%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.72", %%% date = "18 October 2014", %%% time = "14:59:26 MDT", %%% filename = "benfords-law.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "45228 26797 113282 1137798", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Benford's Law; %%% Bradford's Law; First Digit Phenomenon; %%% Gibrat's Law; Gibrat's Rule of Proportionate %%% Growth; Heaps' Law; Herdan's Law; Law of %%% Anomalous Numbers; Lotka's Law; Pareto %%% Distribution; Pareto Law; Pareto Principle; %%% power law; Significant Digit Law; Simon--Yule %%% model of text generation; Stigler's Law; Yule %%% process; Zipf's Law", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography about a numerical %%% curiousity variously known as Benford's Law %%% (see particularly entries Newcomb:1881:NFU, %%% Benford:1938:LAN, Pinkham:1961:DFS, %%% Logan:1978:FDP, Hill:1998:FDP, and %%% Block:2010:GEB, Nigrini:2012:BLA), the Law of %%% Anomalous Numbers, and the Significant Digit %%% Law: in a table of physical constants (and in %%% many other collections of measured numbers), %%% the leading digits do not have equal %%% probability of occurrence: the digit 1 is %%% more common than 2, which is more common than %%% 3, and so on. %%% %%% Publications recorded here appear in about %%% 385 different journals from accounting, %%% aerobiology, animal behavior, auditing, %%% astronomy, bible studies, biology, %%% biometrics, botany, business, chaos theory, %%% chemistry, colloid science, complexity, %%% computer science, conflict resolution, %%% cognitive science, criminology, critical %%% phenomena, demographics, drug design, %%% dynamics, earthquake detection, economics, %%% electoral studies, engineering, entropy, %%% expert systems, extinction, finance, %%% forensics, gambling, geography, geophysics, %%% human resources, hydrology, imaging science, %%% informetrics, language science, library %%% science, linguistics, marine systems, %%% marketing, mathematics, medicine, networking, %%% neuroscience, nuclear engineering, nuclear %%% science, operations research, physics, %%% political analysis, probability, psychology, %%% signal processing, simulation, sociology, %%% statistical mechanics, statistics, %%% stock-market trading, tax accounting, urban %%% development, and urban growth, reflecting the %%% broad interest in the unexpected phenomenon %%% discovered and reported first by the %%% Canadian/American astronomer and %%% mathematician, Simon Newcomb, in a two-page %%% note in 1881, and then independently, and %%% with numerical evidence from much more %%% measured data, by American physicist Frank %%% Benford in 1938. %%% %%% In Benford's Law, the frequency of leading %%% decimal digit p is roughly log10(1 + (1 / %%% p)): that is, approximately 0.301, 0.176, %%% 0.125, 0.097, 0.079, 0.067, 0.058, 0.051, and %%% 0.046 for digits 1 through 9, instead of the %%% expected 1/9 ~= 0.111 for values taken from a %%% uniform distribution of random numbers. %%% %%% Another common statement of Benford's Law is %%% that the probability that a decimal number %%% representing a measured value begins with a %%% nonzero digit not greater than p is log10(1 + %%% p), that is, approximately 0.301, 0.477, %%% 0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and %%% 1.000 for digits 1 through 9. %%% %%% For the second digits, the probabilities are %%% determined by the formula (see %%% Todter:2009:BLI) %%% %%% sum(q = 1:9) log10(1 + 1 / (10*q + p)), %%% %%% that is, approximately 0.120, 0.114, 0.109, %%% 0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and %%% 0.085, for second decimal digits p = 0 %%% through 9. %%% %%% Probabilities for later digits are even %%% closer: see entries Newcomb:1881:NFU, %%% Feldstein:1976:CED, and Todter:2009:BLI. %%% %%% Benford's Law is not restricted to decimal %%% numbers: for base b (as long as b is not %%% huge, according to entry Schatte:1998:BLV), %%% just change the 10 values to b in the %%% previous formulas. Here are some results for %%% selected bases commonly used in computers, %%% showing the probability of the first (D1) or %%% second (D2) digit (first index) for base b %%% (second index): %%% %%% P[D1, 2]: 1.000 %%% P[D2, 2]: 0.585, 0.415 %%% %%% P[D1, 4]: 0.500, 0.292, 0.208 %%% P[D2, 4]: 0.304, 0.261, 0.230, 0.206 %%% %%% P[D1, 8]: 0.333, 0.195, 0.138, 0.107, %%% 0.088, 0.074, 0.064 %%% P[D2, 8]: 0.151, 0.141, 0.133, 0.126, 0.120, %%% 0.115, 0.110, 0.105 %%% %%% P[D1, 10]: 0.301, 0.176, 0.125, 0.097, %%% 0.079, 0.067, 0.058, 0.051, 0.046 %%% P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100, %%% 0.097, 0.093, 0.090, 0.088, 0.085 %%% %%% P[D1, 16]: 0.250, 0.146, 0.104, 0.080, %%% 0.066, 0.056, 0.048, 0.042, 0.038, %%% 0.034, 0.031, 0.029, 0.027, 0.025, %%% 0.023 %%% P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066, %%% 0.065, 0.064, 0.062, 0.061, 0.060, %%% 0.059, 0.058, 0.057, 0.056, 0.055, %%% 0.054 %%% %%% A small filter applied to the 1990 US Census %%% data in the Project Gutenberg file %%% uscen902.txt reports these frequencies of %%% first and second digits for the 5148 integer %%% values with at least 3 digits: %%% %%% F[D1]: 0.298, 0.215, 0.113, 0.082, %%% 0.098, 0.056, 0.055, 0.034, 0.049 %%% F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100, %%% 0.122, 0.076, 0.073, 0.066, 0.130 %%% %%% For the 110 numbers in the atomic weights %%% section of the GNU units utility data file, %%% units.dat, we have %%% %%% F[D1]: 0.391, 0.309, 0.045, 0.036, %%% 0.055, 0.036, 0.036, 0.036, 0.055 %%% F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145, %%% 0.145, 0.055, 0.055, 0.091, 0.082 %%% %%% From a snapshot of the country-area section %%% of the US CIA World Factbook %%% %%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html %%% %%% taken at 18 November 2011, we find 1505 %%% numbers with these frequencies: %%% %%% F[D1]: 0.312, 0.275, 0.100, 0.067, %%% 0.058, 0.062, 0.046, 0.029, 0.050 %%% F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062, %%% 0.067, 0.075, 0.067, 0.083, 0.075 %%% %%% From the country-population section %%% %%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html %%% %%% of that book, including only the 163 values %%% of 1,000,000 or larger, we find %%% %%% F[D1]: 0.301, 0.202, 0.092, 0.135, %%% 0.055, 0.067, 0.055, 0.037, 0.055 %%% F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098, %%% 0.123, 0.086, 0.043, 0.049, 0.092 %%% %%% From the section with the infant mortality %%% rates per 1000 births, %%% %%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html %%% %%% there are 208 values with at least 4 digits, %%% with these frequencies: %%% %%% F[D1]: 0.361, 0.293, 0.043, 0.072, %%% 0.062, 0.087, 0.038, 0.014, 0.029 %%% F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077, %%% 0.077, 0.106, 0.067, 0.043, 0.053 %%% %%% In the 2010 annual financial report for IBM %%% Corporation (its hundredth year of business) %%% %%% ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf %%% %%% there are 6126 numbers of two or more digits %%% that do not look like year dates (19xx and %%% 20xx), and they have these digit frequencies: %%% %%% F[D1]: 0.333, 0.160, 0.163, 0.086, %%% 0.068, 0.053, 0.047, 0.045, 0.046 %%% F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085, %%% 0.095, 0.079, 0.074, 0.079, 0.068 %%% %%% For the first 100,000 primes, we have %%% %%% F[D1]: 0.311, 0.091, 0.090, 0.087, %%% 0.086, 0.085, 0.084, 0.083, 0.082 %%% F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078, %%% 0.078, 0.078, 0.079, 0.078, 0.078 %%% %%% For the Fibonacci numbers, f(n), which %%% satisfy the recurrence f(n) = f(n-1) + f(n-2) %%% with f(1) = f(2) = 1, using the first 10000 %%% such numbers (the last of which has 2091 %%% digits), we find for the 9994 f(n) values %%% with at least two digits these frequencies: %%% %%% F[D1]: 0.301, 0.176, 0.125, 0.097, %%% 0.079, 0.067, 0.058, 0.051, 0.046 %%% F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100, %%% 0.097, 0.094, 0.090, 0.088, 0.085 %%% %%% If we take the same set of Fibonacci numbers, %%% we find these frequencies for values output %%% in base 4: %%% %%% F[D1]: 0.500, 0.292, 0.208 %%% F[D2]: 0.303, 0.262, 0.230, 0.205 %%% %%% The Fibonacci numbers, and the members of %%% many other such sequences, can be proved %%% mathematically to obey Benford's Law exactly %%% (see entries Raimi:1976:FDP, Berger:2011:BLS, %%% and Berger:2011:BTB). %%% %%% Simon Newcomb made another significant %%% appearance in the history of science when he %%% proposed that the then-not-understood %%% perihelion advance of the planet Mercury %%% could be explained by modifying Newton's law %%% of gravitation from a $r^{-2}$ dependence to %%% $r^{-2.000\,000\,157\,4}$. His proposal was %%% later shown to contradict more accurate %%% measurements of the orbit of Earth's Moon. %%% That story is told on pages 93--95 of %%% Clifford M. Will's 1993 book, ``Was Einstein %%% Right?'' (ISBN 0-465-09086-9). %%% %%% Although many papers purport to explain %%% Benford's Law, a recent paper (entry %%% Berger:2011:BLS) argues that several of the %%% prior published explanations are flawed. An %%% earlier paper (entry Raimi:1976:FDP) examines %%% the literature on Benford's Law up to 1976, %%% and points out flaws in several previous %%% explanations of the law. That paper also %%% gives a bibliography of previous important %%% works on the problem. A recent survey (entry %%% Berger:2011:BTB) may provide stronger %%% mathematical grounds for Benford's Law. %%% %%% Benford's Law has been applied to the problem %%% of detection of fraud in data, elections, and %%% finance (see, among other entries, %%% Hill:1998:FDP, Nigrini:1992:DIE, %%% Swanson:2003:DPF, Durtschi:2004:EUB, %%% Geyer:2004:DFD, Bhattacharya:2005:CPA, %%% Cleary:2005:ADA, Lu:2005:DFH, Lu:2006:AFD, %%% Schneider:2006:RAS, Cho:2007:BBL, %%% Diekmann:2007:FDU, Hand:2007:DDD, %%% Todter:2009:BLI, Corazza:2010:CFM, and %%% Roukema:2014:FDA, and the cautionary view in %%% Diekmann:2010:BLF). %%% %%% Benford's Law also applies to floating-point %%% numbers in computer arithmetic (see entries %%% Konheim:1965:MDT, Hamming:1970:DN, %%% Tsao:1974:DSD, Feldstein:1976:CED, %%% Feldstein:1986:OUS, Schatte:1988:ASC), where %%% it has implications for the frequency of %%% significance loss in subtraction of %%% like-signed numbers. %%% %%% This bibliography also includes publications %%% about two related empirical laws: Heaps' Law %%% and Zipf's Law, because they often occur in %%% discussions of Benford's Law. %%% %%% Heaps' Law (see entry Heaps:1978:IRC) is an %%% empirical observation from linguistics that %%% the proportion of words from a vocabulary %%% grows exponentially (but with a small %%% exponent, often between 0.4 and 0.6) with the %%% number of words in the text of documents. %%% %%% Zipf's Law says that if S is some stochastic %%% (random) variable, the probability that S %%% exceeds s is proportional to 1 / s. The %%% variable S might be, for example, the %%% population of a city (small cities are more %%% numerous than large ones). Zipf's Law is %%% a special case of the Pareto distribution %%% (see remark in entry Pareto:1896:CEP). %%% %%% Zipf's law finds application in the design of %%% information retrieval systems (e.g., hash %%% tables, databases, filesystems, and Web %%% searches), as well as in astronomy, biology, %%% computer science, demography, earth science, %%% economics, and physics. See entry %%% Newman:2005:PLP for an outstanding survey %%% that deserves to be widely read by %%% scientists, and entry Baldi:2003:MIW for a %%% book-length treatment. %%% %%% There is an actively-maintained bibliography %%% of Benford's Law at %%% %%% http://www.benfordonline.net/ %%% %%% (see entry Berger:2009:BOB). It includes %%% material from entries Hurlimann:2006:BLB and %%% Nigrini:1992:DIE. Although BibTeX output is %%% mentioned, it may not yet be implemented. %%% %%% There is an online bibliography of Zipf's Law %%% at %%% %%% http://www.nslij-genetics.org/wli/zipf/ %%% %%% (see entry Li:2011:ZLB). %%% %%% There is a collection of several papers on %%% election-fraud detection, some of them using %%% Benford's Law analyses, at %%% %%% http://www-personal.umich.edu/~wmebane/ %%% %%% At version 1.72, the year coverage looked like %%% this: %%% %%% 1881 ( 1) 1926 ( 1) 1971 ( 2) %%% 1882 ( 0) 1927 ( 1) 1972 ( 6) %%% 1883 ( 0) 1928 ( 2) 1973 ( 8) %%% 1884 ( 0) 1929 ( 1) 1974 ( 11) %%% 1885 ( 0) 1930 ( 0) 1975 ( 11) %%% 1886 ( 0) 1931 ( 1) 1976 ( 10) %%% 1887 ( 0) 1932 ( 2) 1977 ( 6) %%% 1888 ( 0) 1933 ( 0) 1978 ( 8) %%% 1889 ( 0) 1934 ( 1) 1979 ( 4) %%% 1890 ( 0) 1935 ( 1) 1980 ( 8) %%% 1891 ( 0) 1936 ( 1) 1981 ( 10) %%% 1892 ( 0) 1937 ( 0) 1982 ( 8) %%% 1893 ( 0) 1938 ( 2) 1983 ( 6) %%% 1894 ( 0) 1939 ( 0) 1984 ( 15) %%% 1895 ( 0) 1940 ( 0) 1985 ( 9) %%% 1896 ( 1) 1941 ( 0) 1986 ( 10) %%% 1897 ( 0) 1942 ( 0) 1987 ( 14) %%% 1898 ( 0) 1943 ( 1) 1988 ( 12) %%% 1899 ( 0) 1944 ( 1) 1989 ( 12) %%% 1900 ( 0) 1945 ( 2) 1990 ( 6) %%% 1901 ( 0) 1946 ( 1) 1991 ( 9) %%% 1902 ( 0) 1947 ( 0) 1992 ( 10) %%% 1903 ( 0) 1948 ( 2) 1993 ( 9) %%% 1904 ( 0) 1949 ( 2) 1994 ( 9) %%% 1905 ( 0) 1950 ( 3) 1995 ( 15) %%% 1906 ( 0) 1951 ( 0) 1996 ( 19) %%% 1907 ( 0) 1952 ( 1) 1997 ( 14) %%% 1908 ( 0) 1953 ( 1) 1998 ( 17) %%% 1909 ( 0) 1954 ( 1) 1999 ( 25) %%% 1910 ( 0) 1955 ( 1) 2000 ( 15) %%% 1911 ( 0) 1956 ( 0) 2001 ( 25) %%% 1912 ( 1) 1957 ( 5) 2002 ( 26) %%% 1913 ( 1) 1958 ( 1) 2003 ( 37) %%% 1914 ( 0) 1959 ( 1) 2004 ( 41) %%% 1915 ( 1) 1960 ( 1) 2005 ( 60) %%% 1916 ( 1) 1961 ( 2) 2006 ( 57) %%% 1917 ( 1) 1962 ( 2) 2007 ( 42) %%% 1918 ( 0) 1963 ( 1) 2008 ( 40) %%% 1919 ( 0) 1964 ( 1) 2009 ( 58) %%% 1920 ( 1) 1965 ( 4) 2010 ( 76) %%% 1921 ( 0) 1966 ( 3) 2011 ( 79) %%% 1922 ( 1) 1967 ( 2) 2012 ( 39) %%% 1923 ( 0) 1968 ( 4) 2013 ( 13) %%% 1924 ( 0) 1969 ( 11) 2014 ( 1) %%% 1925 ( 1) 1970 ( 8) %%% %%% Article: 774 %%% Book: 72 %%% InCollection: 27 %%% InProceedings: 39 %%% Manual: 1 %%% MastersThesis: 4 %%% Misc: 16 %%% PhdThesis: 8 %%% Proceedings: 7 %%% TechReport: 46 %%% Unpublished: 3 %%% %%% Total entries: 997 %%% %%% Data for this bibliography have been %%% collected from %%% %%% * the University of Utah Mathematics %%% Department bibliography archives %%% %%% * the TeX User Group bibliography %%% archives %%% %%% * the Karlsruhe Computer Science %%% bibliography archives %%% %%% * the Karlsruhe virtual catalog at %%% http://www.ubka.uni-karlsruhe.de/kvk_en.html %%% %%% * the US Library of Congress catalog at %%% http://catalog.loc.gov/ %%% %%% * the author's cattobib utility, which %%% provides Z39.50 interfaces to many %%% large libraries around the world, at %%% http://www.math.utah.edu/pub/cattobib/ %%% %%% * the American Institute of Physics %%% Scitation database at %%% http://scitation.aip.org/search_scitation %%% %%% * the American Physical Society PROLA %%% database at %%% http://publish.aps.org/search %%% %%% * the American Mathematical Society %%% MathSciNet database at %%% http://ams.rice.edu/mathscinet/search.html %%% %%% * the Bulletin of the Atomic Scientists %%% (archives available, albeit inconveniently, %%% via http://books.google.com/ and %%% http://bos.sagepub.com/search) %%% %%% * the Canadian Journal of Physics %%% database at %%% http://www.nrcresearchpress.com/search/advanced %%% %%% * the European Mathematical Society %%% Zentralblatt fuer Mathematik database %%% at http://zb.msri.org/ZMATH/zmath/en/ %%% %%% * the Europhysics journal archive at %%% http://www.europhysicsnews.org/ %%% %%% * the JSTOR database at %%% http://www.jstor.org/ %%% %%% * the Nature journal archive at %%% http://www.nature.com/search/ %%% %%% * the journal archives of the National %%% Academy of Science at %%% http://www.pnas.org/ %%% %%% * the Project Euclid archives at %%% http://projecteuclid.org/ %%% %%% * the SAO/NASA Astrophysics Data System at %%% http://adsabs.harvard.edu/ %%% %%% * the Science journal archive at %%% http://www.sciencemag.org/search %%% %%% * the SPIRES high-energy physics %%% literature database at the Stanford %%% Linear Accelerator at Stanford %%% University at %%% http://www.slac.stanford.edu/spires/hep/search/ %%% %%% * the Springer journal database at %%% http://www.springer.com/?SGWID=0-102-13-0-0 %%% %%% * the Wiley journal database at %%% http://onlinelibrary.wiley.com/ %%% %%% * many online library catalogs, including %%% those of the British Library, the %%% Karlsruhe Virtual Library catalog, the %%% Oxford University Library, the University of %%% California library system, and the US %%% Library of Congress. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\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-mjn= "Mark J. Nigrini"} @String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ACCOUNT-HIST-J= "Accounting Historians Journal"} @String{j-ACCOUNT-RES= "Accountability in Research"} @String{j-ACCOUNT-REV= "The Accounting Review"} @String{j-ACCOUNTANCY= "Accountancy: The journal of the {Institute of Chartered Accountants in England and Wales}"} @String{j-ACTA-ARITHMETICA= "Acta Arithmetica"} @String{j-ACTA-ASTRONAUT= "Acta Astronautica"} @String{j-ADV-APPL-STAT= "Advances and Applications in Statistics"} @String{j-ADV-COMPLEX-SYST= "Advances in Complex Systems"} @String{j-AEQUATIONES-MATHEMATICAE= "Aequationes Mathematicae"} @String{j-AEROBIOLOGIA= "Aerobiologia"} @String{j-AM-J-ECON-SOCIOL= "The American Journal of Economics and Sociology"} @String{j-AM-J-MATH= "American Journal of Mathematics"} @String{j-AM-J-MATH-MANAGE-SCI= "American Journal of Mathematical and Management Sciences"} @String{j-AM-SCI= "American Scientist"} @String{j-AMER-J-PHYSICS= "American Journal of Physics"} @String{j-AMER-J-PSYCHOLOGY= "The American Journal of Psychology"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-AMER-STAT= "The American Statistician"} @String{j-ANALYST= "The Analyst"} @String{j-ANIM-BEHAV= "Animal Behaviour"} @String{j-ANN-APPL-PROBAB= "Annals of Applied Probability"} @String{j-ANN-INST-STAT-MATH-TOKYO= "Annals of the Institute of Statistical Mathematics (Tokyo)"} @String{j-ANN-MATH-STAT= "Annals of Mathematical Statistics"} @String{j-ANN-PROBAB= "Annals of Probability"} @String{j-ANN-STAT= "Annals of Statistics"} @String{j-APPL-ECON-LETT= "Applied Economics Letters"} @String{j-APPL-FINANC-ECON= "Applied Financial Economics"} @String{j-APPL-MATH-COMP= "Applied Mathematics and Computation"} @String{j-APPL-STAT= "Applied Statistics"} @String{j-AQUAT-BOT= "Aquatic Botany"} @String{j-ASIA-PAC-MATH-NEWSL= "Asia Pacific Mathematics Newsletter"} @String{j-ASLIB-PROC= "ASLIB Proceedings"} @String{j-ASTROPART-PHYS= "Astroparticle Physics"} @String{j-AUDITING= "Auditing: A Journal of Practice \& Theory"} @String{j-AUSTRALIAN-COMP-J= "Australian Computer Journal"} @String{j-AUSTRALIAN-MATH-SOC-GAZ= "Australian Mathematical Society Gazette"} @String{j-BELL-SYST-TECH-J= "The Bell System Technical Journal"} @String{j-BIOINFORMATICS= "Bioinformatics"} @String{j-BIOMETRIKA= "Biometrika"} @String{j-BIOSYSTEMS= "Biosystems (A6E)"} @String{j-BRAIN-COGN= "Brain and Cognition"} @String{j-BULL-INST-MATH-STAT= "Bulletin --- Institute of Mathematical Statistics"} @String{j-C-R-ACAD-SCI-I= "Comptes rendus de l'Acad{\'e}mie des sciences. 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H. {Freeman and Company}"} @String{pub-W-H-FREEMAN:adr= "New York, NY, USA"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr= "P. O. Box 128, Farrer Road, Singapore 9128"} @String{pub-YALE= "Yale University Press"} @String{pub-YALE:adr= "New Haven, CT, USA"} %%% ==================================================================== %%% Series abbreviations: @String{ser-LNAI= "Lecture Notes in Artificial Intelligence"} @String{ser-LNCS= "Lecture Notes in Computer Science"} @String{ser-LNM= "Lecture Notes in Mathematics"} %%% ==================================================================== %%% Bibliography entries, sorted by year, and then by citation label: @Article{Aban:2006:PET, author = "Inmaculada B. Aban and Mark M. Meerschaert and Anna K. Panorska", title = "Parameter Estimation for the Truncated {Pareto} Distribution", journal = j-J-AM-STAT-ASSOC, volume = "101", number = "473", pages = "270--277", month = mar, year = "2006", CODEN = "JSTNAL", DOI = "http://dx.doi.org/10.1198/016214505000000411", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Thu Aug 26 11:26:31 MDT 2010", bibsource = "http://www.amstat.org/publications/jasa/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Abdel-All:2003:GPP, author = "N. H. Abdel-All and M. A. W. Mahmoud and H. N. Abd-Ellah", title = "Geometrical properties of {Pareto} distribution", journal = j-APPL-MATH-COMP, volume = "145", number = "2--3", pages = "321--339", day = "25", month = dec, year = "2003", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Fri Jan 9 08:41:12 MST 2004", bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @Article{Abe:2002:STE, author = "Sumiyoshi Abe", title = "Stability of {Tsallis} entropy and instabilities of {R{\'e}nyi} and normalized {Tsallis} entropies: a basis for $q$-exponential distributions", journal = j-PHYS-REV-E, volume = "66", number = "??", pages = "046134", day = "24", month = oct, year = "2002", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.66.046134", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.046134", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Abourbih:2010:SSD, author = "Jonathan A. Abourbih and Luke Blaney and Alan Bundy and Fiona McNeill", title = "A Single-Significant-Digit Calculus for Semi-Automated Guesstimation", journal = j-LECT-NOTES-COMP-SCI, volume = "6173", pages = "354--368", year = "2010", CODEN = "LNCSD9", DOI = "http://dx.doi.org/10.1007/978-3-642-14203-1_31", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:43:23 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31", acknowledgement = ack-nhfb, book-DOI = "http://dx.doi.org/10.1007/978-3-642-14203-1", book-URL = "http://www.springerlink.com/content/978-3-642-14203-1", fjournal = "Lecture Notes in Computer Science", } @Article{Abrantes-Metz:2011:TLR, author = "R. M. Abrantes-Metz and S. B. Villas-Boas and G. Judge", title = "Tracking the {Libor} rate", journal = j-APPL-ECON-LETT, volume = "18", number = "10", pages = "893--899", month = "????", year = "2011", DOI = "http://dx.doi.org/10.1080/13504851.2010.515197", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Mon Feb 18 18:17:20 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/13504851.2010.515197", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", keywords = "Benford's Second-Digit Law", remark = "From the abstract: ``Libor rates depart significantly from the expected Benford reference distribution. This raises potential concerns relative to the unbiased nature of the signals coming from the 16 banks from which the Libor is computed and the usefulness of the Libor as a major economic indicator.''", } @Article{Ackermann:2007:DMB, author = "Heiner Ackermann and Alantha Newman and Heiko R{\"o}glin and Berthold V{\"o}cking", title = "Decision-making based on approximate and smoothed {Pareto} curves", journal = j-THEOR-COMP-SCI, volume = "378", number = "3", pages = "253--270", day = "9", month = jun, year = "2007", CODEN = "TCSCDI", ISSN = "0304-3975 (print), 1879-2294 (electronic)", ISSN-L = "0304-3975", bibdate = "Tue Mar 29 08:55:49 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/03043975", acknowledgement = ack-nhfb, fjournal = "Theoretical Computer Science", journal-URL = "http://www.sciencedirect.com/science/journal/03043975", } @Article{Adamic:2011:CSU, author = "Lada Adamic", title = "Complex systems: Unzipping {Zipf}'s law", journal = j-NATURE, volume = "474", number = "7350", pages = "164--165", month = jun, year = "2011", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/474164a", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Tue Nov 15 09:29:15 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", onlinedate = "09 June 2011", } @Article{Adhikari:1968:DMS, author = "A. K. Adhikari and B. P. Sarkar", title = "Distribution of most significant digit in certain functions whose arguments are random variables", journal = j-SANKHYA-B, volume = "30", number = "??", pages = "47--58", month = "????", year = "1968", CODEN = "SANBBV", ISSN = "0581-5738", ISSN-L = "0581-5738", bibdate = "Sat Nov 12 16:09:30 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sankhya Ser. B (Indian J. of Statist.)", fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B. Methodological", } @Article{Adhikari:1969:SRD, author = "A. K. Adhikari", title = "Some results on the distribution of the most significant digit", journal = j-SANKHYA-B, volume = "31", number = "??", pages = "413--420", month = "????", year = "1969", CODEN = "SANBBV", ISSN = "0581-5738", ISSN-L = "0581-5738", bibdate = "Sat Nov 12 16:12:50 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sankhya Ser. B (Indian J. of Statist.)", fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B. Methodological", } @Article{Aigner:1970:EPL, author = "Dennis J. Aigner and Arthur S. Goldberger", title = "Estimation of {Pareto's Law} from Grouped Observations", journal = j-J-AM-STAT-ASSOC, volume = "65", number = "330", pages = "712--723", month = jun, year = "1970", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:44 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314212; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib", URL = "http://www.jstor.org/stable/2284582", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Aigner:1972:CEP, author = "Dennis J. Aigner and Arthur S. Goldberger", title = "Corrigenda: Estimation of {Pareto's Law} from Grouped Observations", journal = j-J-AM-STAT-ASSOC, volume = "67", number = "337", pages = "252--252", month = mar, year = "1972", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:45 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314217; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib", URL = "http://www.jstor.org/stable/2284755", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Ainsworth:2009:QSR, author = "Richard Thompson Ainsworth and Urs Hengartner", title = "{Quebec's Sales Recording Module (SRM)}: Fighting the {Zapper}, {Phantomware}, and Tax Fraud with technology", journal = "Canadian Tax Journal", volume = "57", number = "4", pages = "715--761", month = "????", year = "2009", CODEN = "????", ISSN = "0068-9823", ISSN-L = "0068-9823", bibdate = "Fri Mar 22 08:37:54 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.ctf.ca/ctfweb/Documents/PDF/2009ctj/09ctj4-ainsworth.pdf", acknowledgement = ack-mjn # "\slash " # ack-nhfb, journal-URL = "https://www.ctf.ca/ctfweb", keywords = "Benford's Law", } @Misc{Alagoz:2010:MDB, author = "Ali Alag{\"o}z and Mustafa Ay", title = "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital Analiz. ({Turkish}) [{Benford Law}-Based Digital Analysis of Accounting Oversight]", pages = "17", day = "8", month = jan, year = "2010", bibdate = "Mon Feb 18 09:19:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf", acknowledgement = ack-nhfb, language = "Turkish", } @Article{Aldous:2010:WCO, author = "David Aldous and Tung Phan", title = "When Can One Test an Explanation? {Compare} and Contrast {Benford's Law} and the Fuzzy {CLT}", journal = j-AMER-STAT, volume = "64", number = "3", pages = "221--227", month = aug, year = "2010", CODEN = "ASTAAJ", DOI = "http://dx.doi.org/10.1198/tast.2010.09098", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2757166", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; http://www.math.utah.edu/pub/tex/bib/amstat.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @TechReport{Alexander:2009:RUB, author = "James C. Alexander", title = "Remarks on the use of {Benford's Law}", type = "Working paper", institution = "Department of Mathematics and Cognitive Science, Case Western Reserve University", address = "Cleveland, OH, USA", day = "23", month = nov, year = "2009", bibdate = "Fri Mar 22 08:40:20 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1505147", acknowledgement = ack-mjn # "\slash " # ack-nhfb, } @Article{Allaart:1997:ISC, author = "Pieter C. Allaart", title = "An Invariant-Sum Characterization of {Benford's Law}", journal = j-J-APPL-PROBAB, volume = "34", number = "1", pages = "288--291", month = mar, year = "1997", CODEN = "JPRBAM", DOI = "http://dx.doi.org/10.2307/3215195", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "60E05", MRnumber = "1429075 (98d:60029)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3215195", abstract = "The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit $ d (d = 1, 2, \ldots, 9) $ is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits $ d_1, \ldots, d_k $ is constant for every fixed $k$.