "Henry S. Warren",
booktitle = "Hacker's delight",
title = "Hacker's delight",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xiv + 306",
year = "2003",
ISBN = "0-201-91465-4",
ISBN-13 = "978-0-201-91465-8",
LCCN = "QA76.6 .W375 2003",
bibdate = "Tue Jan 03 18:20:34 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
note = "While this book does not specifically address
computational aspects of floating-point arithmetic
(apart from the nine-page Chapter 15), it has extensive
coverage of, and clever algorithms for, integer
arithmetic operations that are fundamental for
implementing hardware floating-arithmetic and software
multiple-precision arithmetic.",
URL = "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654;
http://www.hackersdelight.org/;
http://www.hackersdelight.org/hackerTOC.pdf;
http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf",
acknowledgement = ack-nhfb,
keywords = "DEC PDP-10; division by constants; Gray code; Hilbert
curves; IEEE 754 floating-point arithmetic; integer
cube root; integer division; integer exponentiation;
integer logarithm; integer square root; prime numbers;
unusual number bases",
remark = "Foreword by Guy L. Steele, Jr., who begins ``When I
first got a summer job at MIT's Project MAC almost 30
years ago, I was delighted to be able to work with the
DEC PDP-10 computer, which was more fun to program in
assembly language than any other computer, bar none,
because of its rich yet tractable set of instructions
for performing bit tests, bit masking, field
manipulation, and operations on integers. Though the
PDP-10 has not been manufactured for quite some years,
there remains a thriving cult of enthusiasts who keep
old PDP-10 hardware running and who run old PDP-10
software---entire operating systems and their
applications---by using personal computers to simulate
the PDP-10 instruction set.''",
subject = "Computer programming; Computer hackers",
tableofcontents = "Preface\par
1. Introduction\par
Notation\par
Instruction Set and Execution Time Model\par
2. Basis\par
Manipulating Rightmost Bits \\
Addition Combined with Logical Operations \\
Inequalities among Logical and Arithmetic Expressions
\\
Absolute Value Function \\
Sign Extension \\
Shift Right Signed from Unsigned \\
Sign Function \\
Three-Valued Compare \\
Transfer of Sign \\
Decoding a ?Zero Means 2**n? Field \\
Comparison Predicates \\
Overflow Detection \\
Condition Code Result of Add, Subtract, and Multiply
\\
Rotate Shifts \\
Double-Length Add/Subtract \\
Double-Length Shifts \\
Multibyte Add, Subtract, Absolute Value \\
Doz, Max, Min \\
Exchanging Registers \\
Alternating among Two or More Values\par
3. Power-of-2 Boundaries\par
Rounding Up/Down to a Multiple of a Known Power of 2
\\
Rounding Up/Down to the Next Power of 2 \\
Detecting a Power-of-2 Boundary Crossing\par
4. Arithmetic Bounds\par
Checking Bounds of Integers \\
Propagating Bounds through Adds and Subtracts \\
Propagating Bounds through Logical Operations \\
Signed Bounds\par
5. Counting Bits\par
Counting 1-bits \\
Parity \\
Counting Leading 0's \\
Counting Trailing 0's\par
6. Searching Words\par
Find First 0-Byte \\
Find First String of 1-Bits of a Given Length\par
7. Rearranging Bits and Bytes\par
Reversing Bits and Bytes \\
Shuffling Bits \\
Transposing a Bit Matrix \\
Compress, or Generalized Extract \\
General Permutations, Sheep and Goats Operation \\
Rearrangements and Index Transformations\par
8. Multiplication\par
Multiword Multiplication \\
High-Order Half of 64-Bit Product \\
High-Order Product Signed from/to Unsigned \\
Multiplication by Constants\par
9. Integer Division\par
Preliminaries \\
Multiword Division \\
Unsigned Short Division from Signed Division \\
Unsigned Long Division\par
10. Integer Division by Constants\par
Signed Division by a Known Power of 2 \\
Signed Remainder from Division by a Known Power of 2
\\
Signed Division and Remainder by Non-powers of 2 \\
Signed Division by Divisors >= 2 \\
Signed Division by Divisors #= -2 \\