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @InProceedings{Altamirano:2009:GTU, author = "C. Altamirano and A. Robledo", editor = "J. Zhou", booktitle = "Complex Sciences", title = "Generalized Thermodynamics Underlying the Laws of {Zipf} and {Benford}", volume = "5", publisher = pub-SV, address = pub-SV:adr, pages = "2232--??", year = "2009", DOI = "http://dx.doi.org/10.1007/978-3-642-02469-6_100", ISBN = "3-642-02468-8", ISBN-13 = "978-3-642-02468-9", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A", acknowledgement = ack-nhfb, } @Article{Altamirano:2010:PTS, author = "Carlo Altamirano and Alberto Robledo", title = "Possible thermodynamic structure underlying the laws of {Zipf} and {Benford}", journal = "ArXiv e-prints", day = "10", month = aug, year = "2010", bibdate = "Mon Nov 21 07:12:08 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1008.1614", abstract = "We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This structure is obtained from a deformed type of statistical mechanics that arises when configurational phase space is incompletely visited in a severe way. Specifically, the restriction is that the accessible fraction of this space has fractal properties. The focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials that when particularized to first digits leads to a previously existing generalization of Benford's law. The inverse functional of this expression leads to Zipf's law; but it naturally includes the bends or tails observed in real data for small and large rank. Remarkably, we find that the entire problem is analogous to the transition to chaos via intermittency exhibited by low-dimensional nonlinear maps. Our results also explain the generic form of the degree distribution of scale-free networks.", acknowledgement = ack-nhfb, remark = "To be published in European Physical Journal B.", } @Article{Altamirano:2011:PTS, author = "C. Altamirano and A. Robledo", title = "Possible thermodynamic structure underlying the laws of {Zipf} and {Benford}", journal = j-EUR-PHYS-J-B, volume = "81", number = "3", pages = "345--351", month = jun, year = "2011", CODEN = "EPJBFY", DOI = "http://dx.doi.org/10.1140/epjb/e2011-10968-5", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Mon Nov 14 17:53:47 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011EPJB...81..345A", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1008.1614", fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", primaryclass = "cond-mat.stat-mech", } @Article{Alvarez-Ramirez:2003:ZMS, author = "Jose Alvarez-Ramirez and Monica Meraz and Gustavo Gallegos", title = "{Zipf--Mandelbrot} scaling law for world track records", journal = j-PHYSICA-A, volume = "328", number = "3--4", pages = "545--560", day = "15", month = oct, year = "2003", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(03)00579-X", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S037843710300579X", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Amin:2007:TVA, author = "Zeinab H. Amin", title = "Tests for the Validity of the Assumption that the Underlying Distribution of Life is {Pareto}", journal = j-J-APPL-STAT, volume = "34", number = "2", pages = "195--201", year = "2007", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Wed Aug 25 11:41:54 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Book{Anastasi:2003:NFI, author = "Joe Anastasi", title = "The new forensics: investigating corporate fraud and the theft of intellectual property", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiv + 270", year = "2003", ISBN = "0-471-26994-8 (hardcover)", ISBN-13 = "978-0-471-26994-6 (hardcover)", LCCN = "HV8079.W47 A5 2003", bibdate = "Tue Nov 22 11:42:36 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/bios/wiley044/2003001697.html; http://www.loc.gov/catdir/description/wiley037/2003001697.html; http://www.loc.gov/catdir/toc/wiley031/2003001697.html", acknowledgement = ack-nhfb, remark = "Brief mention of Benford's Law on pp. 184--185.", subject = "white collar crime investigation; data processing; case studies; fraud investigation; forensic accounting; computer security", } @Article{Anderson:2009:CRC, author = "Thomas Anderson", title = "Conference reviewing considered harmful", journal = j-OPER-SYS-REV, volume = "43", number = "2", pages = "108--116", month = apr, year = "2009", CODEN = "OSRED8", DOI = "http://doi.acm.org/10.1145/1531793.1531815", ISSN = "0163-5980 (print), 1943-586X (electronic)", ISSN-L = "0163-5980", bibdate = "Thu Apr 23 19:43:22 MDT 2009", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "This paper develops a model of computer systems research to help prospective authors understand the often obscure workings of conference program committees. We present data to show that the variability between reviewers is often the dominant factor as to whether a paper is accepted. We argue that paper merit is likely to be Zipf distributed, making it inherently difficult for program committees to distinguish between most papers. We use game theory to show that with noisy reviews and Zipf merit, authors have an incentive to submit papers too early and too often. These factors make conference reviewing, and systems research as a whole, less efficient and less effective. We describe some recent changes in conference design to address these issues, and we suggest some further potential improvements.", acknowledgement = ack-nhfb, fjournal = "ACM SIGOPS Operating Systems Review", } @Article{Anderson:2010:BLC, author = "Theresa Anderson and Larry Rolen and Ruth Stoehr", title = "{Benford's} Law For Coefficients of Modular Forms and Partition Functions", journal = "ArXiv e-prints", day = "3", month = sep, year = "2010", bibdate = "Mon Nov 21 07:10:51 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1009.0780", abstract = "Here we prove that Benford's law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessary asymptotics. This implies that the unrestricted partition function $ p(n) $, as well as other natural partition functions, satisfy Benford's law.", acknowledgement = ack-nhfb, pagecount = "10", } @Article{Anderson:2011:BLC, author = "Theresa C. Anderson and Larry Rolen and Ruth Stoehr", title = "{Benford}'s law for coefficients of modular forms and partition functions", journal = j-PROC-AM-MATH-SOC, volume = "139", number = "5", pages = "1533--1541", year = "2011", CODEN = "PAMYAR", DOI = "http://dx.doi.org/10.1090/S0002-9939-2010-10577-4", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "11F12 (11F20 11P83)", MRnumber = "2763743", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", } @Article{Andrew:2011:OBM, author = "Alex M. Andrew", title = "Obituary: {Beno{\^\i}t Mandelbrot: 20 November 1924--14 October 2010}", journal = "Kybernetes", volume = "40", number = "1--2", pages = "??--??", month = "????", year = "2011", CODEN = "KBNTA3", ISSN = "0368-492X (print), 1758-7883 (electronic)", ISSN-L = "0368-492X", bibdate = "Fri Nov 25 07:32:54 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://en.wikipedia.org/wiki/ernst_von_glasersfeld; http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf; http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825; http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary; http://www.math.yale.edu/mandelbrot/; http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html", acknowledgement = ack-nhfb, } @Misc{Anonymous:1932:FL, author = "Anonymous", title = "Fishpole Lamp", howpublished = "Web site", day = "30", month = apr, year = "1932", bibdate = "Sat Feb 23 14:52:20 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This Web site reports that General Electric researcher Frank Benford invented the electric light pointer, the forerunner of the modern laser pointer.", URL = "http://scienceservice.si.edu/pages/012020.htm", acknowledgement = ack-nhfb, remark = "CD 2478048, E\&MP12.020, Electric Appliances \ Apparatus.", } @Article{Anonymous:1950:BRZ, author = "Anonymous", title = "Book review: {Zipf, George K., \booktitle{Human behavior and the principle of least effort}. Cambridge, (Mass.): Addison-Wesley, 1949, pp. 573}", journal = j-J-CLIN-PSYCHOL, volume = "6", number = "3", pages = "306--306", year = "1950", CODEN = "JCPYAO", DOI = "http://dx.doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO;2-7", ISSN = "0021-9762 (print), 1097-4679 (electronic)", ISSN-L = "0021-9762", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Clinical Psychology", } @Article{Anonymous:1993:WFR, author = "Anonymous", title = "Why failure rates observe {Zipf}'s law in operational software: {M. Trachtenberg. IEEE Transactions on Reliability, {\bf 41}(3), 386 (1992)}", journal = j-MICROELECT-RELIABILITY, volume = "33", number = "13", pages = "2062--2062", month = oct, year = "1993", CODEN = "MCRLAS", DOI = "http://dx.doi.org/10.1016/0026-2714(93)90406-O", ISSN = "0026-2714 (print), 1872-941X (electronic)", ISSN-L = "0026-2714", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/002627149390406O", acknowledgement = ack-nhfb, fjournal = "Microelectronics and Reliability", keywords = "Zipf's Law", } @Article{Anonymous:2002:ZLM, author = "Anonymous", title = "{Zipf}'s law and maximum sustainable growth", journal = j-STAT-PROB-LETT, volume = "56", number = "2", pages = "??--??", day = "15", month = jan, year = "2002", CODEN = "SPLTDC", DOI = "http://dx.doi.org/10.1016/j.jedc.2013.02.004", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165188913000341", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", keywords = "Zipf's Law", onlinedate = "19 February 2013", } @Article{Anonymous:2005:UZL, author = "Anonymous", title = "The use of {Zipf}'s law in animal communication analysis", journal = j-ANIM-BEHAV, volume = "69", number = "1", pages = "??--??", day = "20", month = jan, year = "2005", CODEN = "ANBEA8", DOI = "http://dx.doi.org/10.1016/j.anbehav.2004.08.004", ISSN = "0003-3472 (print), 1095-8282 (electronic)", ISSN-L = "0003-3472", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0003347204003471", acknowledgement = ack-nhfb, fjournal = "Animal Behaviour", journal-URL = "http://www.sciencedirect.com/science/journal/00033472", keywords = "Zipf's Law", } @Misc{Anonymous:2007:ZL, author = "Anonymous", key = "Zipf's Law", title = "{Zipf}'s law", year = "2007", bibdate = "Sat Jan 26 12:46:16 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/datacompression.bib", URL = "http://en.wikipedia.org/wiki/Zipf's_law", acknowledgement = ack-ds, lastaccess = "27 January 2013", rawdata = "Zipf's Law (2007) |http://en.wikipedia.org/wiki/Zipf's_law|", } @Article{Anonymous:2012:SB, author = "Anonymous", title = "The scam busters", journal = j-ECONOMIST, volume = "??", number = "??", pages = "??--??", day = "15", month = dec, year = "2012", CODEN = "EONOEH", ISSN = "0013-0613 (print), 1476-8860 (electronic)", ISSN-L = "0013-0613", bibdate = "Mon Feb 18 19:01:02 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.economist.com/news/finance-and-economics/21568364-how-antitrust-economists-are-getting-better-spotting-cartels-scam-busters", acknowledgement = ack-nhfb, fjournal = "The Economist", keywords = "Benford's Law", } @Article{Antonini:1991:NUD, author = "Rita Giuliano Antonini", title = "On the Notion of Uniform Distribution Mod $1$", journal = j-FIB-QUART, volume = "29", number = "3", pages = "230--234", month = aug, year = "1991", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:01:34 MDT 2011", bibsource = "http://www.fq.math.ca/29-3.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/29-3/antonini.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", keywords = "Benford's Law", } @Article{Antonini:2005:RSC, author = "Rita Giuliano Antonini and Georges Grekos", title = "Regular sets and conditional density: an extension of {Benford}'s law", journal = j-COLLOQ-MATH, volume = "103", number = "2", pages = "173--192", year = "2005", CODEN = "CQMAAQ", DOI = "http://dx.doi.org/10.4064/cm103-2-3", ISSN = "0010-1354 (print), 1730-6302 (electronic)", ISSN-L = "0010-1354", MRclass = "11B05 (11K99)", MRnumber = "2197847 (2006j:11012)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1092.11009", acknowledgement = ack-nhfb, fjournal = "Colloquium Mathematicum", keywords = "asymptotic density; Benford's law; conditional density; first digit problem; logarithmic density; regular set; regular varying function", ZMclass = "11B05 (Topology etc. of sets of numbers); 11K99 (Probabilistic theory)", } @Article{Aono:2008:ISO, author = "June Y. Aono and Liming Guan", title = "The impact of {Sarbanes--Oxley} act on cosmetic earnings management", journal = "Research in Accounting Regulation", volume = "20", number = "??", pages = "205--215", month = oct, year = "2008", CODEN = "????", DOI = "http://dx.doi.org/10.1016/S1052-0457(07)00212-3", ISSN = "1052-0457", ISSN-L = "1052-0457", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S1052045707002123", acknowledgement = ack-nhfb, fjournal = "Research in Accounting Regulation", keywords = "Benford's Law", } @Article{Aoyama:2004:KDP, author = "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma", title = "Kinematics and dynamics of {Pareto--Zipf}'s law and {Gibrat}'s law", journal = j-PHYSICA-A, volume = "344", number = "1--2", pages = "117--121", day = "1", month = dec, year = "2004", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2004.06.099", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009185", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Archambault:2011:EMA, author = "J. Archambault and M. Archambault", title = "Earnings management among firms during the pre-{SEC} era: a {Benford}'s law analysis", journal = j-ACCOUNT-HIST-J, volume = "38", number = "2", pages = "145--170", month = "????", year = "2011", ISSN = "0148-4184", ISSN-L = "0148-4184", bibdate = "Mon Feb 18 11:32:23 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Accounting Historians Journal", journal-URL = "http://www.jstor.org/action/showPublication?journalCode=accohistjour; http://www.aahhq.org/", remark = "JSTOR has a 3-year moving wall, so this article is not yet in that archive; the publisher's Web site is poor, and I cannot find the article there.", } @Article{Arnold:1989:BEP, author = "Barry C. Arnold and S. James Press", title = "{Bayesian} estimation and prediction for {Pareto} data", journal = j-J-AM-STAT-ASSOC, volume = "84", number = "408", pages = "1079--1084", month = "????", year = "1989", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62F15 (62F10)", MRnumber = "92f:62034", bibdate = "Mon May 5 12:36:01 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Book{Arthur:1994:IRP, author = "W. Brian Arthur", title = "Increasing returns and path dependence in the economy", publisher = pub-U-MICHIGAN, address = pub-U-MICHIGAN:adr, pages = "xx + 201", year = "1994", ISBN = "0-472-09496-3 , 0-472-06496-7 (paperback)", ISBN-13 = "978-0-472-09496-7, 978-0-472-06496-0 (paperback)", LCCN = "HD69.S5 A77 1994", bibdate = "Wed Feb 27 07:08:40 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", note = "With a foreword by Kenneth J. Arrow.", series = "Economics, cognition, and society", acknowledgement = ack-nhfb, keywords = "Zipf's Law", subject = "Economies of scale; Mathematical models; Economic development; Economics, Mathematical", } @Article{Auerbach:1913:GBG, author = "Felix Auerbach", title = "{Das Gesetz der Bev{\"o}lkerungskonzentration}. ({German}) [{The} law of population concentration]", journal = "{Petermann's Geographische Mitteilungen}", volume = "59", number = "1", pages = "74--76", month = "????", year = "1913", CODEN = "PGGMA3", ISSN = "0031-6229", ISSN-L = "0031-6229", bibdate = "Thu Nov 24 10:49:06 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper is reported in \cite{Newman:2005:PLP} to be the first discovery of {\em Zipf's Law\/} in connection with city populations (see \cite{Zipf:1932:SSP}). See also \cite{Estoup:1916:GSM}.", URL = "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122", acknowledgement = ack-nhfb, ajournal = "Petermanns Geogr. Mitteilung", ajournal-2 = "Petermanns Geogr. Mitt.", language = "German", } @Article{Ausloos:1999:PMK, author = "M. Ausloos and K. Ivanova", title = "Precise $ (m, k) $-{Zipf} diagram analysis of mathematical and financial time series when $ m = 6 $, $ k = 2 $", journal = j-PHYSICA-A, volume = "270", number = "3--4", pages = "526--542", day = "15", month = aug, year = "1999", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(99)00178-8", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437199001788", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Ausloos:2003:SIZ, author = "M. Ausloos and Ph. Bronlet", title = "Strategy for investments from {Zipf} law(s)", journal = j-PHYSICA-A, volume = "324", number = "1--2", pages = "30--37", day = "1", month = jun, year = "2003", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(02)01845-9", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B82", MRnumber = "2030919", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "International Econophysics Conference IEC2002 (Bali)", URL = "http://www.sciencedirect.com/science/article/pii/S0378437102018459", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Axtell:2001:ZDU, author = "R. L. Axtell", title = "{Zipf} Distribution of {U.S.} Firm Sizes", journal = j-SCIENCE, volume = "293", number = "5536", pages = "1818--1820", day = "7", month = sep, year = "2001", CODEN = "SCIEAS", DOI = "http://dx.doi.org/10.1126/science.1062081", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Wed Feb 27 06:38:34 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/293/5536/1818", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "Zipf's Law", } @Article{AyllonBurguillo:1999:PDS, author = "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera Dom{\'\i}nguez}", title = "El primer d{\'\i}gito significativo. ({Spanish}) [The first significant digit]", journal = "{Epsilon}: Revista de la {Sociedad Andaluza de Educaci{\'o}n Matem{\'a}tica ``Thales''}", volume = "15", number = "3(45)", pages = "339--352", month = "????", year = "1999", ISSN = "1131-9321", ISSN-L = "1131-9321", bibdate = "Sat Feb 16 14:32:14 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "MATHEDUC.02332710", acknowledgement = ack-nhfb, ajournal = "{Rev. Epsil{\'o}n SAEM `Thales'}", journal-URL = "http://thales.cica.es/epsilon/; http://dialnet.unirioja.es/servlet/revista?codigo=504", language = "Spanish", msc2010 = "K60xx", remark = "Reported in \cite{Torres:2007:HDN} to contain an extensive bibliography on Benford's Law. The publisher does not have issues before 2003, and no electronic copy has yet been found on the Internet. Attempts to get this paper via Interlibrary Loan failed on the grounds that ``We are unable to verify any owning libraries within the United States or those that we have ILL privileges.''", xxauthor = "M. P. Dominguez and J. D. A. Burguillo", xxauthor = "Manuel {Perera Dom{\'\i}nguez} and Juan David {Ayll{\'o}n Burguillo}", } @Article{Bach:1998:EPM, author = "Eric Bach", title = "Efficient prediction of {Marsaglia--Zaman} random number generators", journal = j-IEEE-TRANS-INF-THEORY, volume = "44", number = "3", pages = "1253--1257", year = "1998", CODEN = "IETTAW", DOI = "http://dx.doi.org/10.1109/18.669305", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", MRclass = "65C10", MRnumber = "99b:65007", bibdate = "Thu Dec 22 07:42:24 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0915.65003", abstract = "This paper presents two properties of the random number generator by {\it G. Marsaglia} and {\it A. Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl 0733.65005)]. First, it is shown that its successive digits are digits of certain rational $b$-adic numbers. Then, an efficient algorithm is derived to predict an unknown pseudorandom sequence of this type. Two examples of the prediction are given.", acknowledgement = ack-nhfb, classmath = "*65C10 Random number generation 11K45 Pseudo-random numbers, etc.", fjournal = "IEEE Transactions on Information Theory", keywords = "$b$-adic number; algorithm; continued fraction; pseudo-random number generator", ZMreviewer = "K. Uosaki (Tottori)", } @Article{Bachmann:2010:APC, author = "Val{\'e}rie Bachmann and Martin H. Fischer and Hans-Peter Landolt and Peter Brugger", title = "Asymmetric prefrontal cortex functions predict asymmetries in number space", journal = j-BRAIN-COGN, volume = "74", number = "3", pages = "306--311", month = dec, year = "2010", CODEN = "????", DOI = "http://dx.doi.org/10.1016/j.bandc.2010.08.011", ISSN = "0278-2626 (print), 1090-2147 (electronic)", ISSN-L = "0278-2626", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0278262610001272", acknowledgement = ack-nhfb, fjournal = "Brain and Cognition", keywords = "Benford's Law; small-number bias (SNB); Spatial Numerical Association of Response Codes (SNARC) effect", } @Article{Baek:2011:ZLU, author = "Seung Ki Baek and Sebastian Bernhardsson and Petter Minnhagen", title = "{Zipf}'s law unzipped", journal = j-NEW-J-PHYS, volume = "13", number = "4", pages = "043004", month = "????", year = "2011", CODEN = "NJOPFM", DOI = "http://dx.doi.org/10.1088/1367-2630/13/4/043004", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Tue Nov 15 09:32:45 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://iopscience.iop.org/1367-2630/13/4/043004", abstract = "Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups the unique words, or the elements could be inhabitants and the groups the cities in a country and so on. A random group formation (RGF) is presented from which a Bayesian estimate is obtained based on minimal information: it provides the best prediction for the number of groups with $k$ elements, given the total number of elements, groups and the number of elements in the largest group. For each specification of these three values, the RGF predicts a unique group distribution $ N(k) \propto \exp ( - b k) / k^\gamma $, where the power-law index $ \gamma $ is a unique function of the same three values. The universality of the result is made possible by the fact that no system-specific assumptions are made about the mechanism responsible for the group division. The direct relation between $ \gamma $ and the total number of elements, groups and the number of elements in the largest group is calculated. The predictive power of the RGF model is demonstrated by direct comparison with data from a variety of systems. It is shown that $ \gamma $ usually takes values in the interval $ 1 \leq \gamma \leq 2 $ and that the value for a given phenomenon depends in a systematic way on the total size of the dataset. The results are put in the context of earlier discussions on Zipf's and Gibrat's laws, $ N(k) \propto k^{-2} $ and the connection between growth models and RGF is elucidated.", acknowledgement = ack-nhfb, fjournal = "New Journal of Physics", pagecount = "21", } @Article{Bak:1987:SOC, author = "Per Bak and Chao Tang and Kurt Wiesenfeld", title = "Self-organized criticality: An explanation of the $ 1 / f $ noise", journal = j-PHYS-REV-LET, volume = "59", number = "4", pages = "381--384", month = jul, year = "1987", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.59.381", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Thu Feb 28 10:54:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.59.381", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Book{Bak:1996:HNW, author = "Per Bak", title = "How nature works: the science of self-organized criticality", publisher = "Copernicus", address = "New York, NY, USA", pages = "xiii + 212 + 8", year = "1996", ISBN = "0-387-94791-4 (hardcover)", ISBN-13 = "978-0-387-94791-4 (hardcover)", LCCN = "QC173.4.C74 B34 1996", bibdate = "Thu Nov 24 13:34:22 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, keywords = "Zipf's Law", subject = "Critical phenomena (Physics); Complexity (Philosophy); Physics; Philosophy", } @Article{Bakulina:2007:AZL, author = "M. P. Bakulina", title = "Application of {Zipf}'s law for text compression", journal = "Diskretn. Anal. Issled. Oper. Ser. 2", volume = "14", number = "2", pages = "3--13", year = "2007", CODEN = "????", ISSN = "1560-9901", ISSN-L = "1560-9901", MRclass = "94A15", MRnumber = "2542308 (2010i:94076)", MRreviewer = "I. Vajda", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}. Seriya 2", } @Article{Balanzario:2010:SCB, author = "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz", title = "Sufficient conditions for {Benford}'s law", journal = j-STAT-PROB-LETT, volume = "80", number = "23--24", pages = "1713--1719", day = "1--15", month = dec, year = "2010", CODEN = "SPLTDC", DOI = "http://dx.doi.org/10.1016/j.spl.2010.07.014", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "62E10 (62E17)", MRnumber = "2734233 (2011i:62019)", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715210002087", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", keywords = "Benford's Law", } @TechReport{Balanzario:2012:BLM, author = "E. P. Balanzario", title = "{Benford}'s law for mixtures", type = "Preprint", institution = "????", address = "????", month = "????", year = "2012", bibdate = "Mon Feb 18 19:02:15 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Balaz:2010:BLD, author = "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch", title = "{Benford}'s law and distribution functions of sequences in $ (0, 1) $", journal = j-MATH-NOTES-ACAD-SCI-USSR, volume = "88", number = "3--4", pages = "449--463", month = oct, year = "2010", CODEN = "MTHNB2", DOI = "http://dx.doi.org/10.1134/S0001434610090178", ISSN = "0001-4346 (print), 1573-8876 (electronic)", ISSN-L = "0001-4346", bibdate = "Fri Nov 25 10:52:53 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1134%2FS0001434610090178", acknowledgement = ack-nhfb, fjournal = "Mathematical Notes of the {Academy of Sciences of the USSR = Matematicheskie Zametki}", } @Article{Balazh:2010:BLD, author = "V. Balazh and K. Nagasaka and O. Shtraukh", title = "{Benford}'s law and distribution functions of sequences in {$ (0, 1) $}", journal = j-MAT-ZAMETKI, volume = "88", number = "4", pages = "485--501", year = "2010", DOI = "http://dx.doi.org/10.1134/S0001434610090178", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "11K06 (60E05)", MRnumber = "2882211", MRreviewer = "Michael Drmota", bibdate = "Thu Feb 14 07:02:03 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", } @Book{Baldi:2003:MIW, author = "Pierre Baldi and Paolo Frasconi and Padhraic Smyth", title = "Modeling the {Internet} and the {Web}: probabilistic methods and algorithms", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xix + 285", year = "2003", ISBN = "0-470-86492-3 (e-book), 0-470-84906-1", ISBN-13 = "978-0-470-86492-0 (e-book), 978-0-470-84906-4", LCCN = "TK5105.875.I57 B35 2003eb", bibdate = "Fri Jun 3 10:03:23 MDT 2011", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/pagerank.bib", acknowledgement = ack-nhfb, subject = "Internet; Mathematical models; Telecommunication; Traffic; World Wide Web; Cyberspace; Probabilities; Computers; Web; General; Networking; Intranets and Extranets", tableofcontents = "Mathematical Background \\ Probability and Learning from a Bayesian Perspective \\ Parameter Estimation from Data \\ Basic principles \\ A simple die example \\ Mixture Models and the Expectation Maximization Algorithm \\ Graphical Models \\ Bayesian networks \\ Belief propagation \\ Learning directed graphical models from data \\ Classification \\ Clustering \\ Power-Law Distributions \\ Scale-free properties (80/20 rule) \\ Applications to Languages: Zipf's and Heaps' Laws \\ Origin of power-law distributions and Fermi's model \\ Basic WWW Technologies \\ Web Documents \\ SGML and HTML \\ General structure of an HTML document \\ Links \\ Resource Identifiers: URI, URL, and URN \\ Protocols \\ Reference models and TCP/IP \\ The domain name system \\ The Hypertext Transfer Protocol \\ Programming examples \\ Log Files \\ Search Engines \\ Coverage \\ Basic crawling \\ Web Graphs \\ Internet and Web Graphs \\ Power-law size \\ Power-law connectivity \\ Small-world networks \\ Power law of PageRank \\ The bow-tie structure \\ Generative Models for the Web Graph and Other Networks \\ Web page growth \\ Lattice perturbation models: between order and disorder \\ Preferential attachment models, or the rich get richer \\ Copy models \\ PageRank models \\ Applications \\ Distributed search algorithms \\ Subgraph patterns and communities \\ Robustness and vulnerability \\ Notes and Additional Technical References \\ Text Analysis \\ Indexing \\ Compression techniques \\ Lexical Processing \\ Tokenization", } @Article{Banks:1974:AMN, author = "William P. Banks and David K. Hill", title = "The apparent magnitude of number scaled by random production", journal = j-J-EXP-PSYCH-GEN, volume = "102", number = "2", pages = "353--376", month = feb, year = "1974", CODEN = "JPGEDD", DOI = "http://psycnet.apa.org/doi/10.1037/h0035850", ISSN = "0096-3445 (print), 1939-2222 (electronic)", ISSN-L = "0096-3445", bibdate = "Fri Feb 15 06:32:17 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://psycnet.apa.org/journals/xge/102/2/353/; http://psycnet.apa.org/psycinfo/1974-24305-001", acknowledgement = ack-nhfb, fjournal = "Journal of Experimental Psychology: General", } @Article{Banks:2013:BLM, author = "David G. Banks", title = "{Benford's Law} Made Easy: Common Software Eases use of Fraud Search Theorem", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2013", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:11:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294968485", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", } @Article{Barabasi:1999:ESR, author = "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka Albert", title = "Emergence of scaling in random networks", journal = j-SCIENCE, volume = "286", number = "5439", pages = "509--512", day = "15", month = oct, year = "1999", CODEN = "SCIEAS", DOI = "http://dx.doi.org/10.1126/science.286.5439.509", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Tue Nov 15 09:57:42 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/286/5439/509", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "power-law distribution; Zipf's Law", } @Article{Barlow:1985:RED, author = "J. L. Barlow and E. H. Bareiss", title = "On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic", journal = j-COMPUTING, volume = "34", number = "4", pages = "325--347", month = dec, year = "1985", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", MRclass = "65G05", MRnumber = "87c:65045", MRreviewer = "N. N. Abdelmalek", bibdate = "Tue Oct 12 16:33:42 MDT 1999", bibsource = "Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database", acknowledgement = ack-nhfb, affiliation = "Pennsylvania State Univ, Computer Science Dep, University Park, PA, USA", affiliationaddress = "USA", classification = "723", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", journalabr = "Computing (Vienna/New York)", keywords = "computer arithmetic; computer metatheory; floating point arithmetic; logarithmic arithmetic; roundoff error distributions", } @Misc{Barnes:2011:LCS, author = "K. Barnes", title = "Letter to {China Shen Zhou Mining and Resources (AMEX: SHZ)} current shareholders and potential investors from {Absaroka Capital}", howpublished = "Absaroka Capital Management, LLP, Wyoming, USA.", year = "2011", bibdate = "Fri Mar 22 08:42:58 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @Article{Baskerville:2006:SEM, author = "Kim Baskerville and Maya Paczuski", title = "Subgraph ensembles and motif discovery using an alternative heuristic for graph isomorphism", journal = j-PHYS-REV-E, volume = "74", number = "??", pages = "051903", day = "3", month = nov, year = "2006", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.74.051903", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.74.051903", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Baskerville:2007:GAS, author = "Kim Baskerville and Peter Grassberger and Maya Paczuski", title = "Graph animals, subgraph sampling, and motif search in large networks", journal = j-PHYS-REV-E, volume = "76", number = "??", pages = "036107", day = "11", month = sep, year = "2007", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.76.036107", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036107", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Battersby:2009:SAH, author = "Stephen Battersby", title = "Statistical analyses hint at fraud in {Iranian} election", journal = j-NEW-SCIENTIST, volume = "202", number = "2714", pages = "10--??", day = "24", month = jun, year = "2009", CODEN = "NWSCAL", DOI = "http://dx.doi.org/10.1016/S0262-4079(09)61682-1", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0262407909616821", acknowledgement = ack-nhfb, fjournal = "The New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law", xxISSN = "0262-4079, 0028-6664", } @Article{Batty:2008:PSS, author = "Michael Batty", title = "Perspective: The Size, Scale, and Shape of Cities", journal = j-SCIENCE, volume = "318", number = "5864", pages = "769--771", day = "8", month = feb, year = "2008", CODEN = "SCIEAS", DOI = "http://dx.doi.org/10.1126/science.1151419", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Wed Feb 27 06:02:28 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/319/5864/769.abstract", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "200 tallest buildings in world; US cities of one million (or more) population; Zipf's law", } @TechReport{Bauer:2009:DDF, author = "J. Bauer and J. Gross", title = "Difficulties Detecting Fraud? {The} Use of {Benford's Law} on Regression Tables", type = "Report", number = "??", institution = "Institute of Sociology, LMU Munich", address = "Munich, Germany", month = "????", year = "2009", bibdate = "Fri Nov 18 11:46:08 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @TechReport{Bauer:2010:DDF, author = "J. Bauer and J. Gross", title = "Difficulties Detecting Fraud? {The} Use of {Benford's Law} on Regression Tables", type = "Report", institution = "Institute of Sociology, Ludwig-Maximilians-Universit{\"a}t", address = "M{\"u}nchen, Germany", pages = "????", year = "2010", bibdate = "Tue Nov 22 21:15:18 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Bauer:2011:DDF, author = "Johannes Bauer and Jochen Gross", title = "Difficulties Detecting Fraud? {The} Use of {Benford?s Law} on Regression Tables", journal = "Journal of Economics and Statistics (Jahrb{\"u}cher f{\"u}r National{\"o}konomie und Statistik)", volume = "231", number = "5--6", pages = "733--748", month = nov, year = "2011", DOI = "????", bibdate = "Mon Feb 18 18:18:45 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ideas.repec.org/a/jns/jbstat/v231y2011i5-6p733-748.html", acknowledgement = ack-nhfb, journal-URL = "http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/", } @Article{Bawden:2011:BMS, author = "David Bawden", title = "{Beno{\^\i}t Mandelbrot} and the self-similarity of information", journal = j-J-DOC, volume = "67", number = "2", pages = "??--??", month = "????", year = "2011", CODEN = "JDOCAS", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:40:34 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", } @Article{Beber:2010:WNS, author = "Bernd Beber and Alexandria Scacco", title = "What the Numbers Say: a Digit-Based Test for Election Fraud", journal = j-POLIT-ANAL, volume = "20", number = "2", pages = "211--234", month = "Spring", year = "2010", DOI = "http://dx.doi.org/10.1093/pan/mps003", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Mon Feb 18 17:29:42 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pan.oxfordjournals.org/content/20/2/211.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", keywords = "Benford's Law", } @Article{Becker:2011:BLC, author = "T. Becker and A. Greaves-Tunnell and S. J. Miller and R. Ronan and F. W. Strauch", title = "{Benford's Law} and Continuous Dependent Random Variables", journal = "ArXiv e-prints", month = nov, year = "2011", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 17:50:20 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B; http://arxiv.org/abs/1111.0568", abstract = "Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $ 2^n $, equals 1 not 10\% or 11\% of the time, as one would expect if all digits were equally likely, but about 30\% of the time. This phenomenon, known as Benford's Law, has many applications, ranging from detecting tax fraud for the IRS to analyzing round-off errors in computer science.\par The central question is determining which data sets follow Benford's law. Inspired by natural processes such as particle decay, our work examines models for the decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow. The main difficulty is that the resulting random variables are dependent, which we handle by a careful analysis of the dependencies and tools from Fourier analysis to obtain quantified convergence rates.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1111.0568", keywords = "Mathematics - Probability, 11K06, 60A10 (primary), 60E10 (secondary)", primaryclass = "math.PR", } @Article{Beirlant:1996:TIE, author = "Jan Beirlant and Petra Vynckier and Jozef L. Teugels", title = "Tail Index Estimation, {Pareto} Quantile Plots, and Regression Diagnostics", journal = j-J-AM-STAT-ASSOC, volume = "91", number = "436", pages = "1659--??", month = "????", year = "1996", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon May 5 08:26:17 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Belevitch:1988:PQD, author = "Vitold Belevitch", title = "{{\`A}} propos de la queue de la distribution de {Zipf}. ({French}) [{On} the tail of the {Zipf} distribution]", journal = "Ann. Soc. Sci. Bruxelles S{\'e}r. I", volume = "102", number = "3", pages = "73--85 (1989)", year = "1988", CODEN = "ASSBAH", ISSN = "0037-959X", ISSN-L = "0037-959X", MRclass = "92A90", MRnumber = "1016850 (90g:92114)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annales de la Societ{\'e} Scientifique de Bruxelles. S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques et Physiques", language = "French", } @Article{Benford:1938:LAN, author = "Frank Benford", title = "The Law of Anomalous Numbers", journal = j-PROC-AMER-PHIL-SOC, volume = "78", number = "4", pages = "551--572", month = mar, year = "1938", CODEN = "PAPCAA", ISSN = "0003-049X", ISSN-L = "0003-049X", bibdate = "Thu Feb 15 16:28:28 2007", bibsource = "http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "See comments about Benford's biased rounding practices \cite{Diaconis:1979:RP}.", URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G", ZMnumber = "JFM 64.0555.03; Zbl 0018.26502", abstract = "It has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.", acknowledgement = ack-nhfb, author-dates = "1883--December 4, 1948", fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573--585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography \cite{Hurlimann:2006:BLB} cites 325 publications about Benford's Law.", xxURL = "http://en.wikipedia.org/wiki/Frank_Benford", } @Article{Benford:1943:PAG, author = "Frank Benford", title = "The Probable Accuracy of the General Physical Constants", journal = j-PHYS-REV, volume = "63", number = "5--6", pages = "212--212", month = mar, year = "1943", CODEN = "PHRVAO", DOI = "http://dx.doi.org/10.1103/PhysRev.63.212", ISSN = "0031-899X (print), 1536-6065 (electronic)", ISSN-L = "0031-899X", bibdate = "Mon Nov 21 21:52:58 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRev.63.212", acknowledgement = ack-nhfb, fjournal = "Physical Review", journal-URL = "http://prola.aps.org/browse/PR", } @Article{Benguigui:2007:DMC, author = "Lucien Benguigui and Efrat Blumenfeld-Lieberthal", title = "A dynamic model for city size distribution beyond {Zipf}'s law", journal = j-PHYSICA-A, volume = "384", number = "2", pages = "613--627", day = "15", month = oct, year = "2007", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2007.05.059", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437107006061", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @InProceedings{Bennett:1975:SDI, author = "John M. Bennett", booktitle = "Int. Comput. Symp. 1975, Proc., Antibes, (1975)", title = "Storage design for information retrieval: {Scarrott}'s conjecture and {Zipf}'s law", publisher = "????", address = "????", pages = "233--237", year = "1975", bibdate = "Sat Nov 12 10:49:15 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0322.68068", acknowledgement = ack-nhfb, classmath = "68P20 (Information storage and retrieval) 68N01 (General)", } @Article{Bennett:1984:ZLS, author = "J. M. Bennett", title = "{Zipf's Law}, Structured Programming and Creativity", journal = j-AUSTRALIAN-COMP-J, volume = "16", number = "4", pages = "122--129", year = "1984", CODEN = "ACMJB2", ISSN = "0004-8917", ISSN-L = "0004-8917", bibdate = "Fri Mar 9 17:59:26 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "As software projects increase in size, the effort required to implement them increases at a greater rate. The use of higher level languages and adherence to various rules of ``good programming practice'' appear to help only marginally in reducing the impact of this non-linear effect, and progress can only be made by calling on techniques for managing complexity which have emerged in other fields. Hierarchical structures are discussed with particular reference to software as is the effect which appears to be common to a wide range of human activities, and which is known as Zipf's law. The effects of variation in individual programming skills, the roles of creativity, invention and innovation and lessons to be learned from case studies of past failure are also examined.", acknowledgement = ack-nhfb, fjournal = "Australian Computer Journal", keywords = "creativity; innovation; invention; large software projects; project failures; structured programming; Zipf's law", } @TechReport{Berger:2003:BLP, author = "Arno Berger", title = "{Benford}'s law in power-like nonautonomous dynamical systems", type = "Preprint", institution = "Vienna University of Technology", address = "Vienna, Austria", year = "2003", bibdate = "Sat Feb 16 17:18:18 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @TechReport{Berger:2004:DDU, author = "A. Berger", title = "Dynamics and digits: on the ubiquity of {Benford's Law}", type = "Preprint", institution = "Institute of Mechanics, Vienna University of Technology", address = "Vienna, Austria", pages = "3", day = "19", month = nov, year = "2004", bibdate = "Sat Feb 16 17:20:58 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf", acknowledgement = ack-nhfb, } @Article{Berger:2005:BLP, author = "Arno Berger", title = "{Benford}'s law in power-like dynamical systems", journal = j-STOCH-DYNAM, volume = "5", number = "4", pages = "587--607", year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.1142/S0219493705001602", ISSN = "0219-4937", ISSN-L = "0219-4937", MRclass = "37B55 (11K06 37A50 37E05)", MRnumber = "2185507 (2008i:37029)", MRreviewer = "Peter Raith", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Stoch. Dyn.", fjournal = "Stochastics and Dynamics", } @InCollection{Berger:2005:DDU, author = "A. Berger", booktitle = "{EQUADIFF} 2003", title = "Dynamics and digits: on the ubiquity of {Benford}'s law", publisher = "World Sci. Publ., Hackensack, NJ", pages = "693--695", year = "2005", DOI = "http://dx.doi.org/10.1142/9789812702067_0115", MRclass = "37A45 (11K55)", MRnumber = "2185113", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Berger:2005:MDD, author = "Arno Berger", title = "Multi-dimensional dynamical systems and {Benford}'s law", journal = j-DISCRETE-CONTIN-DYN-SYST, volume = "13", number = "1", pages = "219--237", year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.3934/dcds.2005.13.219", ISSN = "1078-0947 (print), 1553-5231 (electronic)", ISSN-L = "1078-0947", MRclass = "37A45 (11K36 28D05 37A50 60F05)", MRnumber = "2128801 (2005m:37016)", MRreviewer = "Reinhard Winkler", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Discrete and Continuous Dynamical Systems. Series A", } @Article{Berger:2005:ODD, author = "Arno Berger and Leonid A. Bunimovich and Theodore P. Hill", title = "One-dimensional dynamical systems and {Benford}'s law", journal = j-TRANS-AM-MATH-SOC, volume = "357", number = "1", pages = "197--219", year = "2005", CODEN = "TAMTAM", DOI = "http://dx.doi.org/10.1090/S0002-9947-04-03455-5", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "37A45 (11K06 37A50 37E05 60F05 82B05)", MRnumber = "2098092 (2005m:37017)", MRreviewer = "Peter Raith", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", } @Article{Berger:2007:DMN, author = "A. Berger and S. Siegmund", title = "On the distribution of mantissae in nonautonomous difference equations", journal = j-J-DIFFERENCE-EQU-APPL, volume = "13", number = "8--9", pages = "829--845", month = "????", year = "2007", CODEN = "JDEAEA", DOI = "http://dx.doi.org/10.1080/10236190701388039", ISSN = "1023-6198 (print), 1563-5120 (electronic)", ISSN-L = "1023-6198", MRclass = "37A45 (37B55 39A11)", MRnumber = "2343033 (2008j:37010)", MRreviewer = "Reinhard Winkler", bibdate = "Tue Feb 19 09:37:52 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Second Memorial Issue in Honour of Bernd Aulbach.", URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Difference Equations and Applications", journal-URL = "http://www.informaworld.com/1023-6198", } @Article{Berger:2007:NMO, author = "Arno Berger and Theodore P. Hill", title = "{Newton}'s Method Obeys {Benford}'s Law", journal = j-AMER-MATH-MONTHLY, volume = "114", number = "7", pages = "588--601", month = aug # "\slash " # sep, year = "2007", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "65G50 (37N30)", MRnumber = "2341322 (2008h:65016)", MRreviewer = "Uwe Sch{\"a}fer", bibdate = "Mon Jan 30 12:00:29 MST 2012", bibsource = "http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i27642270; http://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/27642274", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", } @TechReport{Berger:2009:BOB, author = "A. Berger and T. P. Hill", title = "{Benford} Online Bibliography", institution = "Department of Mathematical and Statistical Sciences, University of Alberta", address = "Edmonton, AB, Canada", year = "2009", bibdate = "Sat Nov 12 16:48:00 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.benfordonline.net", acknowledgement = ack-nhfb, remark = "According to \cite{Berger:2011:BLS}, the authors' online bibliography contains more than 600 references.", } @TechReport{Berger:2010:FFFa, author = "A. Berger and T. P. Hill", title = "Fundamental Flaws in {Feller}'s Classical Derivation of {Benford's Law}", type = "Preprint", institution = "Department of Mathematical and Statistical Sciences, University of Alberta", address = "Edmonton, AB, Canada", pages = "8", year = "2010", bibdate = "Mon Feb 18 17:31:57 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf", abstract = "Feller's classic text \booktitle{An Introduction to Probability Theory and its Applications} \cite{Feller:1968:IPT} contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition (`large spread') for a random variable $X$ to be approximately Benford distributed, that is, for $ \log_{10} X $ to be approximately uniformly distributed modulo one. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious basic errors. Concrete examples and a new inequality clearly demonstrate that large spread (or large spread on a logarithmic scale) does not imply that a random variable is approximately Benford distributed, for any reasonable definition of `spread' or measure of dispersion.", acknowledgement = ack-nhfb, } @Article{Berger:2010:FFFb, author = "Arno Berger and Theodore P. Hill", title = "Fundamental Flaws in {Feller}'s Classical Derivation of {Benford's Law}", journal = "ArXiv e-prints", month = may, year = "2010", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 18:23:13 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B; http://arxiv.org/abs/1005.2598", abstract = "Feller's classic text \booktitle{An Introduction to Probability Theory and its Applications} \cite{Feller:1968:IPT} contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition (`large spread') for a random variable $X$ to be approximately Benford distributed, that is, for $ \log_{10}X $ to be approximately uniformly distributed modulo one. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious basic errors. Concrete examples and a new inequality clearly demonstrate that large spread (or large spread on a logarithmic scale) does not imply that a random variable is approximately Benford distributed, for any reasonable definition of `spread' or measure of dispersion", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1005.2598", keywords = "Mathematics - Probability, Mathematics - Statistics, 62Axx", primaryclass = "math.PR", } @TechReport{Berger:2010:LSD, author = "A. Berger", title = "Large Spread Does Not Imply {Benford's Law}", type = "Preprint", institution = "Department of Mathematical and Statistical Sciences, University of Alberta", address = "Edmonton, AB, Canada", year = "2010", bibdate = "Sat Nov 12 16:46:10 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.math.ualberta.ca/~aberger/Publications.html", acknowledgement = ack-nhfb, } @Article{Berger:2011:BLS, author = "Arno Berger and Theodore P. Hill", title = "{Benford}'s law strikes back: no simple explanation in sight for mathematical gem", journal = j-MATH-INTEL, volume = "33", number = "1", pages = "85--91", month = mar, year = "2011", CODEN = "MAINDC", DOI = "http://dx.doi.org/10.1007/s00283-010-9182-3", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "62A99 (60E05)", MRnumber = "2774458", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat2010.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See letter \cite{Hill:2011:LEB}.", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", } @Article{Berger:2011:BTB, author = "Arno Berger and Theodore P. Hill", title = "A basic theory of {Benford's Law}", journal = j-PROBAB-SURV, volume = "8", pages = "1--126", year = "2011", CODEN = "????", DOI = "http://dx.doi.org/10.1214/11-PS175", ISSN = "1549-5787", ISSN-L = "1549-5787", bibdate = "Tue Nov 15 11:07:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.ps/1311860830", abstract = "Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits and significands, often referred to as {\em Benford's Law\/} (BL) or, in a special case, as the {\em First Digit Law}. The invariance properties that characterize BL are developed in detail. Special attention is given to the emergence of BL in a wide variety of deterministic and random processes. Though mainly expository in nature, the article also provides strengthened versions of, and simplified proofs for, many key results in the literature. Numerous intriguing problems for future research arise naturally.", acknowledgement = ack-nhfb, fjournal = "Probabability Surveys", keywords = "base-invariance; Benford's Law; difference equation; mixture of distributions; random probability measure; scale-invariance; shadowing; significant digits; sum-invariance; uniform distribution mod 1", } @Article{Berger:2011:FSM, author = "Arno Berger and Theodore P. Hill and Bahar Kaynar and Ad Ridder", title = "Finite-state {Markov} Chains Obey {Benford's Law}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "32", number = "3", pages = "665--684", month = "????", year = "2011", CODEN = "SJMAEL", DOI = "http://dx.doi.org/10.1137/100789890", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Wed Aug 24 11:18:18 MDT 2011", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "July 21, 2011", } @Article{Berger:2011:SDP, author = "Arno Berger", title = "Some dynamical properties of {Benford} sequences", journal = j-J-DIFFERENCE-EQU-APPL, volume = "17", number = "2", pages = "137--159", year = "2011", CODEN = "JDEAEA", DOI = "http://dx.doi.org/10.1080/10236198.2010.549012", ISSN = "1023-6198 (print), 1563-5120 (electronic)", ISSN-L = "1023-6198", MRclass = "37A45 (11K06 37Bxx)", MRnumber = "2783341", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012", acknowledgement = ack-nhfb, ajournal = "J. Difference Equ. Appl.", fjournal = "Journal of Difference Equations and Applications", journal-URL = "http://www.informaworld.com/1023-6198", } @InProceedings{Berinde:2009:SOH, author = "Radu Berinde and Graham Cormode and Piotr Indyk and Martin J. Strauss", title = "Space-optimal heavy hitters with strong error bounds", crossref = "Paredaens:2009:PTE", pages = "157--166", year = "2009", DOI = "http://doi.acm.org/10.1145/1559795.1559819", bibdate = "Thu Jul 2 14:05:34 MDT 2009", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "The problem of finding heavy hitters and approximating the frequencies of items is at the heart of many problems in data stream analysis. It has been observed that several proposed solutions to this problem can outperform their worst-case guarantees on real data. This leads to the question of whether some stronger bounds can be guaranteed. We answer this in the positive by showing that a class of `counter-based algorithms' (including the popular and very space-efficient FREQUENT and SPACESAVING algorithms) provide much stronger approximation guarantees than previously known. Specifically, we show that errors in the approximation of individual elements do not depend on the frequencies of the most frequent elements, but only on the frequency of the remaining `tail.' This shows that counter-based methods are the most space-efficient (in fact, space-optimal) algorithms having this strong error bound.\par This tail guarantee allows these algorithms to solve the `sparse recovery' problem. Here, the goal is to recover a faithful representation of the vector of frequencies, $f$. We prove that using space $ O(k) $, the algorithms construct an approximation $ f* $ to the frequency vector $f$ so that the L1 error $ ||f - f*||_1 $ is close to the best possible error $ \hbox {min}_{f_2} || f_2 - f ||_1 $, where $f$ 2 ranges over all vectors with at most $k$ non-zero entries. This improves the previously best known space bound of about $ O(k \log n) $ for streams without element deletions (where $n$ is the size of the domain from which stream elements are drawn). Other consequences of the tail guarantees are results for skewed (Zipfian) data, and guarantees for accuracy of merging multiple summarized streams.", acknowledgement = ack-nhfb, keywords = "frequency estimation; heavy hitters; streaming algorithms", } @Article{Bernhardsson:2011:PPM, author = "Sebastian Bernhardsson and Seung Ki Baek and Petter Minnhagen", title = "A paradoxical property of the monkey book", journal = j-J-STAT-MECH-THEORY-EXP, volume = "2011", number = "??", pages = "P07013", month = jul, year = "2011", CODEN = "JSMTC6", DOI = "http://dx.doi.org/10.1088/1742-5468/2011/07/P07013", ISSN = "1742-5468", ISSN-L = "1742-5468", bibdate = "Mon Nov 21 21:57:13 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1103.2681; http://iopscience.iop.org/1742-5468/2011/07/P07013/", abstract = "A `monkey book' is a book consisting of a random sequence of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book to real books. It is shown that the word distribution statistics for the monkey book is different and quite distinct from a typical real book. In particular, the monkey book obeys Heaps' power law to an extraordinarily good approximation, in contrast to the word distributions for real books, which deviate from Heaps' law in a characteristic way. This discrepancy is traced to the different properties of a `spiked' distribution and its smooth envelope. The somewhat counter-intuitive conclusion is that a `monkey book' obeys Heaps' power law precisely because its word-frequency distribution is not a smooth power law, contrary to the expectation based on simple mathematical arguments that if one is a power law, so is the other.", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Mechanics: Theory and Experiment", keywords = "Heaps' Law", } @Article{Bernik:2007:BLA, author = "V. I. Bernik and N. I. Kalosha", title = "{Benford}'s law and the approximation of logarithms of natural numbers by rational numbers", journal = "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser. F{\=\i}z.-Mat. Navuk", volume = "??", number = "3", pages = "68--73, 127", year = "2007", CODEN = "????", ISSN = "0002-3574", ISSN-L = "0002-3574", MRclass = "11J83 (11A63 11K36)", MRnumber = "2398318 (2008j:11084)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Vests{\=\i} Natsyyanal\cprime na{\u\i} Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya Natsional\cprime no{\u\i} Akademii Nauk Belarusi. Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series", } @Article{Berton:1995:HGT, author = "L. Berton", title = "He's Got their Number. {Scholar} Uses Math to Foil Financial Fraud", journal = j-WALL-ST-J, volume = "??", number = "??", pages = "??--??", day = "10", month = jul, year = "1995", CODEN = "WSJOAF", ISSN = "0099-9660", ISSN-L = "0099-9660", bibdate = "Sat Dec 10 11:17:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Wall Street Journal", } @Article{Bethe:1938:MSE, author = "H. A. Bethe and M. E. Rose and L. P. Smith", title = "The Multiple Scattering of Electrons", journal = j-PROC-AMER-PHIL-SOC, volume = "78", number = "4", pages = "573--585", month = mar, year = "1938", CODEN = "PAPCAA", ISSN = "0003-049X", ISSN-L = "0003-049X", bibdate = "Wed Nov 23 14:27:52 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper, which immediately follows Benford's \cite{Benford:1938:LAN} in this journal issue, is reported in \cite[p. 197]{Logan:1978:FDP} to have been of considerable interest to scientists involved in secret nuclear physics work in World War II. That is how Benford's paper ``in a journal of rather limited circulation and not usually read by mathematicians'' came to be noticed by physicists.", URL = "http://www.jstor.org/stable/984803", acknowledgement = ack-nhfb, author-dates = "Hans Albrecht Bethe (1906--2005)", fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", remark = "Biography supplement in \cite{Lee:2007:HAB} has this as Proc. Am. Philos. Soc., 89, 373--383 (1938), but that seems to be wrong: check??", } @InProceedings{Bhattacharya:2002:KBT, author = "S. Bhattacharya", editor = "????", booktitle = "9th World Congress of Accounting Historians, Deakin University, Melbourne, Australia July 30--August 3, 2002", title = "From {Kautilya} to {Benford} --- Trends in Forensic and Investigative Accounting", publisher = "Accounting Association of Australia and New Zealand", address = "????", pages = "??--??", year = "2002", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:22:29 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "http://ach.sagepub.com/", remark = "I cannot find the published proceedings in online catalogs or bookstores, or in the Deakin University library catalogs. Where only selected papers published from the conference in the journal Accounting History??", review-doi = "http://dx.doi.org/10.1177/103237320200700207", review-url = "http://dro.deakin.edu.au/view/DU:30012663; http://www.highbeam.com/doc/1G1-97484707.html", } @Article{Bhattacharya:2005:CPA, author = "Sukanto Bhattacharya and Kuldeep Kumar and Florentin Smarandache", title = "Conditional probability of actually detecting a financial fraud --- a neutrosophic extension to {Benford}'s law", journal = "International Journal of Applied Mathematics", volume = "17", number = "1", pages = "7--14", year = "2005", CODEN = "????", ISSN = "1311-1728", MRclass = "62G10 (91B28)", MRnumber = "2170667", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math/0504520", abstract = "This study actually draws from and builds on an earlier paper (Kumar and Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to the problem of determining the conditional probability that a financial fraud has been actually committed, given that no Type I error occurred while rejecting the null hypothesis H0: The observed first-digit frequencies approximate a Benford distribution; and accepting the alternative hypothesis H1: The observed first-digit frequencies do not approximate a Benford distribution. We have also suggested a conceptual model to implement such a neutrosophic fraud detection system.", acknowledgement = ack-nhfb, ajournal = "Int. J. Appl. Math.", fjournal = "International Journal of Applied Mathematics", } @Article{Bhattacharya:2008:FAB, author = "S. Bhattacharya and K. Kumar", title = "Forensic Accounting and {Benford's Law} [In the Spotlight]", journal = j-IEEE-SIGNAL-PROCESS-MAG, volume = "25", number = "2", pages = "152--150", month = mar, year = "2008", CODEN = "ISPRE6", DOI = "http://dx.doi.org/10.1109/MSP.2007.914724", ISSN = "1053-5888 (print), 1558-0792 (electronic)", ISSN-L = "1053-5888", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008ISPM...25..152B", acknowledgement = ack-nhfb, fjournal = "IEEE signal processing magazine", } @Article{Bhattacharya:2011:ABA, author = "Sukanto Bhattacharya and Dongming Xu and Kuldeep Kumar", title = "An {ANN}-based auditor decision support system using {Benford}'s law", journal = j-DEC-SUPP-SYS, volume = "50", number = "3", pages = "576--584", month = feb, year = "2011", CODEN = "DSSYDK", DOI = "http://dx.doi.org/10.1016/j.dss.2010.08.011", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001351", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "Benford's Law", } @Article{Bhattacharyya:2005:COP, author = "P. Bhattacharyya and A. Chatterjee and B. K. Chakrabarti", title = "A common origin of the power law distributions in models of market and earthquake", journal = "ArXiv e-prints", year = "2005", bibdate = "Sat Feb 16 17:25:18 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/physics/0510038", acknowledgement = ack-nhfb, } @Article{Billera:1976:PSC, author = "Louis J. Billera and Robert E. Bixby", title = "{Pareto} Surfaces of Complexity $1$", journal = j-SIAM-J-APPL-MATH, volume = "30", number = "1", pages = "81--89", month = jan, year = "1976", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, classification = "B0250 (Combinatorial mathematics); C1160 (Combinatorial mathematics)", corpsource = "Dept. of Math., Cornell Univ., Ithaca, NY, USA", fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", keywords = "1-commodity representation; attainable sets; complexity 1; game theory; graph theory; Pareto surfaces; set theory", treatment = "T Theoretical or Mathematical", } @Book{Blackwell:1954:TGS, author = "David Blackwell and Meyer A. Girshick", title = "Theory of Games and Statistical Decisions", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xi + 355", year = "1954", LCCN = "QA269 .B5", bibdate = "Mon Nov 14 10:04:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://catalog.hathitrust.org/Record/000577721", acknowledgement = ack-nhfb, author-dates = "David Blackwell (1919--2010)", keywords = "Benford's Law", remark = "Brief mention of Benford's Law on page 74, problem 2.7.2 (??).", } @Article{Blank:2000:PLC, author = "Aharon Blank and Sorin Solomon", title = "Power laws in cities population, financial markets and {Internet} sites (scaling in systems with a variable number of components)", journal = j-PHYSICA-A, volume = "287", number = "1--2", pages = "279--288", day = "15", month = nov, year = "2000", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(00)00464-7", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 06:24:21 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437100004647", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Blasius:2009:ZLP, author = "Bernd Blasius and Ralf T{\"o}njes", title = "{Zipf's Law} in the Popularity Distribution of Chess Openings", journal = j-PHYS-REV-LET, volume = "103", number = "21", pages = "218701", day = "16", month = nov, year = "2009", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.103.218701", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", pagecount = "4", } @Article{Block:2010:GEB, author = "Henry W. Block and Thomas H. Savits", title = "A General Example for {Benford} Data", journal = j-AMER-STAT, volume = "64", number = "4", pages = "335--339", month = nov, year = "2010", CODEN = "ASTAAJ", DOI = "http://dx.doi.org/10.1198/tast.2010.09169", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2758565", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; http://www.math.utah.edu/pub/tex/bib/amstat.