Incorporation into a Compiler \\
Miscellaneous Topics \\
Unsigned Division \\
Unsigned Division by Divisors >= 1 \\
Incorporation into a Compiler (Unsigned) \\
Miscellaneous Topics (Unsigned) \\
Applicability to Modulus and Floor Division \\
Similar Methods \\
Sample Magic Numbers \\
Exact Division by Constants \\
Test for Zero Remainder after Division by a
Constant\par
11. Some Elementary Functions\par
Integer Square Root \\
Integer Cube Root \\
Integer Exponentiation \\
Integer Logarithm\par
12. Unusual Bases for Number Systems\par
Base -2 \\
Base -1 + i \\
Other Bases \\
What is the Most Efficient Base?\par
13. Gray Code \\
Gray Code \\
Incrementing a Gray Coded Integer \\
Negabinary Gray Code \\
Brief History and Applications\par
14. Hilbert's Curve\par
A Recursive Algorithm for Generating the Hilbert Curve
\\
Coordinates from Distance along the Hilbert Curve \\
Distance from Coordinates on the Hilbert Curve \\
Incrementing the Coordinates on the Hilbert Curve \\
Non-recursive Generating Algorithms \\
Other Space-Filling Curves \\
Applications\par
15. Floating-Point\par
IEEE Format \\
Comparing Floating-Point Numbers Using Integer
Operations \\
The Distribution of Leading Digits \\
Table of Miscellaneous Values\par
16. Formulas for Primes\par
Introduction \\
Willans's Formulas \\
Wormell's Formula \\
Formulas for Other Difficult Functions\par
Appendix A. Arithmetic Tables for a 4-Bit
Machine\par
Appendix B. Newton's Method\par
Bibliography.",
}
@Proceedings{Gama:2005:MLE,
editor = "Jo{\~a}ao Gama and Rui Camacho and Pavel Brazdil and
Al{\'\i}pio M{\'a}rio Jorge and Lu{\'\i}s Torgo",
booktitle = "{Machine learning --- ECML 2005: 16th European
Conference on Machine Learning, Porto, Portugal,
October 3--7, 2005: proceedings}",
title = "{Machine learning --- ECML 2005: 16th European
Conference on Machine Learning, Porto, Portugal,
October 3--7, 2005: proceedings}",
volume = "3720",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiii + 769",
year = "2005",
ISBN = "3-540-29243-8",
ISBN-13 = "978-3-540-29243-2",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "Q325.5 .E26 2005",
bibdate = "Tue Nov 15 08:57:03 MST 2011",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS # " and " # ser-LNAI,
URL = "http://www.loc.gov/catdir/enhancements/fy0663/2005933045-d.html;
http://www.springerlink.com/openurl.asp?genre=issue\%26issn=0302-9743\%26volume=3720",
acknowledgement = ack-nhfb,
meetingname = "ECML 2005 (2005: Porto, Portugal)",
subject = "Machine learning; Congresses",
}
@Proceedings{Neumann:2005:CAE,
editor = "L{\'a}szl{\'o} Neumann and Mateu Sbert and Bruce Gooch
and Werner Purgathofer",
booktitle = "{Computational aesthetics 2005: Eurographics Workshop
on Computational Aesthetics in Graphics, Visualization
and Imaging, Girona, Spain, 18--20 May 2005}",
title = "{Computational aesthetics 2005: Eurographics Workshop
on Computational Aesthetics in Graphics, Visualization
and Imaging, Girona, Spain, 18--20 May 2005}",
publisher = "Eurographics Association",
address = "Aire-la-Ville, Switzerland",
pages = "245",
year = "2005",
ISBN = "3-905673-27-4",
ISBN-13 = "978-3-905673-27-2",
ISSN = "1816-0859",
bibdate = "Tue Nov 15 06:34:24 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
series = "Computational aesthetics",
acknowledgement = ack-nhfb,
}
@Proceedings{Paredaens:2009:PTE,
editor = "Jan Paredaens and Jianwen Su",
booktitle = "{Proceedings of the twenty-eighth ACM
SIGMOD-SIGACT-SIGART symposium on Principles of
database systems: PODS'09, Providence, Rhode Island,
June 29--July 1, 2009}",
title = "{Proceedings of the twenty-eighth ACM
SIGMOD-SIGACT-SIGART symposium on Principles of
database systems, PODS'09, Providence, Rhode Island,
June 29--July 1, 2009}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 288",
year = "2009",
ISBN = "1-60558-553-X",
ISBN-13 = "978-1-60558-553-6",
LCCN = "????",
bibdate = "Thu Jul 02 12:41:14 2009",
bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
acknowledgement = ack-nhfb,
}