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Benford's Law deals, among other things, with the proportion of numbers whose first significant digit is a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first significant digit $1$ ) in a variety of datasets. In these datasets, which arise in various compendiums or as mixtures of various sets of numbers, the proportion of numbers with first significant digit one is $ 0.3010 $ which is much higher than the commonsense value of $ 1 / 9 $. The reasons for this occurrence have been elusive. Mathematical attempts to explain this phenomenon have been relatively fruitless. Methods involving probability have been somewhat more successful. In this article we give some simple reasons for this occurrence and also give an example of a general mixture of distributions which exactly satisfies this Law. Various other examples and counterexamples are also given.", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Blum:1970:SID, author = "M. Blum", title = "On the Sums of Independently Distributed {Pareto} Variates", journal = j-SIAM-J-APPL-MATH, volume = "19", number = "1", pages = "191--198", month = jul, year = "1970", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Article{Bohachevsky:2006:DBL, author = "Ihor O. Bohachevsky and Mark E. Johnson and Myron L. Stein", title = "A derivation of {Benford}'s law", journal = j-AM-J-MATH-MANAGE-SCI, volume = "26", number = "3--4", pages = "355--370", year = "2006", CODEN = "AMMSDX", ISSN = "0196-6324", ISSN-L = "0196-6324", MRclass = "60E99 (11K36)", MRnumber = "2312400 (2008h:60062)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Journal of Mathematical and Management Sciences", } @Book{Bologna:1995:FAF, author = "Jack Bologna and Robert J. Lindquist", title = "Fraud auditing and forensic accounting: new tools and techniques", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "xv + 249", year = "1995", ISBN = "0-471-10646-1 (hardcover)", ISBN-13 = "978-0-471-10646-3 (hardcover)", LCCN = "HV8079.W47 B65 1995", bibdate = "Tue Nov 22 10:31:53 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/bios/wiley042/95005510.html; http://www.loc.gov/catdir/description/wiley033/95005510.html; http://www.loc.gov/catdir/toc/onix04/95005510.html", acknowledgement = ack-nhfb, remark = "This book does not discuss Benford's Law, but may be helpful background for application of that law to the detection of fraud.", subject = "white collar crime investigation; United States; forensic accounting; fraud investigation", } @Article{Bolton:2002:SFD, author = "Richard J. Bolton and David J. Hand", title = "Statistical Fraud Detection: A Review", journal = j-STAT-SCI, volume = "17", number = "3", pages = "235--255", month = aug, year = "2002", CODEN = "STSCEP", ISSN = "0883-4237", ISSN-L = "0883-4237", bibdate = "Fri May 30 12:48:50 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/statsci.bib", URL = "http://projecteuclid.org/euclid.ss/1042727940", acknowledgement = ack-nhfb, fjournal = "Statistical Science", journal-URL = "http://projecteuclid.org/all/euclid.ss", } @Article{Bonache:2010:DFL, author = "A. B. Bonache and K. Moris and J. Maurice", title = "{D}{\'e}tection de fraudes et loi de {Benford}: Quelques risques associ{\'e}s. ({French}) [{Fraud} detection and {Benford}'s law: Some risks]", journal = "Revue Fran{\c{c}}aise de Comptabilit{\'e}", volume = "??", number = "431", pages = "24--27", month = apr, year = "2010", CODEN = "????", DOI = "????", ISSN = "0484-8764", ISSN-L = "0484-8764", bibdate = "Mon Feb 18 17:33:12 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", acknowledgement = ack-nhfb, journal-URL = "http://www.experts-comptables.fr/csoec/Publications/RFC", language = "French", } @Article{Boring:1920:LNL, author = "Edwin G. Boring", title = "The Logic of the Normal Law of Error in Mental Measurement", journal = j-AMER-J-PSYCHOLOGY, volume = "31", number = "1", pages = "1--33", month = jan, year = "1920", CODEN = "AJPCAA", ISSN = "0002-9556 (print), 1939-8298 (electronic)", ISSN-L = "0002-9556", bibdate = "Thu Dec 01 21:35:43 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/1413989", acknowledgement = ack-nhfb, fjournal = "The American journal of psychology", remark = "A citation search in Google Scholar on 1-Dec-2011 found this article as the only one citing Newcomb's work \cite{Newcomb:1881:NFU} before it was brought to wider view by Raimi's frequently-cited paper \cite{Raimi:1976:FDP}. Boring's article has only brief mention of Newcomb's work, and then solely in connection with the believed randomness of digits of transcendental numbers.", } @Article{Boroda:1984:ZML, author = "M. G. Boroda and A. A. Polikarpov", title = "The {Zipf--Mandelbrot} law and units of different levels of text organization", journal = "Tartu Riikl. {\"U}l. Toimetised", volume = "??", number = "689", pages = "35--60", year = "1984", CODEN = "????", ISSN = "????", MRclass = "92A25", MRnumber = "781731 (86c:92030)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta et Commentationes Universitatis Tartuensis", } @Article{Bose:2011:QMD, author = "Indranil Bose and Selwyn Piramuthu and Michael J. Shaw", title = "Quantitative methods for Detection of Financial Fraud", journal = j-DEC-SUPP-SYS, volume = "50", number = "3", pages = "557--558", month = feb, year = "2011", CODEN = "DSSYDK", DOI = "http://dx.doi.org/10.1016/j.dss.2010.08.005", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001296", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "Benford's Law", } @Article{Boyle:1994:AFS, author = "Jeff Boyle", title = "An application of {Fourier} series to the most significant digit problem", journal = j-AMER-MATH-MONTHLY, volume = "101", number = "9", pages = "879--886", month = nov, year = "1994", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "60F99", MRnumber = "1 300 493", bibdate = "Wed Dec 3 17:17:33 MST 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", } @Article{Bradford:1934:SIS, author = "Samuel C. Bradford", title = "Sources of Information on Specific Subjects", journal = "Engineering: An Illustrated Weekly Journal (London)", volume = "137", number = "??", pages = "85--86", day = "26", month = jan, year = "1934", CODEN = "????", ISSN = "????", bibdate = "Fri Nov 25 11:47:10 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper (reprinted in \cite{Bradford:1985:SIS}) introduces an observation later known as Bradford's Law: there are exponentially-diminishing returns of extending a search for references in journals.", URL = "http://en.wikipedia.org/wiki/Bradford%27s_law", acknowledgement = ack-nhfb, } @Article{Bradford:1985:SIS, author = "Samuel C. Bradford", title = "Sources of Information on Specific Subjects", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "10", number = "4", pages = "173--180", month = oct, year = "1985", CODEN = "JISCDI", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Fri Nov 25 11:49:58 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reprint of \cite{Bradford:1934:SIS}, the source of Bradford's Law.", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", } @Article{Bradley:2009:WBL, author = "Jonathan R. Bradley and David L. Farnsworth", title = "What Is {Benford's Law}?", journal = "Teaching Statistics", volume = "31", number = "1", pages = "2--6", month = jan, year = "2009", CODEN = "????", DOI = "http://dx.doi.org/10.1111/j.1467-9639.2009.00347.x", ISSN = "0141-982X (print), 1467-9639 (electronic)", ISSN-L = "0141-982X", bibdate = "Mon Nov 14 17:09:33 MST 2011", bibsource = "http://onlinelibrary.wiley.com/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Class activity; First significant digit; Goodness of fit; Teaching", onlinedate = "6 Jan 2009", } @Article{Brady:1978:MBL, author = "W. G. Brady", title = "More on {Benford}'s Law", journal = j-FIB-QUART, volume = "16", number = "1", pages = "51--52", month = feb, year = "1978", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:59:24 MDT 2011", bibsource = "http://www.fq.math.ca/16-1.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @InCollection{Brahler:2010:EMS, author = "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena Emke", booktitle = "{Ilmenauer Schriften zur Betriebswirtschaftslehre}. ({German}) [{Illmenauer} writings on economics]", title = "{Der Einsatz mathematisch-statistischer Methoden in der digitalen Betriebspr{\"u}fung}. ({German}) [{The} use of mathematical and statistical methods in the digital audit]", volume = "4/2010", publisher = "Verlag proWiWi e.V.", address = "Ilmenau, Germany", pages = "48", month = apr, year = "2010", ISBN = "3-940882-23-2", ISBN-13 = "978-3-940882-23-3", ISSN = "1866-2145 (print), 2192-4643 (electronic)", LCCN = "????", bibdate = "Mon Feb 18 17:35:58 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf", acknowledgement = ack-nhfb, language = "German", } @InCollection{Brahler:2011:BGS, author = "Gernot Br{\"a}hler and Markus Bensmann and Hans-Ralph Jakobi", editor = "????", booktitle = "Ilmenauer Schriften zur Betriebswirtschaftslehre", title = "{Das Benfordsche Gesetz und seine Anwendbarkeit bei der digitalen Pr{\"u}fung von Fahrtenb{\"u}chern}. ({German}) [{The} {Benford} law and its applicability in the digital examination of logbooks]", volume = "3/2011", publisher = "Verlag proWiWi e.V.", address = "Ilmenau, Germany", pages = "??--??", month = mar, year = "2011", ISBN = "3-940882-28-3", ISBN-13 = "978-3-940882-28-8", ISSN = "1866-2145 (print), 2192-4643 (electronic)", LCCN = "????", bibdate = "Mon Feb 18 18:21:29 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.econstor.eu/dspace/bitstream/10419/55703/1/662518055.pdf", acknowledgement = ack-nhfb, language = "German", } @Article{Brakman:1999:RZT, author = "Steven Brakman and Harry Garretsen and Charles {Van Marrewijk} and Marianne {Van Den Berg}", title = "The Return of {Zipf}: Towards a Further Understanding of the Rank--Size Distribution", journal = j-J-REG-SCI, volume = "39", number = "1", pages = "183--213", year = "1999", DOI = "http://dx.doi.org/10.1111/1467-9787.00129", ISSN = "0022-4146 (print), 1467-9787 (electronic)", ISSN-L = "0022-4146", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Regional Science", } @Article{Brambilla:1976:DDA, author = "Francisco Brambilla", title = "La distribuzione delle aziende secondo le dimensioni. {Verifica} empirica della legge logonormale e di quella di {Zipf} e nuovi modelli interpretativi. ({Italian}) [{The} distribution of firms by size. {Empirical} test of the log-normal law and {Zipf}'s law and new models of interpretation]", journal = "Giornale degli Economisti e Annali de Economia (Nuova Serie)", volume = "35", number = "3--4", pages = "131--153, 235", month = mar # "\slash " # apr, year = "1976", CODEN = "????", ISSN = "0017-0097", ISSN-L = "0017-0097", MRclass = "90A15", MRnumber = "0452510 (56 \#10789)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/23242834", acknowledgement = ack-nhfb, ajournal = "Giorn. Econom. Ann. Econom. (N.S.)", fjournal = "Giornale degli Economisti e Annali de Economia", language = "Italian", } @Article{Bravo-Marquez:2010:HLM, author = "Felipe Bravo-Marquez and Gaston L'Huillier and Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez", title = "Hypergeometric Language Model and {Zipf}-Like Scoring Function for {Web} Document Similarity Retrieval", journal = j-LECT-NOTES-COMP-SCI, volume = "6393", pages = "303--308", year = "2010", CODEN = "LNCSD9", DOI = "http://dx.doi.org/10.1007/978-3-642-16321-0_32", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:49:42 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32", acknowledgement = ack-nhfb, book-DOI = "http://dx.doi.org/10.1007/978-3-642-16321-0", book-URL = "http://www.springerlink.com/content/978-3-642-16321-0", fjournal = "Lecture Notes in Computer Science", } @Article{Breunig:2011:SEI, author = "Christian Breunig and Achim Goerres", title = "Searching for electoral irregularities in an established democracy: Applying {Benford's Law} tests to {Bundestag} elections in {Unified Germany}", journal = j-ELECT-STUDIES, volume = "30", number = "3", pages = "534--545", month = sep, year = "2011", CODEN = "????", DOI = "http://dx.doi.org/10.1016/j.electstud.2011.03.005", ISSN = "0261-3794 (print), 1873-6890 (electronic)", ISSN-L = "0261-3794", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0261379411000370", acknowledgement = ack-nhfb, fjournal = "Electoral Studies", keywords = "Benford's Law", } @Article{Brookes:1977:TBL, author = "Bertram C. Brookes", title = "Theory of the {Bradford Law}", journal = j-J-DOC, volume = "33", number = "3", pages = "180--209", month = "????", year = "1977", CODEN = "JDOCAS", DOI = "http://dx.doi.org/10.1108/eb026641", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:16:18 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", } @Article{Brookes:1978:FRD, author = "Bertram C. Brookes and Jos{\'e} M. Griffiths", title = "Frequency-rank distributions", journal = j-J-AM-SOC-INF-SCI, volume = "29", number = "1", pages = "5--13", month = jan, year = "1978", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/asi.4630290104", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 10:40:13 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1980:FISa, author = "Bertram C. Brookes", title = "The foundations of information science. {Part I}. {Philosophical} aspects", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "2", number = "3--4", pages = "125--133", month = jun, year = "1980", CODEN = "JISCDI", DOI = "http://dx.doi.org/10.1177/016555158000200302", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 10:36:18 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/2/3-4/125.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1980:FISb, author = "Bertram C. Brookes", title = "The foundations of information science. {Part II}. {Quantitative} aspects: classes of things and the challenge of human individuality", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "2", number = "5", pages = "209--221", month = oct, year = "1980", CODEN = "JISCDI", DOI = "http://dx.doi.org/10.1177/016555158000200502", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 11:01:20 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/2/5/209.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1980:FISc, author = "Bertram C. Brookes", title = "The foundations of information science. {Part III}. {Quantitative} aspects: Objective maps and subjective landscapes", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "2", number = "6", pages = "269--275", month = dec, year = "1980", CODEN = "JISCDI", DOI = "http://dx.doi.org/10.1177/016555158000200602", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 10:36:18 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/2/6/269.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1981:FIS, author = "Bertram C. Brookes", title = "The foundations of information science. {Part IV}. {Information} science: the changing paradigm", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "3", number = "1", pages = "3--12", month = feb, year = "1981", CODEN = "JISCDI", DOI = "http://dx.doi.org/10.1177/016555158100300102", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 10:36:18 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/3/1/3", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1984:RTE, author = "Bertram C. Brookes", title = "Ranking techniques and the empirical log law", journal = j-INFO-PROC-MAN, volume = "20", number = "1--2", pages = "37--46", month = "????", year = "1984", CODEN = "IPMADK", DOI = "http://dx.doi.org/10.1016/0306-4573(84)90038-4", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Mon Feb 25 10:38:32 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0306457384900384", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brown:1970:MOU, author = "J. L. {Brown, Jr.} and R. L. Duncan", title = "Modulo One Uniform Distribution of the Sequence of Logarithms of Certain Recursive Sequences", journal = j-FIB-QUART, volume = "8", number = "5", pages = "482--486", month = dec, year = "1970", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:31 MDT 2011", bibsource = "http://www.fq.math.ca/8-5.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", note = "See remark \cite{Kuipers:1973:RPD}.", URL = "http://www.fq.math.ca/Scanned/8-5/brown.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Brown:2005:BLS, author = "Richard J. C. Brown", title = "{Benford}'s law and the screening of analytical data: the case of pollutant concentrations in ambient air", journal = j-ANALYST, volume = "130", number = "9", pages = "1280--1285", month = "????", year = "2005", CODEN = "ANALAO", DOI = "http://dx.doi.org/10.1039/B504462F", ISSN = "0003-2654 (print), 1364-5528 (electronic)", ISSN-L = "0003-2654", bibdate = "Sat Feb 16 17:27:51 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ncbi.nlm.nih.gov/pubmed/16096674", acknowledgement = ack-nhfb, fjournal = "The Analyst", } @Article{Brown:2007:UZL, author = "R. J. C. Brown", title = "The use of {Zipf}'s law in the screening of analytical data: a step beyond {Benford}", journal = j-ANALYST, volume = "132", number = "4", pages = "344", year = "2007", CODEN = "ANALAO", DOI = "http://dx.doi.org/10.1039/b618255k", ISSN = "0003-2654 (print), 1364-5528 (electronic)", ISSN-L = "0003-2654", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2007Ana...132..344B", abstract = "This study shows for the first time the effectiveness of Zipf's law in screening analytical data sets for outliers, data formatting and data transcription errors, particularly when the data sets are small. In the case of pollutant concentrations in ambient air, the multivariate nature of the measurement, and the relationship between the measured values of these multivariant quantities are the characteristics that allow a Zipf's law approach to data screening to be successful. Furthermore, it has been shown that Zipf's law has advantages over other novel data screening techniques, such as Benford's law, in terms of sensitivity and scope", acknowledgement = ack-nhfb, fjournal = "The Analyst", } @Article{Browne:1998:FBL, author = "Malcolm W. Browne", title = "Following {Benford's Law}, or Looking Out for {No. 1}", journal = j-NY-TIMES, volume = "??", number = "??", pages = "F4--F4", day = "4", month = aug, year = "1998", CODEN = "NYTIAO", ISSN = "0362-4331 (print), 1542-667X, 1553-8095", ISSN-L = "0362-4331", bibdate = "Sat Feb 16 14:29:48 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Science section.", URL = "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1", acknowledgement = ack-nhfb, fjournal = "New York Times", journal-URL = "http://www.nytimes.com/", } @Article{Buck:1993:IBF, author = "B. Buck and A. C. Merchant and S. M. Perez", title = "An illustration of {Benford}'s first digit law using alpha decay half lives", journal = j-EUR-J-PHYS, volume = "14", number = "2", pages = "59--63", month = "????", year = "1993", CODEN = "EJPHD4", ISSN = "0143-0807 (print), 1361-6404 (electronic)", ISSN-L = "0143-0807", bibdate = "Mon Nov 14 17:32:53 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/1993EJPh...14...59B", acknowledgement = ack-nhfb, fjournal = "European Journal of Physics", } @TechReport{Bul:2011:BGG, author = "K. Bul", title = "{Das Benford'sche Gesetz}. ({German}) [{Benford's Law}]", type = "Working paper", institution = "Max-von-Laue-gymnasium", address = "Koblenz, Germany", year = "2011", bibdate = "Fri Mar 22 08:44:32 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", language = "German", } @Article{Bumby:1969:FAM, author = "R. Bumby and E. Ellentuck", title = "Finitely additive measures and the first digit problem", journal = j-FUNDAM-MATH, volume = "65", number = "??", pages = "33--42", month = "????", year = "1969", CODEN = "????", ISSN = "0016-2736", ISSN-L = "0016-2736", bibdate = "Sat Nov 12 16:19:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Fundamenta mathematicae", } @Article{Bunt:1984:MPL, author = "Richard B. Bunt and Jennifer M. Murphy and Shikharesh Majumdar", title = "A measure of program locality and its application", journal = j-SIGMETRICS, volume = "12", number = "3", pages = "28--40", month = aug, year = "1984", CODEN = "????", DOI = "http://doi.acm.org/10.1145/1031382.809311", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Thu Jun 26 11:00:50 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "Although the phenomenon of locality has long been recognized as the single most important characteristic of program behaviour, relatively little work has been done in attempting to measure it. Recent work has led to the development of an intrinsic measure of program locality based on the Bradford--Zipf distribution. Potential applications for such a measure are many, and include the evaluation of program restructuring methods (manual and automatic), the prediction of system performance, the validation of program behaviour models, and the enhanced understanding of the phenomena that characterize program behaviour. A consideration of each of these areas is given in connection with the proposed measure, both to increase confidence in the validity of the measure and to illustrate a methodology for dealing with such problems.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", } @Article{Burgos:1996:ZSB, author = "Javier D. Burgos and Pedro Moreno-Tovar", title = "{Zipf}-scaling behavior in the immune system", journal = j-BIOSYSTEMS, volume = "39", number = "3", pages = "227--232", day = "15", month = nov, year = "1996", CODEN = "BSYMBO", DOI = "http://dx.doi.org/10.1016/0303-2647(96)01618-8", ISSN = "0303-2647 (print), 1872-8324 (electronic)", ISSN-L = "0303-2647", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0303264796016188", acknowledgement = ack-nhfb, fjournal = "Biosystems (A6E)", keywords = "Zipf's Law", } @Article{Burke:1991:BLP, author = "John Burke and Eric Kincanon", title = "{Benford}'s law and physical constants: The distribution of initial digits", journal = j-AMER-J-PHYSICS, volume = "59", number = "10", pages = "952--952", month = oct, year = "1991", CODEN = "AJPIAS", DOI = "http://dx.doi.org/10.1119/1.16838", ISSN = "0002-9505 (print), 1943-2909 (electronic)", ISSN-L = "0002-9505", bibdate = "Mon Nov 14 17:31:11 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B; http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1", acknowledgement = ack-nhfb, fjournal = "American Journal of Physics", } @InProceedings{Burns:2009:SSR, author = "B. D. Burns", editor = "N. Taatgen and H. van Rijn", booktitle = "{Proceedings of the Thirty-First Annual Conference of the Cognitive Science Society, Cognitive Science Society, Austin, TX}", title = "Sensitivity to Statistical Regularities: People (Largely) Follow {Benford's Law}", publisher = "????", address = "????", pages = "2872--2877", year = "2009", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Nov 18 11:57:33 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @TechReport{Busta:1992:TRN, author = "B. Busta and R. Sundheim", title = "Tax return numbers tend to obey {Benford}'s law", type = "Working Paper", number = "W93-106-94", institution = "Center for Business Research, St. Cloud State University", address = "St. Cloud, MN, USA", year = "1992", bibdate = "Sat Feb 16 17:29:47 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Busta:1998:UBL, author = "Bruce Busta and Randy Weinberg", title = "Using {Benford's Law} and Neural Networks as a Review Procedure", journal = "Managerial Auditing Journal", volume = "13", number = "6", pages = "356--366", month = "????", year = "1998", CODEN = "????", DOI = "http://dx.doi.org/10.1108/02686909810222375", ISSN = "0268-6902 (print), 1758-7735 (electronic)", ISSN-L = "0268-6902", bibdate = "Tue Nov 22 18:50:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Campanario:2011:BLC, author = "Juan Campanario and Mar{\'\i}a Coslado", title = "{Benford}'s law and citations, articles and impact factors of scientific journals", journal = j-SCIENTOMETRICS, volume = "88", number = "2", pages = "421--432", month = aug, year = "2011", CODEN = "SCNTDX", DOI = "http://dx.doi.org/10.1007/s11192-011-0387-9", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Fri Nov 25 10:43:36 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Scientometrics", } @Article{Campanino:1996:IIM, author = "Massimo Campanino and Stefano Isola", title = "Infinite invariant measures for non-uniformly expanding transformations of $ [0, 1] $: Weak law of large numbers with anomalous scaling", journal = j-FORUM-MATH, volume = "8", number = "1", pages = "71--92", year = "1996", CODEN = "FOMAEF", DOI = "http://dx.doi.org/10.1515/form.1996.8.71", ISSN = "0933-7741 (print), 1435-5337 (electronic)", ISSN-L = "0933-7741", bibdate = "Sat Nov 12 10:33:06 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0837.60022", abstract = "We consider a class of maps of $ [0, 1] $ with an indifferent fixed point at 0 and expanding everywhere else. Using the invariant ergodic probability measure of a suitable, everywhere expanding, induced transformation we are able to study the infinite invariant measure of the original map in some detail. Given a continuous function with compact support in $]0, 1]$, we prove that its time averages satisfy a `weak law of large numbers' with anomalous scaling $ n / \log n $ and give an upper bound for the decay of correlations.", acknowledgement = ack-nhfb, ajournal = "Forum Math.", classmath = "60F05 (Weak limit theorems) 28D05 (Measure-preserving transformations) 37A99 (Ergodic theory)", fjournal = "Forum Mathematicum", keywords = "decay of correlations; invariant ergodic probability measure; weak law of large numbers", } @Article{Campi:2005:ZLM, author = "X. Campi and H. Krivine", title = "{Zipf}'s law in multifragmentation", journal = j-PHYS-REV-C, volume = "72", number = "??", pages = "057602", day = "30", month = nov, year = "2005", CODEN = "PRVCAN", DOI = "http://dx.doi.org/10.1103/PhysRevC.72.057602", ISSN = "0556-2813 (print), 1089-490X, 1538-4497", ISSN-L = "0556-2813", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevC.72.057602", acknowledgement = ack-nhfb, fjournal = "Physical Review C (Nuclear Physics)", journal-URL = "http://prc.aps.org/browse", keywords = "Zipf's Law", } @Article{Canessa:2003:TAFa, author = "Enrique Canessa", title = "Theory of Analogous Force on Number Sets", journal = "ArXiv e-prints", year = "2003", bibdate = "Mon Nov 21 06:56:01 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/cond-mat/0307703", abstract = "A general statistical thermodynamic theory that considers given sequences of $x$-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions $ p_x $ for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering $ p_x $ to describe complex phenomena, the theory leads to derive a distinct analogous force $ f_x $ on number sets proportional to $ (\frac {\partial p_x}{\partial x})_T $ at an analogous system temperature $T$. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.", acknowledgement = ack-nhfb, remark = "To appear in Phys. A.", } @Article{Canessa:2003:TAFb, author = "Enrique Canessa", title = "Theory of analogous force on number sets", journal = j-PHYSICA-A, volume = "328", number = "1--2", pages = "44--52", month = oct, year = "2003", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(03)00526-0", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0378437103005260", abstract = "A general statistical thermodynamic theory that considers given sequences of $x$-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions $ p_x $ for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering $ p_x $ to describe complex phenomena, the theory leads to derive a distinct analogous force $ f_x $ on number sets proportional to $ (\partial p_x / \partial x)T $ at an analogous system temperature $T$. In particular, this leads to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.", acknowledgement = ack-nhfb, fjournal = "Physica A: Statistical Mechanics and its Applications", keywords = "Benford's Law; Fibonacci numbers; prime numbers", } @Article{Cantu:2011:FDA, author = "F. Cantu and S. M. Saiegh", title = "Fraudulent Democracy? {An} Analysis of {Argentina}'s Infamous Decade Using Supervised Machine Learning", journal = j-POLIT-ANAL, volume = "19", number = "4", pages = "409--433", month = "Autumn", year = "2011", DOI = "http://dx.doi.org/10.1093/pan/mpr033", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Mon Feb 18 18:24:47 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pan.oxfordjournals.org/content/19/4/409.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", keywords = "Benford's Law", } @Article{Carslow:1988:AIN, author = "C. Carslow", title = "Anomalies in Income Numbers. {Evidence} of Goal Oriented Behavior", journal = j-ACCOUNT-REV, volume = "63", number = "2", pages = "321--327", month = apr, year = "1988", CODEN = "ACRVAS", ISSN = "0001-4826 (print), 1558-7967 (electronic)", ISSN-L = "0001-4826", bibdate = "Sat Dec 10 11:19:33 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/248109", acknowledgement = ack-nhfb, fjournal = "The Accounting Review", keywords = "Benford's Law", remark = "This paper references neither Newcomb nor Benford, but it uses their digit-frequency formula from \cite{Feller:1966:IPT} to compare with data on revenues of New Zealand companies.", } @Article{Cartlidge:2010:NNO, author = "Edwin Cartlidge", title = "In nature, number one dominates", journal = "Institute of Physics, Environmental Research Letters", volume = "??", number = "??", pages = "??--??", day = "25", month = oct, year = "2010", DOI = "????", bibdate = "Mon Feb 18 17:38:16 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://environmentalresearchweb.org/cws/article/news/44124", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Castillo:1997:FGP, author = "Enrique Castillo and Ali S. Hadi", title = "Fitting the Generalized {Pareto} Distribution to Data", journal = j-J-AM-STAT-ASSOC, volume = "92", number = "440", pages = "1609--1620", month = dec, year = "1997", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Oct 30 06:57:36 MST 2000", bibsource = "http://www.amstat.org/publications/jasa/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", URL = "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM; http://www.jstor.org/stable/2965432", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Chacko:2007:EPB, author = "Manoj Chacko and P. Yageen Thomas", title = "Estimation of a Parameter of Bivariate {Pareto} Distribution by Ranked Set Sampling", journal = j-J-APPL-STAT, volume = "34", number = "6", pages = "703--714", year = "2007", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Wed Aug 25 11:41:54 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Article{Chakravorty:2008:TAE, author = "Douglas N. Hales and V. Sridharan and Abirami Radhakrishnan and Satya S. Chakravorty and Samia M. Siha", title = "Testing the accuracy of employee-reported data: An inexpensive alternative approach to traditional methods", journal = j-EUR-J-OPER-RES, volume = "189", number = "3", pages = "583--593", day = "16", month = sep, year = "2008", CODEN = "EJORDT", DOI = "http://dx.doi.org/10.1016/j.ejor.2006.09.092", ISSN = "0377-2217 (print), 1872-6860 (electronic)", ISSN-L = "0377-2217", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702", acknowledgement = ack-nhfb, fjournal = "European Journal of Operational Research", keywords = "Benford's Law", xxauthor = "S. Chakravorty and Samia M. Siha", } @Article{Chakravorty:2009:TBL, author = "S. Chakravorty and V. Sridharan", title = "Testing {Benford's Law} for improving supply chain decision-making: a field experiment", journal = j-DRUG-DISCOVERY-TODAY, volume = "122", number = "2", pages = "606--618", month = dec, year = "2009", CODEN = "DDTOFS", DOI = "http://dx.doi.org/10.1016/j.ijpe.2009.06.017", ISSN = "1359-6446 (print), 1878-5832 (electronic)", ISSN-L = "1359-6446", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163", acknowledgement = ack-nhfb, fjournal = "Drug Discovery Today", keywords = "Benford's Law", } @Article{Challet:2004:BPD, author = "Damien Challet and Andrea Lombardoni", title = "Bug propagation and debugging in asymmetric software structures", journal = j-PHYS-REV-E, volume = "70", number = "4", pages = "046109", month = oct, year = "2004", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.70.046109", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 08:15:07 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.046109; http://pre.aps.org/abstract/PRE/v70/i4/e046109", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", issue = "4", journal-URL = "http://pre.aps.org/browse", keywords = "Linux; Unix; Zipf's Law", pagecount = "5", } @Article{Chang:2011:CGR, author = "Harry M. Chang", title = "Constructing $n$-gram rules for natural language models through exploring the limitation of the {Zipf--Mandelbrot} law", journal = j-COMPUTING, volume = "91", number = "3", pages = "241--264", month = mar, year = "2011", CODEN = "CMPTA2", DOI = "http://dx.doi.org/10.1007/s00607-010-0116-x", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", MRclass = "68T50", MRnumber = "2776088", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241", acknowledgement = ack-nhfb, fjournal = "Computing. Archives for Scientific Computing", journal-URL = "http://link.springer.com/journal/607", } @PhdThesis{Chen:1978:ZL, author = "Wen-Chen Chen", title = "On {Zipf}'s law", type = "Thesis ({Ph.D.})", school = "University of Michigan", address = "Ann Arbor, MI, USA", pages = "114", year = "1978", MRclass = "Thesis", MRnumber = "2627928", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871", acknowledgement = ack-nhfb, remark = "Available from ProQuest LLC, Ann Arbor, MI, USA. Author given name appears as Wen-Cheng in MathSciNet database.", } @Article{Chen:1980:WFZ, author = "Wen Chen Chen", title = "On the weak form of {Zipf}'s law", journal = j-J-APPL-PROBAB, volume = "17", number = "3", pages = "611--622", year = "1980", CODEN = "JPRBAM", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "62E10 (62F10)", MRnumber = "580021 (81m:62021)", MRreviewer = "Patrick L. Brockett", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3212955", ZMnumber = "Zbl 0435.60017", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", } @Article{Chen:1986:RBL, author = "Ye-Sho Chen and Ferdinand F. Leimkuhler", title = "A relationship between {Lotka's Law}, {Bradford's Law}, and {Zipf's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "37", number = "5", pages = "307--314", year = "1986", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO;2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", } @Article{Chen:1987:AZL, author = "Ye-Sho Chen and Ferdinand F. Leimkuhler", title = "Analysis of {Zipf}'s law: An index approach", journal = j-INFO-PROC-MAN, volume = "23", number = "3", pages = "171--182", day = "1", month = apr, year = "1987", CODEN = "IPMADK", DOI = "http://dx.doi.org/10.1016/0306-4573(87)90002-1", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0306457387900021", ZMnumber = "0614.62150", abstract = "A rigorous analysis of Zipf's law is made using an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified. Using this approach, the shape of Zipf-type curves can be described in terms of three distinct regions and two parameters of the Mandelbrot--Zipf law. This result has considerable practical significance, since it provides rigorous foundations for the application of Zipf's law.", acknowledgement = ack-nhfb, classmath = "62P99 (Appl. of statistics)", fjournal = "Information Processing and Management", keywords = "index approach; Mandelbrot-Zipf law; Zipf's law", } @Article{Chen:1989:ZLT, author = "Ye-Sho Chen", title = "{Zipf}'s laws in text modeling", journal = "International Journal of General Systems. Methodology, Applications, Education", volume = "15", number = "3", pages = "233--252", year = "1989", CODEN = "IJGSAX", DOI = "http://dx.doi.org/10.1080/03081078908935048", ISSN = "0308-1079, 1026-7492, 1563-5104", ISSN-L = "0308-1079", MRclass = "92A90", MRnumber = "1015844", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Internat. J. Gen. Systems", fjournal = "International Journal of General Systems. Methodology, Applications, Education", } @Article{Chen:1991:ZLN, author = "Ye-Sho Chen", title = "{Zipf}'s law in natural languages, programming languages, and command languages: the {Simon--Yule} approach", journal = j-INT-J-SYST-SCI, volume = "22", number = "11", pages = "2299--2312", year = "1991", CODEN = "IJSYA9", DOI = "http://dx.doi.org/10.1080/00207729108910791", ISSN = "0020-7721", ISSN-L = "0020-7721", bibdate = "Sat Nov 12 10:50:55 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0793.68020", abstract = "Zipf's law and issues in natural languages, programming languages and command languages related to it, are reviewed. We point out the need for a unified theory to resolve the issues. Based on Herbert Simon's creative process for scientific discovery, we evaluate four leading theories of language generation. As a result, the Simon--Yule model of text generation is selected as a promising theory. The implications of the theory related to the issues in natural languages, programming languages and command languages are discussed.", acknowledgement = ack-nhfb, classmath = "68N15 (Programming languages) 68T50 (Natural language processing)", fjournal = "International Journal of Systems Science", keywords = "command languages; natural languages; programming languages; Simon-Yule model; text generation; Zipf's law", } @Article{Chen:1997:NHS, author = "Weishing Chen and Tai-Hsi Wu", title = "A non-homogeneous software reliability model based on {Zipf}'s law", journal = "International Journal of Quality \& Reliability Management", volume = "14", number = "4", pages = "409--431", month = "????", year = "1997", DOI = "http://dx.doi.org/10.1108/02656719710170666", ISSN = "0265-671X (print), 1758-6682 (electronic)", ISSN-L = "0265-671X", bibdate = "Fri Nov 25 07:08:17 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Chen:2004:MFM, author = "Yanguang Chen and Yixing Zhou", title = "Multi-fractal measures of city-size distributions based on the three-parameter {Zipf} model", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "22", number = "4", pages = "793--805", day = "1", month = nov, year = "2004", CODEN = "CSFOEH", DOI = "http://dx.doi.org/10.1016/j.chaos.2004.02.059", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0960077904001031", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", keywords = "Zipf's Law", } @Article{Chen:2012:MRB, author = "Yanguang Chen", title = "The mathematical relationship between {Zipf}'s law and the hierarchical scaling law", journal = j-PHYSICA-A, volume = "391", number = "11", pages = "3285--3299", day = "1", month = jun, year = "2012", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2011.12.031", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437111009678", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Chen:2012:ZLF, author = "Yanguang Chen", title = "{Zipf}'s law, $ 1 / f $ noise, and fractal hierarchy", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "45", number = "1", pages = "63--73", day = "15", month = jan, year = "2012", CODEN = "CSFOEH", DOI = "http://dx.doi.org/10.1016/j.chaos.2011.10.001", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0960077911001901", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", keywords = "Zipf's Law", } @Article{Chen:2012:ZLH, author = "Yanguang Chen", title = "{Zipf}'s law, hierarchical structure, and cards-shuffling model for urban development", journal = j-DISCRETE-DYN-NAT-SOC, pages = "480196", year = "2012", CODEN = "DDNSFA", DOI = "http://dx.doi.org/10.1155/2012/480196", ISSN = "1026-0226 (print), 1607-887X (electronic)", ISSN-L = "1026-0226", MRclass = "91D10", MRnumber = "2914043", MRreviewer = "Sandra L. Arlinghaus", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Discrete Dyn. Nat. Soc.", fjournal = "Discrete Dynamics in Nature and Society. An International Multidisciplinary Research and Review Journal", pagecount = "21", } @Article{Chida:2011:LSI, author = "Satoshi Chida and Naoto Miyoshi", title = "Limiting size index distributions for ball-bin models with {Zipf}-type frequencies", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "63", number = "4", pages = "745--768", year = "2011", CODEN = "AISXAD", DOI = "http://dx.doi.org/10.1007/s10463-010-0276-7", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", MRclass = "60C05 (60F15 60J27)", MRnumber = "2805906 (2012f:60035)", MRreviewer = "Elvira Di Nardo", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annals of the Institute of Statistical Mathematics (Tokyo)", } @Article{Cho:2007:BBL, author = "Wendy K. Tam Cho and Brian J. Gaines", title = "Breaking the ({Benford}) law: statistical fraud detection in campaign finance", journal = j-AMER-STAT, volume = "61", number = "3", pages = "218--223", month = aug, year = "2007", CODEN = "ASTAAJ", DOI = "http://dx.doi.org/10.1198/000313007X223496", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2393725", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; http://www.math.utah.edu/pub/tex/bib/amstat2000.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496; http://www.tandfonline.com/doi/abs/10.1198/000313007X223496", abstract = "Benford's law is seeing increasing use as a diagnostic tool for isolating pockets of large datasets with irregularities that deserve closer inspection. Popular and academic accounts of campaign finance are rife with tales of corruption, but the complete dataset of transactions for federal campaigns is enormous. Performing a systematic sweep is extremely arduous; hence, these data are a natural candidate for initial screening by comparison to Benford's distributions.", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Chou:2009:BLN, author = "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and Zuozheng Wang and Huan Zheng", title = "{Benford's Law} and Number Selection in Fixed-Odds Numbers Game", journal = j-J-GAMBL-STUD, volume = "25", number = "4", pages = "503--521", month = dec, year = "2009", CODEN = "JGSTEM", DOI = "http://dx.doi.org/10.1007/s10899-009-9145-9", ISSN = "1050-5350 (print), 1573-3602 (electronic)", ISSN-L = "1050-5350", bibdate = "Sat Feb 16 15:35:14 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s10899-009-9145-9", acknowledgement = ack-nhfb, fjournal = "Journal of Gambling Studies", } @Article{Chuang:2009:FPS, author = "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen", title = "Feature-preserved sampling over streaming data", journal = j-TKDD, volume = "2", number = "4", pages = "15:1--15:??", month = jan, year = "2009", CODEN = "????", DOI = "http://doi.acm.org/10.1145/1460797.1460798", ISSN = "1556-4681 (print), 1556-472X (electronic)", ISSN-L = "1556-4681", bibdate = "Fri Apr 24 17:59:51 MDT 2009", bibsource = "http://www.acm.org/pubs/contents/journals/tkdd/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "In this article, we explore a novel sampling model, called {\em feature preserved sampling\/} ({\em FPS\/}) that sequentially generates a high-quality sample over sliding windows. The sampling quality we consider refers to the degree of consistency between the sample proportion and the population proportion of each attribute value in a window. Due to the time-variant nature of real-world datasets, users are more likely to be interested in the most recent data. However, previous works have not been able to generate a high-quality sample over sliding windows that precisely preserves up-to-date population characteristics. Motivated by this shortcoming, we have developed the {\em FPS\/} algorithm, which has several advantages: (1) it sequentially generates a sample from a time-variant data source over sliding windows; (2) the execution time of {\em FPS\/} is linear with respect to the database size; (3) the {\em relative\/} proportional differences between the sample proportions and population proportions of most distinct attribute values are guaranteed to be below a specified error threshold, $ \epsilon $, while the {\em relative\/} proportion differences of the remaining attribute values are as close to $ \epsilon $ as possible, which ensures that the generated sample is of high quality; (4) the sample rate is close to the user specified rate so that a high quality sampling result can be obtained without increasing the sample size; (5) by a thorough analytical and empirical study, we prove that {\em FPS\/} has acceptable space overheads, especially when the attribute values have Zipfian distributions, and {\em FPS\/} can also excellently preserve the population proportion of multivariate features in the sample; and (6) {\em FPS\/} can be applied to infinite streams and finite datasets equally, and the generated samples can be used for various applications. Our experiments on both real and synthetic data validate that {\em FPS\/} can effectively obtain a high quality sample of the desired size. In addition, while using the sample generated by {\em FPS\/} in various mining applications, a significant improvement in efficiency can be achieved without compromising the model's precision.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Knowledge Discovery from Data (TKDD)", keywords = "sampling; Streaming mining", } @Article{Cigler:1961:NET, author = "J. Cigler and G. Helmberg", title = "{Neuere Entwicklungen der Theorie der Gleichverteilung}. ({German}) [{Recent} developments in the theory of uniform distribution]", journal = j-DEUTSCH-MATH-V, volume = "64", number = "??", pages = "1--50", month = "????", year = "1961", CODEN = "????", ISSN = "????", bibdate = "Sat Nov 12 16:33:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Jber. Deutsch. Math.--Verein", language = "German", } @Article{Cigler:1964:MSU, author = "J. Cigler", title = "Methods of summability and uniform distribution $ \bmod 1 $", journal = j-COMPOS-MATH, volume = "16", number = "??", pages = "44--51", year = "1964", CODEN = "CMPMAF", ISSN = "0010-437X (print), 1570-5846 (electronic)", ISSN-L = "0010-437X", bibdate = "Mon Nov 14 10:15:31 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Compositio Mathematica", } @TechReport{Ciofalo:2005:EBF, author = "Michele Ciofalo", title = "Entropy, {Benford}'s first digit law, and the distribution of everything", type = "Report", institution = "Dipartimento di Ingegneria Nucleare, Universit{\`a} degli Studi di Palermo", address = "Palermo, Italy", pages = "34", year = "2005", bibdate = "Sun Feb 17 08:23:55 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf", acknowledgement = ack-nhfb, } @Article{Clark:1977:ESL, author = "Douglas W. Clark and C. Cordell Green", title = "An Empirical Study of List Structure in {Lisp}", journal = j-CACM, volume = "20", number = "2", pages = "78--87", month = feb, year = "1977", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 06:31:28 MST 2001", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Static measurements of the list structure of five large Lisp programs are reported and analyzed. These measurements reveal substantial regularity, or predictability, among pointers to atoms and especially among pointers to lists. Pointers to atoms are found to obey, roughly, Zipf's law, which governs word frequencies in natural languages; pointers to lists usually point to a location physically nearby in memory. The use of such regularities in the space-efficient representation of list structure is discussed.", acknowledgement = ack-nhfb, classcodes = "C6130 (Data handling techniques); C6140D (High level languages)", classification = "723", comment = "Great paper; evidence pro CDR-coding, con fancy CONS", corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", journalabr = "Commun ACM", keywords = "computer programming languages; data processing --- Data Structures; empirical study; LISP; list structure; measurements; regularity", oldlabel = "ClarkG77", treatment = "P Practical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77", } @Article{Clauset:2007:FST, author = "Aaron Clauset and Maxwell Young and Kristian Skrede Gleditsch", title = "On the Frequency of Severe Terrorist Events", journal = j-J-CONFL-RESOLUT, volume = "51", number = "1", pages = "58--87", month = feb, year = "2007", CODEN = "JCFRAL", DOI = "http://dx.doi.org/10.1177/0022002706296157", ISSN = "0022-0027 (print), 1552-8766 (electronic)", ISSN-L = "0022-0027", bibdate = "Thu Nov 24 14:07:17 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jcr.sagepub.com; http://jcr.sagepub.com/content/51/1/58.abstract; http://www.jstor.org/journals/00220027.html", abstract = "In the spirit of Lewis Richardson's original study of the statistics of deadly conflicts, we study the frequency and severity of terrorist attacks worldwide since 1968. We show that these events are uniformly characterized by the phenomenon of ``scale invariance,'' that is, the frequency scales as an inverse power of the severity, $ P(x) \approx x{- \alpha } $. We find that this property is a robust feature of terrorism, persisting when we control for economic development of the target country, the type of weapon used, and even for short time scales. Further, we show that the center of the distribution oscillates slightly with a period of roughly 13 years, that there exist significant temporal correlations in the frequency of severe events, and that current models of event incidence cannot account for these variations or the scale invariance property of global terrorism. Finally, we describe a simple toy model for the generation of these statistics and briefly discuss its implications.", acknowledgement = ack-nhfb, fjournal = "Journal of Conflict Resolution", } @Article{Clauset:2007:PLD, author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman", title = "Power-law distributions in empirical data", journal = "ArXiv Physics e-prints", day = "7", month = jun, year = "2007", bibdate = "Thu Feb 28 08:52:43 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "arXiv:0706.1062.", URL = "http://arxiv.org/abs/0706.1062v1", acknowledgement = ack-nhfb, pagecount = "27", } @Article{Clauset:2007:PLDa, author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman", title = "Power-law distributions in empirical data", journal = "ArXiv Physics e-prints", day = "2", month = feb, year = "2009", DOI = "http://dx.doi.org/10.1137/070710111", bibdate = "Thu Feb 28 08:52:43 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "arXiv:0706.1062.", URL = "http://arxiv.org/abs/0706.1062v1", acknowledgement = ack-nhfb, pagecount = "43", } @Article{Clauset:2009:PLDb, author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman", title = "Power-Law Distributions in Empirical Data", journal = j-SIAM-REVIEW, volume = "51", number = "4", pages = "661--703", month = "????", year = "2009", CODEN = "SIREAD", DOI = "http://dx.doi.org/10.1137/070710111", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Mon May 17 17:56:49 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Cleary:2005:ADA, author = "Richard Cleary and Jay C. Thibodeau", title = "Applying Digital Analysis Using {Benford's Law} to Detect Fraud: The Dangers of Type {I} Errors", journal = j-AUDITING, volume = "24", number = "1", pages = "77--81", month = may, year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.2308/aud.2005.24.1.77", ISSN = "0278-0380 (print), 1558-7991 (electronic)", ISSN-L = "0278-0380", bibdate = "Tue Nov 15 09:17:46 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://aaapubs.org/loi/ajpt; http://link.aip.org/link/AJPTXX/v24/i1/p77/s1", acknowledgement = ack-nhfb, fjournal = "Auditing: A Journal of Practice \& Theory", } @Article{Clippe:2012:BLT, author = "Paulette Clippe and Marcel Ausloos", title = "{Benford}'s law and {Theil} transform of financial data", journal = j-PHYSICA-A, volume = "391", number = "24", pages = "6556--6567", day = "15", month = dec, year = "2012", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2012.07.063", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Thu Feb 14 05:56:39 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437112007546", acknowledgement = ack-nhfb, fjournal = "Physica A: Statistical Mechanics and its Applications", } @Article{Coderre:1999:FDU, author = "David Coderre", title = "Fraud Detection Using Digital Analysis", journal = j-EDPACS, volume = "27", number = "3", pages = "1--8", month = "????", year = "1999", CODEN = "EDPCDF", DOI = "http://dx.doi.org/10.1201/1079/43249.27.3.19990901/30268.1", ISSN = "0736-6981 (print), 1936-1009 (electronic)", ISSN-L = "0736-6981", bibdate = "Sat Jan 07 09:20:49 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1", acknowledgement = ack-nhfb, fjournal = "EDPACS", keywords = "Benford's Law", onlinedate = "21 Dec 2006", } @Article{Cohen:1976:EFD, author = "Daniel I. A. Cohen", title = "An explanation of the first digit phenomenon", journal = j-J-COMB-THEORY-A, volume = "20", number = "3", pages = "367--370", month = may, year = "1976", CODEN = "JCBTA7", ISSN = "0097-3165", ISSN-L = "0097-3165", bibdate = "Thu Feb 15 16:29:51 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Combinatorial Theory (Series A)", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Cohen:1984:PNF, author = "D. I. A. Cohen and T. M. Katz", title = "Prime numbers and the first digit phenomenon", journal = j-J-NUMBER-THEORY, volume = "18", number = "3", pages = "261--268", month = jun, year = "1984", CODEN = "JNUTA9", DOI = "http://dx.doi.org/10.1016/0022-314X(84)90061-1", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Fri Nov 25 13:58:58 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Number Theory", } @Article{Cohen:2005:PCL, author = "Edith Cohen and Carsten Lund", title = "Packet classification in large {ISPs}: design and evaluation of decision tree classifiers", journal = j-SIGMETRICS, volume = "33", number = "1", pages = "73--84", month = jun, year = "2005", CODEN = "????", DOI = "http://doi.acm.org/10.1145/1064212.1064222", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Fri Jun 27 09:21:27 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "Packet classification, although extensively studied, is an evolving problem. Growing and changing needs necessitate the use of larger filters with more complex rules. The increased complexity and size pose implementation challenges on current hardware solutions and drive the development of software classifiers, in particular, decision-tree based classifiers. Important performance measures for these classifiers are time and memory due to required high throughput and use of limited fast memory. We analyze Tier 1 ISP data that includes filters and corresponding traffic from over a hundred edge routers and thousands of interfaces. We provide a comprehensive view on packet classification in an operational network and glean insights that help us design more effective classification algorithms. We propose and evaluate decision tree classifiers with {\em common branches}. These classifiers have linear worst-case memory bounds and require much less memory than standard decision tree classifiers, but nonetheless, we show that on our data have similar average and worst-case time performance. We argue that common-branches exploit structure that is present in real-life data sets. We observe a strong Zipf-like pattern in the usage of rules in a classifier, where a very small number of rules resolves the bulk of traffic and most rules are essentially never used. Inspired by this observation, we propose {\em traffic-aware\/} classifiers that obtain superior average-case and bounded worst-case performance. Good average-case can boost performance of software classifiers that can be used in small to medium sized routers and are also important for traffic analysis and traffic engineering.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "access control lists; decision trees; packet filtering; routing", } @Article{Coile:1977:LFD, author = "Russell C. Coile", title = "{Lotka}'s Frequency Distribution of Scientific Productivity", journal = j-J-AM-SOC-INF-SCI, volume = "28", number = "6", pages = "366--370", month = nov, year = "1977", CODEN = "AISJB6", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 08:08:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", keywords = "Lotka's Law", } @Article{Condon:1928:SV, author = "E. U. Condon", title = "Statistics of vocabulary", journal = j-SCIENCE, volume = "67", number = "1733", pages = "300--??", day = "16", month = mar, year = "1928", CODEN = "SCIEAS", DOI = "http://dx.doi.org/10.1126/science.67.1733.300", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Fri Nov 25 09:04:50 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", } @Article{Cong:2004:WTP, author = "Lin Cong and Zhipeng Li", title = "On {Wilson}'s theorem and {Polignac} conjecture", journal = "ArXiv e-prints", day = "2", month = aug, year = "2004", bibdate = "Mon Feb 18 07:03:53 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math.NT/0408018", abstract = "We introduce Wilson's theorem and Clement's result and present a necessary and sufficient condition for $p$ and $ p + 2 k $ to be primes where $k$ is a positive integer. By using Simiov's Theorem, we derive an improved version of Clement's result and characterizations of Polignac twin primes which parallel previous characterizations.", acknowledgement = ack-nhfb, } @Misc{Conway:2010:CFM, author = "D. Conway", title = "{Benford's Law} Tests for {Wikileaks} Data", howpublished = "Zero Intelligence Agents website.", day = "1", month = aug, year = "2010", bibdate = "Mon Feb 18 17:39:45 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.drewconway.com/zia/?p=2234", acknowledgement = ack-nhfb, } @InCollection{Corazza:2010:CFM, author = "Marco Corazza and Andrea Ellero and Alberto Zorzi", booktitle = "Mathematical and statistical methods for actuarial sciences and finance", title = "Checking financial markets via {Benford}'s law: the {S\&P 500} case", publisher = "Springer Italia", address = "Milan, Italy", pages = "93--102", year = "2010", DOI = "http://dx.doi.org/10.1007/978-88-470-1481-7_10", MRclass = "62P05", MRnumber = "2676191", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Corominas-Murtra:2010:UZL, author = "Bernat Corominas-Murtra and Ricard V. Sol{\'e}", title = "Universality of {Zipf}'s law", journal = j-PHYS-REV-E, volume = "82", number = "1", pages = "011102", day = "1", month = jul, year = "2010", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.82.011102", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", MRclass = "82B03 (62B10)", MRnumber = "2736361 (2011j:82002)", MRreviewer = "N. N. Ganikhodjaev", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.011102", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "9", } @Article{Corominas-Murtra:2011:EZL, author = "Bernat Corominas-Murtra and Jordi Fortuny and Ricard V. Sol{\'e}", title = "Emergence of {Zipf}'s law in the evolution of communication", journal = j-PHYS-REV-E, volume = "83", number = "1", pages = "036115", day = "28", month = mar, year = "2011", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.83.036115", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.83.036115", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "9", } @Article{Costas:2008:NCC, author = "Eduardo Costas and Victoria L{\'o}pez-Rodas and F. Javier Toro and Antonio Flores-Moya", title = "The number of cells in colonies of the cyanobacterium {{\em Microcystis aeruginosa\/}} satisfies {Benford}'s law", journal = j-AQUAT-BOT, volume = "89", number = "3", pages = "341--343", month = oct, year = "2008", CODEN = "AQBODS", DOI = "http://dx.doi.org/10.1016/j.aquabot.2008.03.011", ISSN = "0304-3770 (print), 1879-1522 (electronic)", ISSN-L = "0304-3770", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0304377008000533", acknowledgement = ack-nhfb, fjournal = "Aquatic Botany", keywords = "Benford's Law", } @Article{Courtland:2010:CML, author = "Rachel Courtland", title = "Curious mathematical law is rife in nature", journal = j-NEW-SCIENTIST, volume = "208", number = "2782", pages = "10--10", day = "16", month = oct, year = "2010", CODEN = "NWSCAL", DOI = "http://dx.doi.org/10.1016/S0262-4079(10)62497-9", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0262407910624979", acknowledgement = ack-nhfb, fjournal = "The New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law; earthquake detection", xxISSN = "0262-4079, 0028-6664", } @Article{Cristelli:2012:TMT, author = "Matthieu Cristelli and Michael Batty and Luciano Pietronero", title = "There is More than a Power Law in {Zipf}", journal = j-SCI-REP, volume = "2", number = "??", pages = "1--7", month = nov, year = "2012", CODEN = "SRCEC3", DOI = "http://dx.doi.org/10.1038/srep00812", ISSN = "2045-2322", ISSN-L = "2045-2322", bibdate = "Tue Feb 26 07:32:11 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/srep/2012/121108/srep00812/full/srep00812.html", accepted = "28 August 2012", acknowledgement = ack-nhfb, articleno = "812", fjournal = "Scientific Reports", onlinedate = "08 November 2012", received = "15 August 2012", } @Article{Czirok:1995:CBS, author = "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo Havlin and H. Eugene Stanley", title = "Correlations in binary sequences and a generalized {Zipf} analysis", journal = j-PHYS-REV-E, volume = "52", number = "??", pages = "446--??", day = "1", month = jul, year = "1995", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.52.446", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.446", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Czirok:1996:POP, author = "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and Tam{\'a}s Vicsek", title = "Possible origin of power-law behavior in $n$-tuple {Zipf} analysis", journal = j-PHYS-REV-E, volume = "53", number = "??", pages = "6371--??", day = "1", month = jun, year = "1996", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.53.6371", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.6371", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Dahui:2005:TRZ, author = "Wang Dahui and Li Menghui and Di Zengru", title = "True reason for {Zipf}'s law in language", journal = j-PHYSICA-A, volume = "358", number = "2--4", pages = "545--550", day = "15", month = dec, year = "2005", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2005.04.021", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437105004085", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @InProceedings{Dallacasa:2006:TBS, author = "F. Dallacasa and Valerio Dallacasa", editor = "????", booktitle = "{5th International Conference: APLIMAT 2006, Slovak University of Technology, Bratislava}", title = "Temporal behaviour of stock data from {Benford}'s law", publisher = "????", address = "????", pages = "425--432", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:32:15 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", price = "US\$", URL = "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf", acknowledgement = ack-nhfb, } @Article{Davis:1976:SRI, author = "Basil Davis", title = "Some Remarks on Initial Digits", journal = j-FIB-QUART, volume = "14", number = "1", pages = "13--14", month = feb, year = "1976", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:59:05 MDT 2011", bibsource = "http://www.fq.math.ca/14-1.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/14-1/davis.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Deakin:1993:ADB, author = "Michael A. B. Deakin", title = "Another derivation of {Benford}'s law", journal = j-AUSTRALIAN-MATH-SOC-GAZ, volume = "20", number = "5", pages = "162--163", year = "1993", CODEN = "????", ISSN = "0311-0729", ISSN-L = "0311-0729", MRclass = "11K36", MRnumber = "1268513 (95j:11072)", MRreviewer = "Jean-Loup Mauclaire", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Australian Mathematical Society Gazette", } @Article{Debreceny:2010:DMJ, author = "S. Debreceny and Glen L. Gray", title = "Data mining journal entries for fraud detection: An exploratory study", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "11", number = "3", pages = "157--181", month = sep, year = "2010", CODEN = "IJAIA7", DOI = "http://dx.doi.org/10.1016/j.accinf.2010.08.001", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "See discussion \cite{Grabski:2010:DDM,Kriel:2010:DDM}.", URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000540; http://www.sciencedirect.com/science/journal/14670895", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Benford's Law", } @Article{DeCeuster:1998:HPB, author = "M. J. K. DeCeuster and G. Dhaene and T. Schatteman", title = "On the hypothesis of psychological barriers in stock markets and {Benford}'s law", journal = j-J-EMPIR-FINANCE, volume = "5", number = "3", pages = "263--279", month = sep, year = "1998", CODEN = "JEFIEC", DOI = "http://dx.doi.org/10.1016/S0927-5398(97)00024-8", ISSN = "0927-5398 (print), 1879-1727 (electronic)", ISSN-L = "0927-5398", bibdate = "Sun Nov 13 11:33:46 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0927539897000248", acknowledgement = ack-nhfb, fjournal = "Journal of Empirical Finance", } @Article{Decker:2007:GPC, author = "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E. Moses", title = "Global Patterns of City Size Distributions and Their Fundamental Drivers", journal = j-PLOS-ONE, volume = "2", number = "9", pages = "e934", month = sep, year = "2007", CODEN = "POLNCL", DOI = "http://dx.doi.org/10.1371/journal.pone.0000934", ISSN = "1932-6203", bibdate = "Wed Feb 27 06:29:22 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0000934", abstract = "Urban areas and their voracious appetites are increasingly dominating the flows of energy and materials around the globe. Understanding the size distribution and dynamics of urban areas is vital if we are to manage their growth and mitigate their negative impacts on global ecosystems. For over 50 years, city size distributions have been assumed to universally follow a power function, and many theories have been put forth to explain what has become known as Zipf's law (the instance where the exponent of the power function equals unity). Most previous studies, however, only include the largest cities that comprise the tail of the distribution. Here we show that national, regional and continental city size distributions, whether based on census data or inferred from cluster areas of remotely-sensed nighttime lights, are in fact lognormally distributed through the majority of cities and only approach power functions for the largest cities in the distribution tails. To explore generating processes, we use a simple model incorporating only two basic human dynamics, migration and reproduction, that nonetheless generates distributions very similar to those found empirically. Our results suggest that macroscopic patterns of human settlements may be far more constrained by fundamental ecological principles than more fine-scale socioeconomic factors.", acknowledgement = ack-nhfb, fjournal = "PLoS One", keywords = "Zipf's Law", pagecount = "6", } @TechReport{Deckert:2010:IBL, author = "Joseph Deckert and Mikhail Myagkov and Peter C. Ordeshook", title = "The Irrelevance of {Benford's Law} for Detecting Fraud in Elections", type = "{CALTECH} working paper", number = "9", institution = "California Institute of Technology", address = "Pasadena, CA, USA", pages = "27", day = "9", month = mar, year = "2010", bibdate = "Mon Feb 18 17:40:53 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://vote.caltech.edu/drupal/node/327", acknowledgement = ack-nhfb, remark = "From the abstract: ``..., we argue here that Benford's Law is essentially useless as a forensic indicator of fraud.''", } @Article{Deckert:2011:BLD, author = "Joseph Deckert and Mikhail Myagkov and Peter C. Ordeshook", title = "{Benford's Law} and the Detection of Election Fraud", journal = j-POLIT-ANAL, volume = "19", number = "3", pages = "245--268", month = "Summer", year = "2011", DOI = "http://dx.doi.org/10.1093/pan/mpr014", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Mon Feb 18 18:26:03 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mebane:2011:CBL} for a rebuttal.", URL = "http://pan.oxfordjournals.org/content/19/3/245.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", remark = "The authors argue that application of Benford's Law tests to election results to detect fraud is inconclusive and ``essentially equivalent to a toss of a coin''.", } @InProceedings{DelAcebo:2005:BLN, author = "Esteve {Del Acebo} and Mateu Sbert", title = "{Benford's Law} for Natural and Synthetic Images", crossref = "Neumann:2005:CAE", pages = "169--176", year = "2005", DOI = "http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176", bibdate = "Tue Nov 15 08:46:47 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf", acknowledgement = ack-nhfb, } @Article{Deligny:2010:RRL, author = "H. Deligny and P. Jolissaint", title = "Relations de r{\'e}currence lin{\'e}aires, primitivit{\'e} et loi de {Benford}. ({French}) [{Linear} recurrence relations, primitivity, and {Benford's Law}]", journal = "ArXiv e-prints", day = "23", month = jul, year = "2010", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 18:14:51 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D; http://arxiv.org/abs/1007.5349", abstract = "We prove that many sequences of positive numbers $ (a_n) $ defined by finite linear difference equations $ a_{n + k} = c_{k - 1} a_{n + k - 1} + \ldots {} + c_0 a_n $ with suitable nonnegative reals coefficients $ c_i $ satisfy Benford's Law on the first digit in many bases $ b > 2 $. Our techniques rely on Perron--Frobenius theory via the companion matrix of the characteristic polynomial of the defining equation.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1007.5349", keywords = "Mathematics - Dynamical Systems, Mathematics - Rings and Algebras, 11A99", language = "French", primaryclass = "math.DS", } @Article{Deligny:2013:RRL, author = "Hugues Deligny and Paul Jolissaint", title = "Relations de r{\'e}currence lin{\'e}aires, primitivit{\'e} et loi de {Benford}. ({French}) [{Linear} recurrence relations, primitivity, and {Benford}'s law]", journal = j-ELEM-MATH, volume = "68", number = "1", pages = "9--21", year = "2013", DOI = "http://dx.doi.org/10.4171/EM/213", ISSN = "0013-6018 (print), 1420-8962 (electronic)", ISSN-L = "0013-6018", MRnumber = "3016461", bibdate = "Thu Feb 14 07:02:03 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elemente der Mathematik", language = "French", } @Article{Denisov:1997:FBS, author = "S. Denisov", title = "Fractal binary sequences: {Tsallis} thermodynamics and the {Zipf} law", journal = j-PHYS-LET-A, volume = "235", number = "5", pages = "447--451", day = "17", month = nov, year = "1997", CODEN = "PYLAAG", DOI = "http://dx.doi.org/10.1016/S0375-9601(97)00688-9", ISSN = "0375-9601 (print), 1873-2429 (electronic)", ISSN-L = "0375-9601", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0375960197006889", acknowledgement = ack-nhfb, fjournal = "Physics Letters A", journal-URL = "http://www.sciencedirect.com/science/journal/03759601", keywords = "Zipf's Law", } @Article{Depken:2008:BZB, author = "Craig A. {Depken II}", title = "{Benford}, {Zipf} and the blogosphere", journal = j-APPL-ECON-LETT, volume = "15", number = "9", pages = "689--692", month = "????", year = "2008", DOI = "http://dx.doi.org/10.1080/13504850600735270", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Sat Jan 07 09:18:33 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", onlinedate = "04 Jul 2008", } @Article{Devooght:1957:LZM, author = "J. Devooght", title = "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the {Zipf--Mandelbrot} law]", journal = "Acad. Roy. Belg. Bull. Cl. Sci. (5)", volume = "43", pages = "244--251", year = "1957", CODEN = "????", ISSN = "0001-4141", ISSN-L = "0001-4141", MRclass = "94.0X", MRnumber = "0088412 (19,516a)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe des Sciences. Koninklijke Belgische Academie. Mededelingen van de Klasse der Wetenschappen. 5e S{\'e}rie", language = "French", } @TechReport{Diaconis:1973:LMI, author = "Persi Diaconis", title = "Limits of measures of the integers with applications to random number generators and the distribution of leading digits", type = "Memorandum", number = "NS-211", institution = "Department of Statistics, Harvard University", address = "Cambridge, MA, USA", day = "22", month = mar, year = "1973", bibdate = "Sat Nov 12 16:23:20 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @PhdThesis{Diaconis:1974:WSA, author = "Persi Diaconis", title = "Weak and Strong Averages in probability and the theory numbers", type = "{Ph.D.} thesis", school = "Department of Statistics, Harvard University", address = "Cambridge, MA, USA", pages = "xvii + 117", year = "1974", bibdate = "Mon Nov 14 10:26:03 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Diaconis:1977:DLD, author = "Persi Diaconis", title = "The distribution of leading digits and uniform distribution $ \bmod 1 $", journal = j-ANN-PROBAB, volume = "5", number = "1", pages = "72--81", month = feb, year = "1977", CODEN = "APBYAE", DOI = "http://dx.doi.org/10.1214/aop/1176995891", ISSN = "0091-1798", ISSN-L = "0091-1798", bibdate = "Sun Apr 20 10:44:17 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/annprobab1970.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.aop/1176995891", acknowledgement = ack-nhfb, fjournal = "Annals of Probability", journal-URL = "http://projecteuclid.org/all/euclid.aop", keywords = "Benford's Law", } @Article{Diaconis:1979:RP, author = "Persi Diaconis and David Freedman", title = "On Rounding Percentages", journal = j-J-AM-STAT-ASSOC, volume = "74", number = "366", pages = "359--364", month = jun, year = "1979", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Nov 23 11:24:59 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "The authors extend prior work on correctness of sums of rounded percentages \cite{Mosteller:1967:DSR}, and criticize biased rounding practices in \cite{Benford:1938:LAN}.", URL = "http://www.jstor.org/stable/2284288", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", keywords = "Benford's Law", remark = "When percentage-column entries are rounded, their sum may differ from 100\%. The authors use a prior proof \cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded values, the probability of a correct sum is $ \sqrt {6 / (\pi n)} \approx 1.382 / \sqrt {n} $. They show that rounding may produce large changes in computed chi-squared values, and they conclude their article with this recommendation: ``it is important to calculate with many-digit accuracy when computing $ \chi^2 $ for large sample sizes.''", } @TechReport{Diekmann:2002:DFM, author = "Andreas Diekmann", title = "{Diagnose von Fehlerquellen und methodische Qualit{\"a}t in der sozialwissenschaftlichen Forschung}. ({German}) [{Diagnosis} of errors and methodological quality in social science research]", type = "Report", number = "ITA-02-04", institution = "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung", address = "Vienna, Austria", pages = "????", year = "2002", bibdate = "Thu Nov 17 19:11:00 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @TechReport{Diekmann:2004:DEE, author = "Andreas Diekmann", title = "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit der Benford Verteilung}. ({German}) [{Data} falsification. {Results} from experiments with the {Benford} distribution]", type = "Report", institution = "ETH Z{\"u}rich", address = "Z{\"u}rich, Switzerland", year = "2004", bibdate = "Fri Nov 18 12:09:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @TechReport{Diekmann:2004:FDU, author = "Andreas Diekmann", title = "Not the First Digit! {Using} {Benford's Law} to Detect Fraudulent Scientific Data", type = "Report", institution = "ETH Z{\"u}rich", address = "Z{\"u}rich, Switzerland", pages = "26", month = oct, year = "2004", bibdate = "Sat Dec 10 11:12:29 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf", abstract = "Digits in statistical data produced by natural or social processes are often distributed in a manner described by ``Benford's law''. Recently, a test against this distribution was used to identify fraudulent accounting data. This test is based on the supposition that real data follow the Benford distribution while fabricated data do not. Is it possible to apply Benford tests to detect fabricated or falsified scientific data as well as fraudulent financial data? We approached this question in two ways. First, we examined the use of the Benford distribution as a standard by checking digit frequencies in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). These experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, the digits of the published regression coefficients were approximately Benford distributed. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first and more on the second and higher-digits", acknowledgement = ack-nhfb, } @Article{Diekmann:2007:FDU, author = "Andreas Diekmann", title = "Not the First Digit! {Using} {Benford's Law} to Detect Fraudulent Scientific Data", journal = j-J-APPL-STAT, volume = "34", number = "3--4", pages = "321--329", year = "2007", CODEN = "????", DOI = "http://dx.doi.org/10.1080/02664760601004940", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", MRnumber = "2380543", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", URL = "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940", abstract = "Digits in statistical data produced by natural or social processes are often distributed in a manner described by `Benford's law'. Recently, a test against this distribution was used to identify fraudulent accounting data. This test is based on the supposition that first, second, third, and other digits in real data follow the Benford distribution while the digits in fabricated data do not. Is it possible to apply Benford tests to detect fabricated or falsified scientific data as well as fraudulent financial data? We approached this question in two ways. First, we examined the use of the Benford distribution as a standard by checking the frequencies of the nine possible first and ten possible second digits in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). The digits in these experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, both digits of the published regression coefficients were approximately Benford distributed or at least followed a pattern of monotonic decline. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. Surprisingly, first digits of faked data also exhibited a pattern of monotonic decline, while second, third, and fourth digits were distributed less in accordance with Benford's law. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first (i.e., leftmost) and more on later digits.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", keywords = "Benford's Law; data fabrication; digital analysis; distribution of digits from regression coefficients; first digit law; Zipf's Law", } @Article{Diekmann:2010:BLF, author = "Andreas Diekmann and Ben Jann", title = "{Benford's Law} and Fraud Detection: Facts and Legends", journal = j-GER-ECON-REV, volume = "11", number = "3", pages = "397--401", month = aug, year = "2010", CODEN = "????", DOI = "http://dx.doi.org/10.1111/j.1468-0475.2010.00510.x", ISSN = "1465-6485 (print), 1468-0475 (electronic)", ISSN-L = "1465-6485", bibdate = "Mon Nov 14 17:09:33 MST 2011", bibsource = "http://onlinelibrary.wiley.com/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "German Economic Review", keywords = "Benford's law; false negative; false positive; fraud detection; regression coefficients", onlinedate = "6 Apr 2010", } @Article{Diekmann:2012:MUB, author = "Andreas Diekmann", title = "Making Use of ``{Benford's Law}'' for the Randomized Response Technique", journal = j-SOC-METH-RES, volume = "41", number = "2", pages = "325--334", month = may, year = "2012", DOI = "http://dx.doi.org/10.1177/0049124112452525", ISSN = "0049-1241 (print), 1552-8294 (electronic)", ISSN-L = "0049-1241", bibdate = "Mon Feb 18 19:03:24 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://smr.sagepub.com/content/41/2/325; http://www.socio.ethz.ch/news/Diekmann_Benford_RRT_SMR_2012.pdf", acknowledgement = ack-nhfb, fjournal = "Sociological Methods and Research", } @Article{diGiovanni:2013:FET, author = "Julian di Giovanni and Andrei A. Levchenko", title = "Firm entry, trade, and welfare in {Zipf}'s world", journal = j-J-INT-ECON, volume = "89", number = "2", pages = "283--296", day = "15", month = mar, year = "2013", CODEN = "JIECBE", DOI = "http://dx.doi.org/10.1016/j.jinteco.2012.08.002", ISSN = "0022-1996 (print), 1873-0353 (electronic)", ISSN-L = "0022-1996", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022199612001365", acknowledgement = ack-nhfb, fjournal = "Journal of International Economics", journal-URL = "http://www.sciencedirect.com/science/journal/09247963", keywords = "Zipf's Law", } @Article{Docampo:2009:BLA, author = "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio Flores-Moya", title = "{Benford}'s law applied to aerobiological data and its potential as a quality control tool", journal = j-AEROBIOLOGIA, volume = "25", number = "4", pages = "275--283", month = dec, year = "2009", CODEN = "AROBFT", DOI = "http://dx.doi.org/10.1007/s10453-009-9132-8", ISSN = "0393-5965 (print), 1573-3025 (electronic)", ISSN-L = "0393-5965", bibdate = "Fri Nov 25 10:47:33 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132", acknowledgement = ack-nhfb, fjournal = "Aerobiologia", } @Article{Dolgikh:2001:PCS, author = "Dmitry G. Dolgikh and Andrei M. Sukhov", title = "Parameters of cache systems based on a {Zipf}-like distribution", journal = j-COMP-NET-AMSTERDAM, volume = "37", number = "6", pages = "711--716", day = "15", month = dec, year = "2001", CODEN = "????", DOI = "http://dx.doi.org/10.1016/S1389-1286(01)00243-2", ISSN = "1389-1286 (print), 1872-7069 (electronic)", ISSN-L = "1389-1286", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.elsevier.com/locate/issn/13891286; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html; http://www.sciencedirect.com/science/article/pii/S1389128601002432", acknowledgement = ack-nhfb, fjournal = "Computer Networks (Amsterdam, Netherlands: 1999)", journal-URL = "http://www.sciencedirect.com/science/journal/13891286", keywords = "Zipf's Law", } @Article{Dorfleitner:2009:PBE, author = "Gregor Dorfleitner and Christian Klein", title = "Psychological barriers in {European} stock markets: Where are they?", journal = j-GLOB-FINANCE-J, volume = "19", number = "3", pages = "268--285", month = oct, year = "2009", CODEN = "????", DOI = "http://dx.doi.org/10.1016/j.gfj.2008.09.001", ISSN = "1044-0283 (print), 1873-5665 (electronic)", ISSN-L = "1044-0283", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S1044028308000549", acknowledgement = ack-nhfb, fjournal = "Global Finance Journal", keywords = "Benford's Law", } @Article{Dorogovtsev:2006:FON, author = "S. N. Dorogovtsev and J. F. F. Mendes and J. G. Oliveira", title = "Frequency of occurrence of numbers in the {World Wide Web}", journal = j-PHYSICA-A, volume = "360", number = "2", pages = "548--556", month = feb, year = "2006", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2005.06.064", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://arxiv.org/abs/physics/0504185; http://www.sciencedirect.com/science/article/pii/S0378437105006874", acknowledgement = ack-nhfb, fjournal = "Physica A: Statistical Mechanics and its Applications", keywords = "Benford's Law", } @Article{Doyle:2011:ITA, author = "Laurance R. Doyle and Brenda McCowan and Simon Johnston and Sean F. Hanser", title = "Information theory, animal communication, and the search for extraterrestrial intelligence", journal = j-ACTA-ASTRONAUT, volume = "68", number = "3--4", pages = "406--417", month = feb # "\slash " # mar, year = "2011", CODEN = "AASTCF", DOI = "http://dx.doi.org/10.1016/j.actaastro.2009.11.018", ISSN = "0094-5765 (print), 1879-2030 (electronic)", ISSN-L = "0094-5765", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0094576509005682", acknowledgement = ack-nhfb, fjournal = "Acta Astronautica", keywords = "Benford's Law; Zipf's Law", } @Article{Drake:2000:CAA, author = "P. D. Drake and M. J. Nigrini", title = "Computer assisted analytical procedures using {Benford}'s law", journal = j-J-ACCOUNT-EDUC, volume = "18", number = "2", pages = "127--146", month = "Spring", year = "2000", CODEN = "????", DOI = "http://dx.doi.org/10.1016/S0748-5751(00)00008-7", ISSN = "0748-5751 (print), 1873-1996 (electronic)", ISSN-L = "0748-5751", bibdate = "Tue Nov 22 10:36:47 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0748575100000087; http://www.sciencedirect.com/science/journal/07485751", acknowledgement = ack-nhfb, fjournal = "Journal of Accounting Education", } @Article{Dubinsky:2001:MFF, author = "Bruce G. Dubinsky", title = "Math formula fights fraud", journal = "Legal Times of {Washington}", volume = "XXIV", number = "9", pages = "??--??", day = "26", month = feb, year = "2001", ISSN = "0732-7536", ISSN-L = "0732-7536", bibdate = "Sat Feb 16 17:35:39 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", xxjournal = "Legal Times", } @Article{Dumbgen:2007:EBA, author = "L. D{\"u}mbgen and C. Leuenberger", title = "Explicit bounds for the approximation error in {Benford}'s law", journal = "ArXiv e-prints", month = may, year = "2007", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0705.4488", keywords = "Mathematics - Probability, 60E15, 60F99", primaryclass = "math.PR", } @Article{Dumbgen:2008:EBA, author = "Lutz D{\"u}mbgen and Christoph Leuenberger", title = "Explicit bounds for the approximation error in {Benford}'s law", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "99--112", year = "2008", CODEN = "????", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E15 (60F99)", MRnumber = "2386066 (2009b:60056)", MRreviewer = "Pieter C. Allaart", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://arxiv.org/abs/0705.4488; http://weber.math.washington.edu/~ejpecp/ECP/index.php", abstract = "Benford's law states that for many random variables $ X > 0 $ its leading digit $ D = D(X) $ satisfies approximately the equation $ P(D = d) = \log_{10}(1 + 1 / d) $ for $ d = 1, 2, \ldots {}, 9 $. This phenomenon follows from another, maybe more intuitive fact, applied to $ Y := \log_{10}(X) $: For many real random variables $Y$, the remainder $ U := Y - \floor (Y) $ is approximately uniformly distributed on $ [0, 1) $. The present paper provides new explicit bounds for the latter approximation in terms of the total variation of the density of $Y$ or some derivative of it. These bounds are an interesting alternative to traditional Fourier methods which yield mostly qualitative results. As a by-product we obtain explicit bounds for the approximation error in Benford's law.", acknowledgement = ack-nhfb, fjournal = "Electronic Communications in Probability", } @Article{Duncan:1967:AUD, author = "R. L. Duncan", title = "An Application of Uniform Distributions to the {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "5", number = "2", pages = "137--140", month = apr, year = "1967", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:04:52 MDT 2011", bibsource = "http://www.fq.math.ca/5-2.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/5-2/duncan.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Duncan:1969:NID, author = "R. L. Duncan", title = "Note on the Initial Digit Problem", journal = j-FIB-QUART, volume = "7", number = "5", pages = "474--475", month = dec, year = "1969", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:21 MDT 2011", bibsource = "http://www.fq.math.ca/7-5.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/7-5/duncan.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Dunn:1980:SFW, author = "Stanley Dunn", title = "Surveyor's Forum: {Working} on Interpretations", journal = j-COMP-SURV, volume = "12", number = "2", pages = "255--255", month = jun, year = "1980", CODEN = "CMSVAN", DOI = "http://doi.acm.org/10.1145/356810.356817", ISSN = "0010-4892", ISSN-L = "0360-0300", bibdate = "Thu Jun 19 09:27:10 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/surveys/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.", acknowledgement = ack-nhfb, fjournal = "ACM Computing Surveys", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204", } @Article{Duran:1974:ACS, author = "J. Peter Duran", title = "Almost convergence, summability and ergodicity", journal = j-CAN-J-MATH, volume = "26", number = "??", pages = "372--387", month = "????", year = "1974", CODEN = "CJMAAB", DOI = "http://dx.doi.org/10.4153/CJM-1974-039-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:45 MDT 2011", bibsource = "http://cms.math.ca/cjm/v26/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/canjmath1970.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", remark = "In relation to Benford's Law, see theorem 6.2.", } @Article{Duranton:2006:SFZ, author = "Gilles Duranton", title = "Some foundations for {Zipf}'s law: Product proliferation and local spillovers", journal = j-REG-SCI-URBAN-ECON, volume = "36", number = "4", pages = "542--563", day = "1", month = jul, year = "2006", CODEN = "RSUEDM", DOI = "http://dx.doi.org/10.1016/j.regsciurbeco.2006.03.008", ISSN = "0166-0462 (print), 1879-2308 (electronic)", ISSN-L = "0166-0462", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0166046206000354", acknowledgement = ack-nhfb, fjournal = "Regional Science and Urban Economics", journal-URL = "http://www.sciencedirect.com/science/journal/01660462", keywords = "Zipf's Law", } @Book{Durrett:1991:PTE, author = "Richard Durrett", title = "Probability: theory and examples", publisher = "Wadsworth and Brooks\slash Cole Advanced Books and Software", address = "Pacific Grove, CA, USA", pages = "ix + 453", year = "1991", ISBN = "0-534-13206-5", ISBN-13 = "978-0-534-13206-4", LCCN = "QA273 .D865 1991", bibdate = "Mon Nov 21 10:06:18 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", price = "US\$49.95", series = "The Wadsworth and Brooks\slash Cole statistics\slash probability series", acknowledgement = ack-nhfb, remark = "Benford's Law is treated on pp. 300ff. Hill \cite[page 893]{Hill:1995:BII} reports that Durrett has a proof that the $k$-th digit of powers of integers follows Benford's Law.", subject = "Probabilities", } @Book{Durrett:2005:PTE, author = "Richard Durrett", title = "Probability: theory and examples", publisher = "Thomson Brooks\slash Cole", address = "Belmont, CA, USA", edition = "Third", pages = "xi + 497", year = "2005", ISBN = "0-534-42441-4", ISBN-13 = "978-0-534-42441-1", LCCN = "QA273 .D865 2005", bibdate = "Mon Nov 21 10:00:11 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Duxbury advanced series", acknowledgement = ack-nhfb, remark = "Benford's Law is treated on pp. 337ff. Hill \cite[page 893]{Hill:1995:BII} reports that the 1991 edition has a proof that the $k$-th digit of powers of integers follows Benford's Law.", subject = "Probabilities", } @Article{Durtschi:2004:EUB, author = "C. Durtschi and W. Hillison and C. Pacini", title = "The Effective Use of {Benford's Law} to Assist in Detecting Fraud in Accounting Data", journal = j-J-FORENSIC-ACCOUNT, volume = "5", number = "1", pages = "17--34", month = "????", year = "2004", CODEN = "????", ISSN = "1524-5586", bibdate = "Sun Nov 13 11:35:18 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Forensic Accounting", } @Article{Edwards:2011:LFP, author = "Roderick Edwards and Laura Collins", title = "Lexical Frequency Profiles and {Zipf's Law}", journal = "Language Learning", volume = "61", number = "1", pages = "1--30", year = "2011", DOI = "http://dx.doi.org/10.1111/j.1467-9922.2010.00616.x", ISSN = "0023-8333 (print), 1467-9922 (electronic)", ISSN-L = "0023-8333", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "L2 vocabulary learning; L2 vocabulary size; modeling vocabulary learning; Zipf's law", } @Article{Egghe:1985:CLL, author = "L. Egghe", title = "Consequences of {Lotka's Law} for the {Law of Bradford}", journal = j-J-DOC, volume = "41", number = "3", pages = "173--189", month = "????", year = "1985", CODEN = "JDOCAS", DOI = "http://dx.doi.org/10.1108/eb026780", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:23:22 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", keywords = "Bradford's Law", } @Article{Egghe:1999:LZM, author = "L. Egghe", title = "On the law of {Zipf--Mandelbrot} for multi-word phrases", journal = j-J-AM-SOC-INF-SCI, volume = "50", number = "3", pages = "233--241", month = "????", year = "1999", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO;2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Sep 10 06:09:31 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", onlinedate = "17 Feb 1999", } @Book{Egghe:2005:PLI, author = "Leo Egghe", title = "Power laws in the information production process: {Lotkaian} informetrics", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "xvii + 427", year = "2005", ISBN = "0-12-088753-3, 0-08-048011-X (e-book)", ISBN-13 = "978-0-12-088753-8, 978-0-08-048011-4 (e-book)", LCCN = "Z669.8 .E44 2005", bibdate = "Mon Feb 25 10:42:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See pages 204--205 for Benford's Law discussion.", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject-dates = "Lotka, Alfred James, (1880--1949)", tableofcontents = "Basic theory of Lotkaian informetrics \\ Three-dimensional Lotkaian informetrics \\ Lotkaian concentration theory \\ Lotkaian fractal complexity theory \\ Lotkaian informetrics of systems in which items can have multiple sources \\ Further applications in Lotkaian informetrics \\ Lotkaian informetrics: an introduction", } @Article{Egghe:2006:DHL, author = "L. Egghe", title = "The dependence of the height of a {Lorenz} curve of a {Zipf} function on the size of the system", journal = j-MATH-COMP-MODELLING, volume = "43", number = "7--8", pages = "870--879", day = "15", month = apr, year = "2006", CODEN = "MCMOEG", DOI = "http://dx.doi.org/10.1016/j.mcm.2005.09.033", ISSN = "0895-7177 (print), 1872-9479 (electronic)", ISSN-L = "0895-7177", MRclass = "94A15 (91B82)", MRnumber = "2218323 (2006k:94033)", MRreviewer = "Ulrich Tamm", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S089571770500508X", acknowledgement = ack-nhfb, fjournal = "Mathematical and Computer Modelling", keywords = "Zipf's Law", } @Article{Egghe:2007:UHL, author = "Leo Egghe", title = "Untangling {Herdan's Law} and {Heaps' Law}: Mathematical and informetric arguments", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "58", number = "5", pages = "702--709", year = "2007", CODEN = "JASIEF", DOI = "http://dx.doi.org/10.1002/asi.20524", ISSN = "1532-2890", ISSN-L = "1532-2882", bibdate = "Mon Feb 25 08:31:49 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", keywords = "Heaps' law in information retrieval; Herdan's law in linguistics", } @Article{Egghe:2010:NSP, author = "Leo Egghe", title = "A new short proof of {Naranan}'s theorem, explaining {Lotka's Law} and {Zipf's Law}", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "61", number = "12", pages = "2581--2583", year = "2010", CODEN = "JASIEF", DOI = "http://dx.doi.org/10.1002/asi.21431", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", } @Article{Egghe:2011:BLS, author = "Leo Egghe", title = "{Benford}'s law is a simple consequence of {Zipf}'s law", journal = "ISSI Newsletter", volume = "7", number = "3", pages = "55--56", month = sep, year = "2011", DOI = "????", bibdate = "Mon Feb 18 18:27:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.issi-society.info/archives/newsletter27.pdf", abstract = "We show that benford's law (describing the logarithmic distribution of the numbers 1, 2, \ldots{}, 9 as first digits of data in decimal form) can be deduced from the classical law of zipf. this explains Bensford's law as a scientometric or informetric law.", acknowledgement = ack-nhfb, } @Article{Egghe:2012:AGL, author = "Leo Egghe and Raf Guns", title = "Applications of the generalized law of {Benford} to informetric data", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "63", number = "8", pages = "1662--1665", month = aug, year = "2012", CODEN = "JASIEF", DOI = "http://dx.doi.org/10.1002/asi.22690", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Mon Feb 18 19:05:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.22690/abstract", abstract = "In a previous work (Egghe, 2011), the first author showed that Benford's law (describing the logarithmic distribution of the numbers 1, 2, \ldots{}, 9 as first digits of data in decimal form) is related to the classical law of Zipf with exponent 1. The work of Campanario and Coslado (2011), however, shows that Benford's law does not always fit practical data in a statistical sense. In this article, we use a generalization of Benford's law related to the general law of Zipf with exponent $ \beta > 0 $. Using data from Campanario and Coslado, we apply nonlinear least squares to determine the optimal $ \beta $ and show that this generalized law of Benford fits the data better than the classical law of Benford.", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", } @TechReport{Eliahou:2011:MDP, author = "Shalom Eliahou and Bruno Mass{\'e} and Dominique Schneider", title = "On the mantissa distribution of powers of natural and prime numbers", type = "Preprint", institution = "Universit{\'e} du Littoral C{\^o}te d'Opale", address = "Nord-Pas-de-Calais, France", pages = "14", day = "15", month = nov, year = "2011", bibdate = "Mon Feb 18 18:27:51 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://fr.wikipedia.org/wiki/Universit%C3%A9_du_Littoral_C%C3%B4te_d%27Opale; http://www-lmpa.univ-littoral.fr/publications/articles/lmpa447.pdf", acknowledgement = ack-nhfb, } @Article{Eliahou:2012:MDP, author = "Shalom Eliahou and Bruno Mass{\'e} and Dominique Schneider", title = "On the mantissa distribution of powers of natural and prime numbers", journal = "Acta Mathematica Hungarica", volume = "??", number = "??", pages = "1--5", month = jun, year = "2012", DOI = "http://dx.doi.org/10.1007/s10474-012-0244-1", ISSN = "0001-5954, 0236-5294, 1588-2632", ISSN-L = "0001-5954", bibdate = "Mon Feb 18 19:06:54 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007%2Fs10474-012-0244-1", acknowledgement = ack-nhfb, } @Article{Eliazar:2011:LLZ, author = "Iddo Eliazar", title = "Limit laws for {Zipf}'s law", journal = j-J-PHYS-A, volume = "44", number = "2", pages = "022001", year = "2011", CODEN = "JPHAC5", DOI = "http://dx.doi.org/10.1088/1751-8113/44/2/022001", ISSN = "1751-8113", ISSN-L = "0305-4470", MRclass = "62G30 (91D20)", MRnumber = "2749082 (2011i:62083)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "Zbl 1204.62196", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. A. Mathematical and Theoretical", journal-URL = "http://iopscience.iop.org/0305-4470", pagecount = "6", } @Article{Eliazar:2012:PLC, author = "Iddo I. Eliazar and Morrel H. Cohen", title = "Power-law connections: From {Zipf} to {Heaps} and beyond", journal = j-INFO-PROC-MAN, volume = "23", number = "3", pages = "56--74", day = "1", month = may, year = "2012", CODEN = "IPMADK", DOI = "http://dx.doi.org/10.1016/j.aop.2013.01.013", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0003491613000171", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", keywords = "Zipf's Law", } @Article{elSehity:2005:PDA, author = "Tarek el Sehity and Erik Hoelzl and Erich Kirchler", title = "Price developments after a nominal shock: {Benford's Law} and psychological pricing after the euro introduction", journal = j-INT-J-RES-MARK, volume = "22", number = "4", pages = "471--480", month = dec, year = "2005", CODEN = "IJRME6", DOI = "http://dx.doi.org/10.1016/j.ijresmar.2005.09.002", ISSN = "0167-8116 (print), 1873-8001 (electronic)", ISSN-L = "0167-8116", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167811605000522", acknowledgement = ack-nhfb, fjournal = "International Journal of Research in Marketing", keywords = "Benford's Law", } @Article{Elshoff:1978:SSC, author = "James L. Elshoff", title = "A study of the structural composition of {PL/I} programs", journal = j-SIGPLAN, volume = "13", number = "6", pages = "29--37", month = jun, year = "1978", CODEN = "SINODQ", DOI = "http://doi.acm.org/10.1145/987515.987518", ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic)", ISSN-L = "0362-1340", bibdate = "Wed Jun 18 16:08:52 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Some research on a theory of the structural composition of an algorithm has recently been reported. The theory embodies models of operator and operand distributions that have been proposed by Bayer, Zipf, and Zweben. This paper reports a study in which the three models of operator distributions are compared with the measured distributions found in 34 PL/I programs. Two of three models, one by Zipf and one by Zweben, are shown to correlate highly with the measured distributions. Two variations of the Zipf model are then formulated and tested with good results. Also, the relationship between the method of counting operators and the models is investigated.", acknowledgement = ack-nhfb, classification = "C4240 (Programming and algorithm theory); C6140D (High level languages)", corpsource = "Computer Sci. Dept., General Motors Res. Labs., Warren, MI, USA", fjournal = "ACM SIG{\-}PLAN Notices", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706", keywords = "counting operators; operator distributions; PL/1; PL/1 programs; programming theory; structural composition", treatment = "T Theoretical or Mathematical", } @Article{Engel:2003:BLE, author = "Hans-Andreas Engel and Christoph Leuenberger", title = "{Benford}'s law for exponential random variables", journal = j-STAT-PROB-LETT, volume = "63", number = "4", pages = "361--365", day = "15", month = jul, year = "2003", CODEN = "SPLTDC", DOI = "http://dx.doi.org/10.1016/S0167-7152(03)00101-9", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "60E99 (60C05)", MRnumber = "1996184 (2004d:60050)", MRreviewer = "Ulrich M. Hirth", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715203001019", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", keywords = "Benford's Law", } @Book{Estoup:1916:GSM, author = "J. B. Estoup", title = "Gammes St{\'e}nographiques: m{\'e}thode \& exercices pour l'acquisition de la vitesse ({French}) [Stenographic ranges: method and exercises for achieving speed]", publisher = "Institut St{\'e}nographique de France", address = "Paris, France", edition = "Fourth", pages = "151", year = "1916", LCCN = "????", bibdate = "Thu Nov 24 14:24:28 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This on shorthand writing is the earliest known publication of the power-law distribution of word frequencies, generally credited to \cite{Zipf:1932:SSP}.", acknowledgement = ack-nhfb, keywords = "Zipf's Law", language = "French", } @Article{Faber:1985:AML, author = "Vance Faber and Andrew B. {White, Jr.} and G. Milton Wing", title = "Analysis of a model that leads to the {Pareto} law of wealth distribution", journal = j-J-MATH-ANAL-APPL, volume = "112", number = "2", pages = "579--594", year = "1985", CODEN = "JMANAK", DOI = "http://dx.doi.org/10.1016/0022-247X(85)90264-1", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "90A14", MRnumber = "813621 (87b:90027)", bibdate = "Mon Feb 18 17:05:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", } @Article{Fairthorne:1969:PDE, author = "Robert A. Fairthorne", title = "Progress in Documentation: Empirical Hyperbolic Distributions ({Bradford--Zipf--Mandelbrot}) for Bibliometric Description and Prediction", journal = j-J-DOC, volume = "25", number = "4", pages = "313--343", month = dec, year = "1969", CODEN = "JDOCAS", DOI = "http://dx.doi.org/10.1108/eb026481", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 06:27:27 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reprinted in \cite{Fairthorne:2005:PDE}.", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", remark = "According to \cite{Potter:1981:LLR}, this paper is the first to link the distributions of Bradford, Zipf, Mandelbrot, and Lotka.", } @Article{Fairthorne:2005:PDE, author = "Robert A. Fairthorne", title = "Progress in Documentation: Empirical Hyperbolic Distributions ({Bradford--Zipf--Mandelbrot}) for Bibliometric Description and Prediction", journal = j-J-DOC, volume = "61", number = "2", pages = "171--193", month = "????", year = "2005", CODEN = "JDOCAS", DOI = "http://dx.doi.org/10.1108/00220410510585179", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 06:27:27 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reprint of \cite{Fairthorne:1969:PDE}.", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", remark = "According to \cite{Potter:1981:LLR}, this paper is the first to link the distributions of Bradford, Zipf, Mandelbrot, and Lotka.", } @Article{Family:1989:KDG, author = "Fereydoon Family and Paul Meakin", title = "Kinetics of droplet growth processes: Simulations, theory, and experiments", journal = j-PHYS-REV-A, volume = "40", number = "7", pages = "3836--3854", month = oct, year = "1989", CODEN = "PLRAAN", DOI = "http://dx.doi.org/10.1103/PhysRevA.40.3836", ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519", ISSN-L = "1050-2947", bibdate = "Thu Feb 28 10:49:20 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevA.40.3836", acknowledgement = ack-nhfb, fjournal = "Physical Review A (Atomic, Molecular, and Optical Physics)", journal-URL = "http://pra.aps.org/browse", } @Misc{Farbaniec:2011:AFD, author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c", title = "Application of the first digit law in credibility evaluation of the financial accounting data based on particular cases", howpublished = "Lecture slides for 10th International Congress on Internal Control, Internal Audit, Fraud and Anti-Corruption Issues, Krak{\'o}w, September 14--16, 2011.", pages = "27", year = "2011", bibdate = "Thu Dec 01 21:27:25 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://benford.pl/documents/benford_pikw.pdf", acknowledgement = ack-nhfb, } @InProceedings{Farbaniec:2011:UBL, author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c", editor = "????", booktitle = "10th International Congress on Internal Control, Internal Audit, Fraud and Anti-Corruption Issues, Krak{\'o}w, September 14--16, 2011", title = "Using {Benford}'s law to detect irregularities in the collection of data", publisher = "????", address = "????", pages = "??--??", year = "2011", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Thu Dec 01 21:32:03 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Farkas:2010:SUN, author = "Janos Farkas and Gy{\"o}rgy Gyurky", title = "The significance of using the {Newcomb--Benford} law as a test of nuclear half-life calculations", journal = "Acta Physica Polonica, B", volume = "41", pages = "1213--1221", year = "2010", CODEN = "APOBBB", ISSN = "0587-4254 (print), 1509-5770 (electronic)", ISSN-L = "0587-4254", bibdate = "Mon Nov 14 16:21:42 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F; http://arxiv.org/abs/1006.3615", abstract = "Half-life number sequences collected from nuclear data charts are found to obey the Newcomb--Benford law. Based on this fact, it has been suggested recently, that this law should be used to test the quality of nuclear decay models. In this paper we briefly recall how, when and why the Newcomb--Benford law can be observed in a set of numbers with a given probability distribution. We investigate the special case of nuclear half-lives, and show that the law provides no additional clue in understanding decay half-lives. Thus, it can play no significant role in testing nuclear decay theories.", acknowledgement = ack-nhfb, ajournal = "Acta Phys. Pol. B", ajournal-2 = "Acta Phys. Polon. B", archiveprefix = "arXiv", eprint = "1006.3615", primaryclass = "math-ph", } @Article{Fedorowicz:1982:TFZ, author = "Jane Fedorowicz", title = "The Theoretical Foundation of {Zipf's Law} and Its Application to the Bibliographic Database Environment", journal = j-J-AM-SOC-INF-SCI, volume = "33", number = "5", pages = "285--293", year = "1982", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/asi.4630330507", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", } @Article{Fedorowicz:1984:DEU, author = "Jane Fedorowicz", title = "Database evaluation using multiple regression techniques", journal = j-SIGMOD, volume = "14", number = "2", pages = "70--76", year = "1984", CODEN = "SRECD8", ISBN = "0-89791-128-8", ISBN-13 = "978-0-89791-128-3", ISSN = "0163-5808 (print), 1943-5835 (electronic)", ISSN-L = "0163-5808", bibdate = "Mon Dec 9 07:58:51 MST 1996", bibsource = "Compendex database; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "A model of the inverted file of an automated bibliographic system is constructed using the Zipf distribution of word frequency. By ascertaining the parameters of the Zipfian model of the inverted file system, one can estimate the minimum data storage requirements of the database. In addition, given a few additional system parameters, access time for a specified query can be estimated. The estimation procedures are accomplished using logarithmic transformations and multiple regression techniques. This paper introduces the Zipfian models, their regression formulation, and their results and interpretation for application to database evaluation.", acknowledgement = ack-nhfb, affiliation = "Northwestern Univ, Kellogg Graduate Sch of Management, Evanston, IL, USA", affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of Management, Evanston, IL, USA", classification = "723; 901; 922", conference = "SIGMOD '84, Proceedings of Annual Meeting (ACM Special Interest Group on Management of Data).", fjournal = "SIGMOD Record (ACM Special Interest Group on Management of Data)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J689", keywords = "access time model; bibliographic techniques; database systems; evaluation; information storage systems; mathematical models; multiple regression techniques; Zipfian model", meetingaddress = "Boston, MA, USA", sponsor = "ACM, Special Interest Group on Management of Data, New York, NY, USA", } @Article{Fedorowicz:1987:DPE, author = "Jane Fedorowicz", title = "Database Performance Evaluation in an Indexed File Environment", journal = j-TODS, volume = "12", number = "1", pages = "85--110", month = mar, year = "1987", CODEN = "ATDSD3", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", bibdate = "Sat Apr 14 10:34:48 MDT 2001", bibsource = "Compendex database; Database/Graefe.bib; Database/Wiederhold.bib; http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf; http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/; http://www.acm.org/pubs/toc/Abstracts/tods/13675.html", abstract = "The use of database systems for managerial decision making often incorporates information-retrieval capabilities with numeric report generation. Of great concern to the user of such a system is the response time associated with issuing a query to the database. This study presents a procedure for estimating response time for one of the most frequently encountered physical storage mechanisms, the indexed file. The model provides a fairly high degree of accuracy, but is simple enough so that the cost of applying the model is not exorbitant. The model incorporates the knowledge that the distribution of access key occurrences is known to follow Zipf's law. It first estimates the access time required to complete the query, which includes the time needed for all input and output transactions, and CPU time used in performing the search. The effects of multiple users on an individual's response time are then assessed using a simple regression estimation technique. The two-step procedure allows for the separation of access time from multiuser influences.", acknowledgement = ack-nhfb, affiliation = "Boston Univ, Boston, MA, USA", affiliationaddress = "Boston Univ, Boston, MA, USA", annote = "a procedure for estimating response time; distribution of access key occurrences follow Zipf's law. Early version with Kellogg, J. L. Model provides a fairly high degree of accuracy but is simple. The effects of multiple users are assessed using simple regression estimation.", classification = "723; 912; 922", fjournal = "ACM Transactions on Database Systems", generalterms = "Design; Performance", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", keywords = "data processing --- File organization; database performance; database systems; indexed file environment; MANAGEMENT --- Information Systems; multiple users, design; Performance; performance; response time; statistical methods --- regression analysis; Zipf's law", subject = "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems Management, File organization. {\bf H.2.2}: Information Systems, DATABASE MANAGEMENT, Physical Design, Access methods. {\bf H.3.2}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Storage, File organization. {\bf H.3.3}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Search and Retrieval, Retrieval models.", } @Article{Feldstein:1976:CED, author = "Alan Feldstein and Richard Goodman", title = "Convergence Estimates for the Distribution of Trailing Digits", journal = j-J-ACM, volume = "23", number = "2", pages = "287--297", month = apr, year = "1976", CODEN = "JACOAH", DOI = "http://doi.acm.org/10.1145/321941.321948", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "An analysis is made of the distribution of trailing digits (tail end digits) of positive real floating-point numbers represented in arbitrary base $ \beta $ and randomly chosen from a logarithmic distribution. The analysis shows that the $n$ th digit for $ n \geq 2 $ is actually approximately uniformly distributed. The approximation depends upon both $n$ and the base beta. It becomes better as $n$ increases, and it is exact in the limit as $ n \rightarrow \infty $. A table of this distribution is presented for various $ \beta $ and $n$, along with a table of the maximum digit by digit deviation $ \Delta $ of the logarithmic distribution from the uniform distribution. Various asymptotic results for $ \Delta $ are included.", acknowledgement = ack-nhfb, classification = "723", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", journalabr = "J Assoc Comput Mach", keywords = "Benford's Law; computer arithmetic; computer programming; Law of Anomalous Numbers; Zipf's Law", } @Article{Feldstein:1986:OUS, author = "Alan Feldstein and Peter Turner", title = "Overflow, underflow, and severe loss of significance in floating-point addition and subtraction", journal = j-IMA-J-NUMER-ANAL, volume = "6", number = "2", pages = "241--251", month = apr, year = "1986", CODEN = "IJNADH", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65G05", MRnumber = "89h:65065", bibdate = "Sat Dec 23 14:52:49 2000", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "In this paper it is shown that, under the assumption of the logarithmic distribution of numbers, floating-point addition and subtraction can result in overflow or underflow with alarming frequency --- a frequency that increases rapidly with machine speed unless the range of the exponent is also increased. If numbers are assumed to be distributed in accordance with Sweeney's (1965) experiments, then severe loss of significance occurs with large probability in floating point subtraction. These results have implications for computer design and lead to the suggestion of a long word format which will reduce the risks to acceptable levels.", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic distribution; overflow; underflow; Zipf's Law", } @Book{Feller:1950:IPT, author = "William Feller", title = "Introduction to Probability Theory", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "????", year = "1950", LCCN = "QA273 .F37", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Wiley series in probability and mathematical statistics. Probability and mathematical statistics", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", } @Book{Feller:1957:IPT, author = "William Feller", title = "Introduction to Probability Theory", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "461 (vol. 1), 626 (vol. 2)", year = "1957", LCCN = "QA273 .F3712", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://catdir.loc.gov/catdir/toc/onix01/57010805.html", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", } @Book{Feller:1966:IPT, author = "William Feller", title = "Introduction to Probability Theory", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "xviii + 626", year = "1966", ISSN = "0271-6232", LCCN = "QA273 .F3727 1966", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Wiley series in probability and mathematical statistics. Probability and mathematical statistics", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", remark = "Benford's Law is discussed on p. 62.", } @Book{Feller:1968:IPT, author = "William Feller", title = "Introduction to Probability Theory and its Applications", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xviii + 509", year = "1968", ISBN = "0-471-25708-7", ISBN-13 = "978-0-471-25708-0", LCCN = "QA273 .F3713", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a discussion of flaws in the derivation of Benford's Law in this book.", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", remark = "Pages 63--64 (of xxiv + 669) in 1971 printing have only brief mention of two papers \cite{Benford:1938:LAN,Pinkham:1961:DFS}.", } @Article{FerreriCancho:2002:ZLR, author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}", title = "{Zipf}'s law and random texts", journal = j-ADV-COMPLEX-SYST, volume = "5", number = "1", pages = "1--6", year = "2002", CODEN = "????", DOI = "http://dx.doi.org/10.1142/S0219525902000468", ISSN = "0219-5259", bibdate = "Sat Nov 12 11:00:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1090.91595", abstract = "Random-text models have been proposed as an explanation for the power law relationship between word frequency and rank, the so-called Zipf's law. They are generally regarded as null hypotheses rather than models in the strict sense. In this context, recent theories of language emergence and evolution assume this law as a priori information with no need of explanation. Here, random texts and real texts are compared through (a) the so-called lexical spectrum and (b) the distribution of words having the same length. It is shown that real texts fill the lexical spectrum much more efficiently and regardless of the word length, suggesting that the meaningfulness of Zipf's law is high.", acknowledgement = ack-nhfb, classmath = "91F20 (Linguistics)", fjournal = "Advances in Complex Systems", journal-URL = "http://www.worldscinet.com/acs/acs.shtml", keywords = "Human language; monkey languages; random texts; scaling; Zipf's law", } @Article{FerreriCancho:2003:LEO, author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}", title = "Least effort and the origins of scaling in human language", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "100", number = "3", pages = "788--791", day = "4", month = feb, year = "2003", CODEN = "PNASA6", DOI = "http://dx.doi.org/10.1073/pnas.0335980100", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Tue Nov 15 09:44:47 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/search", keywords = "Zipf's Law", onlinedate = "January 22, 2003", } @Article{FerreriCancho:2005:CZL, author = "Ramon {Ferrer i Cancho} and Oliver Riordan and B{\'e}la Bollob{\'a}s", title = "The consequences of {Zipf}'s law for syntax and symbolic reference", journal = j-PROC-R-SOC-LOND-SER-B-BIO-SCI, volume = "272", number = "1562", pages = "561--565", day = "7", month = mar, year = "2005", CODEN = "PRLBA4", DOI = "http://dx.doi.org/10.1098/rspb.2004.2957", ISSN = "0962-8452 (print), 1471-2954 (electronic)", ISSN-L = "0962-8452", bibdate = "Tue Nov 15 11:27:26 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rspb.royalsocietypublishing.org/content/272/1562/561.full", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society of London. Series B. Biological sciences", } @Article{Fewster:2009:SEB, author = "Rachel M. Fewster", title = "A Simple Explanation of {Benford's Law}", journal = j-AMER-STAT, volume = "63", number = "1", pages = "26--32", month = feb, year = "2009", CODEN = "ASTAAJ", DOI = "http://dx.doi.org/10.1198/tast.2009.0005", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2655700", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; http://www.math.utah.edu/pub/tex/bib/amstat2000.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Filipponi:1995:SPA, author = "Piero Filipponi and Renato Menicocci", title = "Some Probabilistic Aspects of the Terminal Digits of {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "33", number = "4", pages = "325--331", month = aug, year = "1995", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:02:19 MDT 2011", bibsource = "http://www.fq.math.ca/33-4.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Fischer:2010:HCS, author = "Martin H. Fischer and Richard A. Mills and Samuel Shaki", title = "How to cook a {SNARC}: Number placement in text rapidly changes spatial-numerical associations", journal = j-BRAIN-COGN, volume = "72", number = "3", pages = "333--336", month = apr, year = "2010", CODEN = "????", DOI = "http://dx.doi.org/10.1016/j.bandc.2009.10.010", ISSN = "0278-2626 (print), 1090-2147 (electronic)", ISSN-L = "0278-2626", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0278262609002024", acknowledgement = ack-nhfb, fjournal = "Brain and Cognition", keywords = "Benford's Law; Spatial Numerical Association of Response Codes (SNARC)", } @Article{Flehinger:1966:PRI, author = "B. J. (Betty J.) Flehinger", title = "On the probability that a random integer has initial digit {$A$}", journal = j-AMER-MATH-MONTHLY, volume = "73", number = "10", pages = "1056--1061", month = dec, year = "1966", CODEN = "AMMYAE", DOI = "http://dx.doi.org/10.2307/2314636", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Sat Nov 12 15:33:14 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2314636", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", } @Book{Fleiss:1981:SMR, author = "Joseph L. Fleiss", title = "Statistical Methods for Rates and Proportions", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "xviii + 321", year = "1981", ISBN = "0-471-06428-9", ISBN-13 = "978-0-471-06428-2", LCCN = "QA279 .F58 1981", bibdate = "Fri Mar 22 08:46:57 MDT 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Wiley series in probability and mathematical statistics", URL = "http://www.loc.gov/catdir/description/wiley032/80026382.html; http://www.loc.gov/catdir/enhancements/fy0607/80026382-b.html; http://www.loc.gov/catdir/toc/onix02/80026382.html", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Analysis of variance; Sampling (Statistics); Biometry", } @Book{Fleiss:2003:SMR, author = "Joseph L. Fleiss and Bruce A. Levin and Myunghee Cho Paik", title = "Statistical Methods for Rates and Proportions", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xxvii + 760", year = "2003", ISBN = "0-471-52629-0 (hardcover)", ISBN-13 = "978-0-471-52629-2 (hardcover)", LCCN = "QA279 .F58 2003", bibdate = "Fri Mar 22 08:46:57 MDT 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Wiley series in probability and statistics", URL = "http://www.loc.gov/catdir/bios/wiley042/2002191005.html; http://www.loc.gov/catdir/description/wiley034/2002191005.html; http://www.loc.gov/catdir/toc/wiley031/2002191005.html", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Analysis of variance; Sampling (Statistics); Biometry", tableofcontents = "Preface \\ Preface to the Second Edition \\ Preface to the First Edition \\ 1. An Introduction to Applied Probability \\ 2. Statistical Inference for a Single Proportion \\ 3. Assessing Significance in a Fourfold Table \\ 4. Determining Sample Sizes Needed to Detect a Difference Between Two Proportions \\ 5. How to Randomize \\ \\ 6. Comparative Studies: Cross-Sectional, Naturalistic, or Multinomial Sampling \\ \\ 7. Comparative Studies: Prospective and Retrospective Sampling \\ 8. Randomized Controlled Trials \\ 9. The Comparison of Proportions from Several Independent Samples \\ 10. Combining Evidence from Fourfold Tables \\ 11. Logistic Regression \\ 12. Poisson Regression \\ 13. Analysis of Data from Matched Samples \\ 14. Regression Models for Matched Samples \\ 15. Analysis of Correlated Binary Data \\ 16. Missing Data \\ 17. Misclassification Errors: Effects, Control, and Adjustment \\ 18. The Measurement of Interrater Agreement \\ 19. The Standardization of Rates \\ Appendix A. Numerical Tables \\ Appendix B. The Basic Theory of Maximum Likelihood", } @Article{Fontanari:2004:SNM, author = "J. F. Fontanari and L. I. Perlovsky", title = "Solvable null model for the distribution of word frequencies", journal = j-PHYS-REV-E, volume = "70", number = "??", pages = "042901", day = "25", month = oct, year = "2004", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.70.042901", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.042901", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Formann:2010:NBL, author = "A. K. Formann and R. J. Morris", title = "The {Newcomb--Benford Law} in Its Relation to Some Common Distributions", journal = j-PLOS-ONE, volume = "51", month = may, year = "2010", CODEN = "POLNCL", DOI = "http://dx.doi.org/10.1371/journal.pone.0010541", ISSN = "1932-6203", ISSN-L = "1932-6203", bibdate = "Mon Nov 14 18:19:09 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010PLoSO...510541F", acknowledgement = ack-nhfb, ages = "10541", fjournal = "PLoS One", } @Article{Franel:1917:PTL, author = "J. Franel", title = "{{\`A}} propos des tables de logarithmes. ({French}) [{On} tables of logarithms]", journal = "Festschrift Naturforschenden der Gesellschaft in Z{\"u}rich Vierteljahrsschrift", volume = "62", number = "??", pages = "286--295", month = "????", year = "1917", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 10:09:40 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "French", } @Article{Friar:2012:GSB, author = "James L. Friar and Terrance Goldman and Juan P{\'e}rez-Mercader", title = "Genome Sizes and the {Benford} Distribution", journal = j-PLOS-ONE, volume = "7", number = "5", pages = "e36624", month = "????", year = "2012", CODEN = "POLNCL", DOI = "http://dx.doi.org/10.1371/journal.pone.0036624", ISSN = "1932-6203", ISSN-L = "1932-6203", bibdate = "Mon Feb 18 19:08:17 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", accepted = "11 April 2012", acknowledgement = ack-nhfb, fjournal = "PLoS One", onlinedate = "18 May 2012", received = "7 April 2011", } @Article{Friedberg:1984:DFD, author = "Steven H. Friedberg", title = "The distribution of first digits", journal = j-COLLEGE-MATH-J, volume = "15", number = "2", pages = "120--125", month = mar, year = "1984", ISSN = "0746-8342 (print), 1931-1346 (electronic)", ISSN-L = "0746-8342", bibdate = "Sat Feb 16 17:38:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2686516", acknowledgement = ack-nhfb, fjournal = "College Mathematics Journal", } @InProceedings{Fu:2007:GBL, author = "D. Fu and Y. Q. Shi and W. Su", editor = "Edward J. {Delp III} and Ping Wah Wong", booktitle = "{Society of Photo-Optical Instrumentation Engineers (SPIE)} Conference Series", title = "A generalized {Benford}'s law for {JPEG} coefficients and its applications in image forensics", volume = "6505", publisher = pub-SPIE, address = pub-SPIE:adr, month = feb, year = "2007", DOI = "http://dx.doi.org/10.1117/12.704723", ISSN = "0277-786X (print), 1996-756X (electronic)", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series", URL = "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F", acknowledgement = ack-nhfb, } @Article{Fuchs:1984:PDP, author = "A. Fuchs and G. Letta", title = "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}. ({French}) [{On} the problem of the first decimal digit]", journal = "{Bollettino della Unione Matem{\`a}tica Italiana. Serie VI. B}", volume = "3", pages = "451--461", year = "1984", ISSN = "0392-4041", ISSN-L = "0392-4041", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0557.60011", ajournal = "Boll. Unione Mat. Ital., VI. Ser., B", keywords = "analytical density; asymptotic density; first-digit problem", language = "French", ZMclass = "60B99 (Probability theory on general structures)", ZMreviewer = "R. Scozzafava", } @Article{Fuchs:1994:PDP, author = "Aim{\'e} Fuchs and Giorgio Letta", title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour les nombres premiers. ({French}) [The problem for the first decimal digit of prime numbers", journal = "Rendiconti della Accademia Nazionale delle Scienze detta dei XL. Serie V. Memorie di Matem{\`a}tica", volume = "18", number = "1", pages = "81--87", month = "????", year = "1994", bibdate = "Sat Feb 16 17:40:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf", ZMnumber = "0838.11004", acknowledgement = ack-nhfb, ajournal = "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.", keywords = "asymptotic densities; logarithmic density; primes; relative densities", language = "French", xxjournal = "Rend. Acad. Naz. Sci. Detta", xxvolume = "XL", ZMclass = "11B05 (Topology etc. of sets of numbers); 11K16 (Normal numbers, etc.)", ZMreviewer = "I. Z. Ruzsa (Budapest)", } @Article{Fuchs:1996:PDP, author = "Aim{\'e} Fuchs and Giorgio Letta", title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour les nombres premiers. ({French}) [The problem for the first decimal digit of prime numbers", journal = j-ELECT-J-COMB, volume = "3", number = "2", pages = "R25:1--R25:7", month = "????", year = "1996", ISSN = "1077-8926 (print), 1097-1440 (electronic)", ISSN-L = "1077-8926", bibdate = "Sat Feb 16 17:40:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The Foata Festschrift volume.", URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf", ZMnumber = "0853.11006", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Combinatorics", language = "French", xxpages = "601--607", } @Article{Fujiwara:2004:DPZ, author = "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki Aoyama and Mauro Gallegati and Wataru Souma", title = "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An} analysis with {European} firms", journal = j-PHYSICA-A, volume = "335", number = "1--2", pages = "197--216", day = "1", month = apr, year = "2004", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2003.12.015", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011294", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Fujiwara:2004:GPZ, author = "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di Guilmi} and Wataru Souma and Mauro Gallegati", title = "{Gibrat} and {Pareto--Zipf} revisited with {European} firms", journal = j-PHYSICA-A, volume = "344", number = "1--2", pages = "112--116", day = "1", month = dec, year = "2004", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2004.06.098", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009173", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Fujiwara:2004:ZLF, author = "Yoshi Fujiwara", title = "{Zipf} law in firms bankruptcy", journal = j-PHYSICA-A, volume = "337", number = "1--2", pages = "219--230", day = "1", month = jun, year = "2004", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2004.01.037", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B38", MRnumber = "2092316", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437104001165", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Book{Furlan:1946:HSU, author = "Luigi Vladimir Furlan", title = "{Das Harmoniegesetz der Statistik: Eine Untersuchung {\"u}ber die metrische Interdependenz der sozialen Erscheinungen}. ({German}) [{The} {Law of Harmony} in statistics: an investigation of the metrical interdependence of social phenomena]", volume = "2", publisher = "Verlag f{\"u}r Recht und Gesellschaft A.-G.", address = "Basel, Switzerland", pages = "xii + 504", year = "1946", LCCN = "HA29 .F85", bibdate = "Mon Nov 14 09:40:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "{Beihefte zum Assekuranzjahrbuch}", acknowledgement = ack-nhfb, author-dates = "1886--", keywords = "Benford--Furlan Law", language = "German", } @Article{Furry:1945:DND, author = "W. H. Furry and Henry Hurwitz", title = "Distribution of Numbers and Distribution of Significant Figures", journal = j-NATURE, volume = "155", number = "3924", pages = "52--53", day = "13", month = jan, year = "1945", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/155052a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Sun Sep 18 11:51:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Furusawa:2003:ZLG, author = "Chikara Furusawa and Kunihiko Kaneko", title = "{Zipf's Law} in Gene Expression", journal = j-PHYS-REV-LET, volume = "90", number = "??", pages = "088102", day = "26", month = feb, year = "2003", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.90.088102", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Gabaix:1999:ZLC, author = "Xavier Gabaix", title = "{Zipf}'s law for cities: An explanation", journal = j-Q-J-ECON, volume = "114", number = "3", pages = "739--767", year = "1999", CODEN = "QJECAT", DOI = "http://dx.doi.org/10.1162/003355399556133", ISSN = "0033-5533 (print), 1531-4650 (electronic)", ISSN-L = "0033-5533", bibdate = "Sat Nov 12 10:57:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0952.91059", abstract = "Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than $S$ is proportional to $ 1 / S $. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf's law.", acknowledgement = ack-nhfb, ajournal = "Q. J. Econ.", classmath = "91B62 (Dynamic economic models etc.) 91B72 (Spatial models)", fjournal = "The Quarterly Journal of Economics", keywords = "local growth; Zipf's law", } @Article{Gabaix:2003:TPL, author = "Xavier Gabaix and Parameswaran Gopikrishnan and Vasiliki Plerou and H. Eugene Stanley", title = "A theory of power-law distributions in financial market fluctuations", journal = j-NATURE, volume = "423", number = "6937", pages = "267--270", day = "15", month = may, year = "2003", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/nature01624", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Wed Feb 27 06:45:03 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Zipf's Law", } @Article{Gaite:2006:CSZ, author = "Jos{\'e} Gaite", title = "Cut-out sets and the {Zipf} law for fractal voids", journal = j-PHYSICA-D, volume = "223", number = "2", pages = "248--255", day = "15", month = nov, year = "2006", CODEN = "PDNPDT", DOI = "http://dx.doi.org/10.1016/j.physd.2006.09.021", ISSN = "0167-2789 (print), 1872-8022 (electronic)", ISSN-L = "0167-2789", MRclass = "28A80", MRnumber = "2307212", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167278906003848", acknowledgement = ack-nhfb, fjournal = "Physica. D, Nonlinear phenomena", keywords = "Zipf's Law", } @Article{Gambini:2012:PDD, author = "Alessandro Gambini and Giovanni Mingari Scarpello and Daniele Ritelli", title = "Probability of digits by dividing random numbers: a $ \psi $ and $ \zeta $ functions approach", journal = j-EXPO-MATH, volume = "30", number = "3", pages = "223--238", month = "????", year = "2012", CODEN = "????", DOI = "http://dx.doi.org/10.1016/j.exmath.2012.03.001", ISSN = "0723-0869 (print), 1878-0792 (electronic)", ISSN-L = "0723-0869", bibdate = "Thu Feb 14 05:56:39 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0723086912000230", acknowledgement = ack-nhfb, ajournal = "Expo. Math.", fjournal = "Expositiones Mathematicae", hoc-program-1 = "func p(r) return(1/20 + (1/2)*(psi((r + 11)/10) - psi(r/10 + 1)))", hoc-program-2 = "for (r = 0; r < 10; ++r) printf({"}%2d: %.5f {"}, r, p(r)); println {""}", journal-URL = "http://www.sciencedirect.com/science/journal/07230869", keywords = "Euler $\psi$ function; Hurwitz $\zeta$ function", remark = "This paper proves formulas for the probability of first-digit occurrences in the ratios of random integers, and compares the predictions with the somewhat different ones from Benford's Law. Their work simplifies a result of Ces{\`a}ro (1885), and predicts that the probability of the first quotient digit being $r$ is given by $ p(r) = 1 / 20 + (1 / 2)*(\psi ((r + 11) / 10) - \psi (r / 10 + 1))) $. That predicts these pairs of $ (r, p(r)) $: $ (0, 0.12673) $, $ (1, 0.11736) $, $ (2, 0.10992) $, $ (3, 0.10390) $, $ (4, 0.09894) $, $ (5, 0.09478) $, $ (6, 0.09125) $, $ (7, 0.08822) $, $ (8, 0.08560) $, $ (9, 0.08330) $. Those values may be compared with the Benford's Law prediction for the second digit (possibly zero) of $ (0, 0.120) $, $ (1, 0.114) $, $ (2, 0.109) $, $ (3, 0.104) $, $ (4, 0.100) $, $ (5, 0.097) $, $ (6, 0.093) $, $ (7, 0.090) $, $ (8, 0.088) $, and $ (9, 0.085) $.", } @Article{Gan:2006:ZLS, author = "Li Gan and Dong Li and Shunfeng Song", title = "Is the {Zipf} law spurious in explaining city-size distributions?", journal = j-ECONOM-LETT, volume = "92", number = "2", pages = "256--262", day = "1", month = aug, year = "2006", CODEN = "ECLEDS", DOI = "http://dx.doi.org/10.1016/j.econlet.2006.03.004", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176506000772", acknowledgement = ack-nhfb, fjournal = "Economics Letters", keywords = "Zipf's Law", } @InCollection{Gangopadhyay:2013:EZL, author = "Kausik Gangopadhyay and Banasri Basu", title = "Evolution of {Zipf}'s law for {Indian} urban agglomerations via-{\`a}-vis {Chinese} urban agglomerations", crossref = "Abergel:2013:ESR", pages = "119--129", year = "2013", DOI = "http://dx.doi.org/10.1007/978-88-470-2553-0_8", MRclass = "91B80", MRnumber = "2963609", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "New Econ. Windows", acknowledgement = ack-nhfb, } @Article{Garcia:2011:FPA, author = "Juan Manuel Garcia Garcia", title = "A fixed-point algorithm to estimate the {Yule-Simon} distribution parameter", journal = j-APPL-MATH-COMP, volume = "217", number = "21", pages = "8560--8566", day = "1", month = jul, year = "2011", CODEN = "AMHCBQ", DOI = "http://dx.doi.org/10.1016/j.amc.2011.03.092", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Tue Oct 25 12:05:30 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/00963003", URL = "http://www.sciencedirect.com/science/article/pii/S0096300311004607", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @Article{Gauvrit:2008:PLB, author = "Nicolas Gauvrit and Jean-Paul Delahaye", title = "Pourquoi la loi de {Benford} n'est pas myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is not mysterious]", journal = "Math{\'e}matiques et Sciences Humaines = Mathematics and Social Sciences", volume = "46", number = "182", pages = "7--15", year = "2008", CODEN = "????", ISSN = "0987-6936 (print), 1950-6821 (electronic)", ISSN-L = "0987-6936", MRclass = "62A01 (91E10)", MRnumber = "2433183 (2009f:62008)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf", acknowledgement = ack-nhfb, ajournal = "Math. Sci. Hum. Math. Soc. Sci.", fjournal = "Math{\'e}matiques et Sciences Humaines= Mathematics and Social Sciences", language = "French", } @Article{Gauvrit:2009:LBG, author = "Nicolas Gauvrit and Jean-Paul Delahaye", title = "Loi de {Benford} g{\'e}n{\'e}rale. ({French}) [{General} {Benford}'s law]", journal = "Math. Sci. Hum. Math. Soc. Sci.", volume = "??", number = "186", pages = "5--15", year = "2009", CODEN = "????", ISSN = "0987-6936 (print), 1950-6821 (electronic)", ISSN-L = "0987-6936", MRclass = "62E10 (11A63 37A45)", MRnumber = "2562062 (2010i:62029)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://msh.revues.org/document11034.html", acknowledgement = ack-nhfb, fjournal = "Math{\'e}matiques et Sciences Humaines. Mathematics and Social Sciences", language = "French", } @Article{Gauvrit:2009:SRI, author = "N. Gauvrit and J.-P. Delahaye", title = "Scatter and regularity imply {Benford}'s law \ldots{} and more", journal = "ArXiv e-prints", month = oct, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G; http://arxiv.org/abs/0910.1359", abstract = "A random variable (r.v.) $X$ is said to follow Benford's law if $ \log (X) $ is uniform $ \bmod 1 $. Many experimental data sets prove to follow an approximate version of it, and so do many mathematical series and continuous random variables. This phenomenon received some interest, and several explanations have been put forward. Most of them focus on specific data, depending on strong assumptions, often linked with the log function. Some authors hinted --- implicitly --- that the two most important characteristics of a random variable when it comes to Benford are regularity and scatter. In a first part, we prove two theorems, making up a formal version of this intuition: scattered and regular r.v.'s do approximately follow Benford's law. The proofs only need simple mathematical tools, making the analysis easy. Previous explanations thus become corollaries of a more general and simpler one. These results suggest that Benford's law does not depend on properties linked with the log function. We thus propose and test a general version of the Benford's law. The success of these tests may be viewed as an a posteriori validation of the analysis formulated in the first part.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0910.1359", keywords = "Mathematics - Probability, Statistics - Methodology, G.3", primaryclass = "math.PR", } @InCollection{Gauvrit:2011:SRI, author = "N. Gauvrit and J-P. Delahaye", title = "Scatter and Regularity Implies {Benford's Law}\ldots{} and More", crossref = "Zenil:2011:RTC", pages = "53--69", year = "2011", bibdate = "Mon Feb 18 18:29:00 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Geiringer:1948:RVF, author = "Hilda Geiringer", title = "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz der Statistik: Eine Untersuchung {\"u}ber die metrische Interdependenz der sozialen Erscheinungen}. ({German}) [{The} {Law of Harmony} in statistics: an investigation of the metrical interdependence of social phenomena]", journal = j-J-AM-STAT-ASSOC, volume = "43", number = "242", pages = "325--328", month = jun, year = "1948", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Nov 14 09:42:45 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "See \cite{Furlan:1946:HSU}.", URL = "http://www.jstor.org/stable/2280379", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Gelbukh:2001:ZHL, author = "Alexander Gelbukh and Grigori Sidorov", title = "{Zipf} and {Heaps Laws}' Coefficients Depend on Language", journal = j-LECT-NOTES-COMP-SCI, volume = "2004", pages = "332--??", year = "2001", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Sat Feb 2 13:03:22 MST 2002", bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm; http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", } @InCollection{Gell-Mann:1997:ETZ, author = "Murray Gell-Mann", title = "Empirical Theory --- {Zipf}'s Law", crossref = "Gell-Mann:1997:QJA", pages = "92--97", year = "1997", bibdate = "Mon Sep 01 10:20:00 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Genolini:2010:EIP, author = "Christophe Genolini and Tarak Driss", title = "Eveiller l'int{\'e}r{\^e}t pour la statistique par l'exemple. ({French}) [{Raising} interest in statistics by example]", journal = "Statistique et Enseignement", volume = "1", number = "2", pages = "49--57", month = "????", year = "2010", CODEN = "????", DOI = "????", ISSN = "2108-6745", ISSN-L = "2108-6745", bibdate = "Mon Feb 18 17:43:03 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16", acknowledgement = ack-nhfb, journal-URL = "http://www.statistique-et-enseignement.fr/", keywords = "Benford's Law", language = "French", } @TechReport{Gent:2001:BL, author = "Ian Gent and Toby Walsh", title = "{Benford's Law}", type = "Report", institution = "School of Computer Science, University of St. Andrews, and Department of Computer Science, University of York", address = "St. Andrews, Scotland and York, England", pages = "7", day = "2", month = feb, year = "2001", bibdate = "Fri Nov 18 08:37:38 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf", abstract = "Benford's Law predicts the frequency of the leading digit in numbers met in a wide range of naturally occurring phenomena. In data following Benford's Law, numbers start with a small leading digit more often those with a large leading digit. Here we demonstrate that Benford's Law also describes a wide range of computational phenomena. In particular, we show that a number of different statistics associated with computation like space and runtime often follow Benford's Law. We also show that search cost on input data that follows Benford's Law is often very different to that on more uniform data. These results could be used to improve algorithm performance (for example, for load balancing or disk de-fragmentation), as well as to help model algorithm performance. Benford's Law can also be used to generate data for benchmarking algorithms that may be more realistic than purely random data.", acknowledgement = ack-nhfb, remark = "PDF file no longer at the St. Andrews URL on 18 November 2011, but recovered from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.", } @Article{Geyer:2004:DFD, author = "Christina Lynn Geyer and Patricia Pepple Williamson", title = "Detecting fraud in data sets using {Benford's Law}", journal = j-COMM-STAT, volume = "B33", number = "1", pages = "229--246", month = "????", year = "2004", CODEN = "CSSCDB", DOI = "http://dx.doi.org/10.1081/SAC-120028442", ISSN = "0361-0918", ISSN-L = "0361-0918", MRclass = "62-07", MRnumber = "2044866", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Comm. Statist. Simulation Comput.", fjournal = "Communications in Statistics. Simulation and Computation", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Geyer:2012:ABL, author = "A. Geyer and J. Mart{\'\i}", title = "Applying {Benford}'s law to volcanology", journal = "Geology", volume = "40", number = "4", pages = "327--330", month = apr, year = "2012", DOI = "http://dx.doi.org/10.1130/G32787.1", bibdate = "Mon Feb 18 19:11:36 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://geology.gsapubs.org/content/40/4/327", acknowledgement = ack-nhfb, } @Book{Gibrat:1931:IE, author = "Robert Gibrat", title = "Les In{\'e}galit{\'e}s {\'e}conomiques", publisher = "Librairie du Recueil Sirey", address = "Paris, France", pages = "286", year = "1931", LCCN = "HB251.GIB", bibdate = "Mon Feb 18 14:43:11 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; library.ox.ac.uk:210/ADVANCE", note = "Applications: aux in{\'e}galit{\'e}s des richesses, {\`a} la concentration des entreprises, aux populations des villes, aux statistiques des familles, etc. d'une loi nouvelle. La loi de l'effet proportionnel.", URL = "http://en.wikipedia.org/wiki/Gibrat%27s_law", acknowledgement = ack-nhfb, author-dates = "1904--1980", remark-1 = "According to at least one library catalog (SWB), this book may be the author's doctoral dissertation from l'Universit{\'e} de Paris in 1931.", remark-2 = "This book is cited as the origin of Gibrat's Law, or Gibrat's rule of proportionate growth, that ``the size of a firm and its growth rate are independent''.", } @TechReport{Giles:2005:BLN, author = "David E. Giles", title = "{Benford's Law} and Naturally Occurring Prices in Certain {ebaY} Auctions", type = "Econometrics Working Paper", number = "EWP0505", institution = "Department of Economics, University of Victoria", address = "Victoria, BC, Canada", month = may, year = "2005", ISSN = "1485-6441", bibdate = "Thu Feb 15 16:24:39 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://web.uvic.ca/econ/ewp0505.pdf", abstract = "We show that certain the winning bids for certain ebaY auctions obey Benford's Law. One implication of this is that it is unlikely that these bids are subject to collusion among bidders, or ``shilling'' on the part of sellers. Parenthetically, we also show that numbers from the naturally occurring Fibonacci and Lucas sequences also obey Benford's Law.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Giles:2007:BLN, author = "D. E. Giles", title = "{Benford's Law} and naturally occurring prices in certain {eBay} auctions", journal = j-APPL-ECON-LETT, volume = "14", number = "3", pages = "157--161", year = "2007", CODEN = "????", DOI = "http://dx.doi.org/10.1080/13504850500425667", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Wed Nov 16 09:49:53 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/toc/rael20/current", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", keywords = "Benford's Law; Fibonacci sequences; Lucas sequences", } @Article{Gini:1957:SFD, author = "Corrado Gini", title = "Sulla frequenza delle cifre iniziali dei numeri osservati. ({Italian}) [{On} the frequency of initial digits of observed numbers]", journal = "{Bulletin de l'Institut International de Statistique}", volume = "35", number = "2", pages = "57--76", year = "1957", CODEN = "BISQA3", ISSN = "????", MRclass = "62.00", MRnumber = "0117807 (22 \#8581)", bibdate = "Sun Sep 18 11:54:25 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "29th session, 2nd delivery, Rio de Janerio.", acknowledgement = ack-nhfb, ajournal = "Bull. Inst. Internat. Stat.", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", language = "Italian", xxvolume = "34 (wrong!)", } @Article{Gisin:2009:EEV, author = "Vladimir Gisin and Andrey Markov and Igor Vinukov", title = "Estimation of extreme values of returns using the {Zipf--Mandelbrot} flow", journal = j-INT-J-PURE-APPL-MATH, volume = "50", number = "2", pages = "245--250", year = "2009", CODEN = "????", ISSN = "1311-8080", ISSN-L = "1314-3395", MRclass = "60G70 (91B28 91B84)", MRnumber = "2488836", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Pure and Applied Mathematics", } @Article{Giuliano:2010:UPI, author = "Rita Giuliano and {\'E}lise Janvresse", title = "A unifying probabilistic interpretation of {Benford}'s law", journal = "Uniform Distribution Theory", volume = "5", number = "2", pages = "169--182", year = "2010", CODEN = "????", ISSN = "1336-913X", ISSN-L = "1336-913X", MRclass = "60J10 (11K99 60A99)", MRnumber = "2781415", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf", acknowledgement = ack-nhfb, ajournal = "Unif. Distrib. Theory", fjournal = "Uniform Distribution Theory", } @Article{Giuliano:2011:WCS, author = "Rita Giuliano", title = "Weak convergence of sequences from fractional parts of random variables and applications", journal = j-THEORY-PROBAB-MATH-STAT, volume = "83", number = "??", pages = "49--58", month = "????", year = "2011", CODEN = "TPMSCO", DOI = "????", ISSN = "0094-9000 (print), 1547-7363 (electronic)", ISSN-L = "0094-9000", MRclass = "60F05, 60G52, 60G70, 11K06 (62G07, 42A10, 42A61)", MRnumber = "http://www.ams.org/mathscinet-getitem?mr=2768848", bibdate = "Mon Feb 18 17:47:02 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf", acknowledgement = ack-nhfb, fjournal = "Theory of Probability and Mathematical Statistics", journal-URL = "http://www.ams.org/publications/journals/journalsframework/tpms", keywords = "Benford's Law", } @TechReport{Gonzales-Garcia:2009:BLM, author = "J. Gonzales-Garcia and G. Pastor", title = "{Benford's Law} and Macroeconomic Data Quality", type = "Working Paper", institution = "International Monetary Fund", address = "????", year = "2009", bibdate = "Tue Nov 22 18:53:16 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437", acknowledgement = ack-nhfb, } @Article{Good:1965:LE, author = "I. J. Good", title = "Letter to the Editor", journal = j-AMER-STAT, volume = "19", number = "3", pages = "43--43", month = jun, year = "1965", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Mon Nov 14 09:56:33 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2681423", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", keywords = "Benford's Law", remark = "Refers to \cite{Pinkham:1961:DFS}, and cites a review of that article published by Good in Mathematical Reviews (1962), page 214, which I have not yet been able to locate.", } @InCollection{Gorroochurn:2012:BPB, author = "Prakash Gorroochurn", title = "{Benford} and the Peculiar Behavior of the First Significant Digit (1938)", crossref = "Gorroochurn:2012:CPP", chapter = "27", pages = "233--239", year = "2012", DOI = "http://dx.doi.org/10.1002/9781118314340.ch27", bibdate = "Sat Feb 23 17:26:17 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "(Benford) distribution; a distribution of distributions; and Benford's law; Benford and the peculiar behavior of the first significant digit (1938); First 100 Fibonacci Numbers; first-digit law or Benford's law; scale invariance; the leading digit and its behavior", } @Article{Goto:1992:SEB, author = "Kazuo Got{\^o}", title = "Some examples of {Benford} sequences", journal = "Math. J. Okayama Univ.", volume = "34", pages = "225--232 (1994)", year = "1992", CODEN = "MJOKAP", ISSN = "0030-1566", ISSN-L = "0030-1566", MRclass = "11K36", MRnumber = "1272624 (95c:11097)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Journal of Okayama University", } @Article{Gottwald:2002:NBL, author = "Georg A. Gottwald and Matthew Nicol", title = "On the nature of {Benford's Law}", journal = j-PHYSICA-A, volume = "303", number = "3--4", pages = "387--396", day = "15", month = jan, year = "2002", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(01)00497-6", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "60C05 (28D05 60E05 82B05)", MRnumber = "1917635 (2003d:60015)", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://adsabs.harvard.edu/abs/2002PhyA..303..387G; http://www.sciencedirect.com/science/article/pii/S0378437101004976", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Goudsmit:1944:SFN, author = "S. A. Goudsmit and W. H. Furry", title = "Significant Figures of Numbers in Statistical Tables", journal = j-NATURE, volume = "154", number = "3921", pages = "800--801", day = "23", month = dec, year = "1944", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/154800a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Sun Sep 18 11:57:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See later work \cite{Logan:1978:FDP}, and severe criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.", URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf", abstract = "A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.", acknowledgement = ack-nhfb, author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)", fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed the concept of electron spin, a critical step forward in the quantum mechanics of many-electron systems. Surprisingly, that work did not get them the Nobel Prize, but it did spur Wolfgang Pauli to present his Exclusion Principle in 1925, for which he received the 1945 Nobel Prize in Physics. After World War II, Goudsmit was the scientific head of the Alsos mission to capture German nuclear scientists. In the 1950s, he founded the journal Physical Review Letters. During the 1960s and 1970s, he was Editor-in-Chief of the main American physics journal, the Physical Review.", } @Article{Goudsmit:1977:PEP, author = "Samuel Goudsmit", title = "Pitfalls in Elementary Probability", journal = j-PROC-AMER-PHIL-SOC, volume = "121", number = "2", pages = "188--189", day = "29", month = apr, year = "1977", CODEN = "PAPCAA", ISSN = "0003-049X", bibdate = "Fri Mar 22 08:50:02 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Based on a lecture presented November 11, 1976.", URL = "http://www.jstor.org/stable/986527", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", keywords = "Benford's Law; biased coin flips; biased dice throws; roulette wheels", } @Article{Grabski:2010:DDM, author = "Severin Grabski", title = "Discussion of {``Data mining journal entries for fraud detection: An exploratory study''}", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "11", number = "3", pages = "182--185", month = sep, year = "2010", CODEN = "IJAIA7", DOI = "http://dx.doi.org/10.1016/j.accinf.2010.07.008", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.", URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000394", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Benford's Law", } @Article{Green:1986:BRP, author = "M. W. Green", title = "Book Reviews: {{\em Pareto Distributions}}, by {B. C. Arnold}", journal = j-APPL-STAT, volume = "35", number = "2", pages = "215--215", year = "1986", CODEN = "APSTAG", ISSN = "0035-9254 (print), 1467-9876 (electronic)", ISSN-L = "0035-9254", bibdate = "Sat Apr 21 10:24:36 MDT 2001", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Applied Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues", } @InProceedings{Grekos:2003:RSC, author = "G. Grekos and R. Giuliano-Antonini", editor = "????", booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July 6--12, 2003}", title = "Regular sets and conditional density: an extension of {Benford}'s law", publisher = "????", address = "????", pages = "??--??", year = "2003", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:43:43 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Grendar:2007:ENP, author = "Marian Grendar and George Judge and Laura Schechter", title = "An empirical non-parametric likelihood family of data-based {Benford}-like distributions", journal = j-PHYSICA-A, volume = "380", number = "??", pages = "429--438", day = "1", month = jul, year = "2007", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2007.02.062", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://adsabs.harvard.edu/abs/2007PhyA..380..429G; http://www.sciencedirect.com/science/article/pii/S0378437107001963", acknowledgement = ack-nhfb, fjournal = "Physica A: Statistical Mechanics and its Applications", keywords = "Benford's Law", } @InProceedings{Guettler:2012:BGQ, author = "S. Guettler and F. Thiemann and R. A. E. Mueller", editor = "M. Clasen and G. Fr{\"o}hlich and H. Bernhardt and K. Hildebrand and B. Theuvsen", booktitle = "{Informationstechnologie f{\"u}r eine nachhaltige Landbewirtschaftung. Fokus Forstwirtschaft. Referate der 32. GIL-Jahrestagung, 29. Februar--1. M{\"a}rz 2012, Freising}. ({German}) [Information technology for sustainable land management. Focus on forestry. Papers of the 32nd GIL Annual Conference 29, February--1 March 2012, Freising]", title = "{Benfords Gesetz: Ein Qualit{\"a}tstest f{\"u}r statistische Reihen angewendet auf Handelsdaten f{\"u}r Agrarprodukte}. ({German}) [{Benford's Law}: a quality test applied for statistical series on trade data for agricultural products]", volume = "194", publisher = "Gesellschaft f{\"u}r Informatik.", address = "Bonn, Germany", pages = "111--114", year = "2012", ISBN = "3-88579-288-5", ISBN-13 = "978-3-88579-288-8", ISSN = "1617-5468", LCCN = "????", bibdate = "Tue Feb 19 05:44:08 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes in Informatics", URL = "http://www.gil-net.de/Publikationen/24_111.pdf", acknowledgement = ack-nhfb, bookpages = "334 (est.)", language = "German", } @Article{Gunnel:2009:DBL, author = "S. G{\"u}nnel and K.-H. T{\"o}dter", title = "Does {Benford's Law} Hold in Economic Research and Forecasting?", journal = j-EMPIRICA, volume = "36", number = "3", pages = "273--292", month = aug, year = "2009", CODEN = "????", DOI = "http://dx.doi.org/10.1007/s10663-008-9084-1", ISSN = "0340-8744 (print), 1573-6911 (electronic)", ISSN-L = "0340-8744", bibdate = "Thu Nov 17 19:16:10 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.springerlink.com/content/100261/", abstract = "First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford's law. This phenomenon has been used in business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford's law holds in economic research and forecasting. First, we examine the distribution of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford's law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content.", acknowledgement = ack-nhfb, fjournal = "Empirica", } @Article{Gunther:1992:PCZ, author = "R. G{\"u}nther and B. Schapiro and P. Wagner", title = "Physical complexity and {Zipf}'s law", journal = j-INT-J-THEOR-PHYS, volume = "31", number = "3", pages = "525--543", year = "1992", CODEN = "IJTPBM", DOI = "http://dx.doi.org/10.1007/BF00740003", ISSN = "0020-7748 (print), 1572-9575 (electronic)", ISSN-L = "0020-7748", MRclass = "58F40", MRnumber = "1154668 (92k:58252)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Theoretical Physics", journal-URL = "http://link.springer.com/journal/10773", } @Article{Gunther:1996:ZLE, author = "R. G{\"u}nther and L. Levitin and B. Schapiro and P. Wagner", title = "{Zipf}'s law and the effect of ranking on probability distributions", journal = j-INT-J-THEOR-PHYS, volume = "35", number = "2", pages = "395--417", year = "1996", CODEN = "IJTPBM", DOI = "http://dx.doi.org/10.1007/BF02083823", ISSN = "0020-7748 (print), 1572-9575 (electronic)", ISSN-L = "0020-7748", bibdate = "Sat Nov 12 10:53:57 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0843.60002", abstract = "Ranking procedures are widely used in the description of many different types of complex systems. Zipf's law is one of the most remarkable frequency-rank relationships and has been observed independently in physics, linguistics, biology, demography, etc. We show that ranking plays a crucial role in making it possible to detect empirical relationships in systems that exist in one realization only, even when the statistical ensemble to which the systems belong has a very broad probability distribution. Analytical results and numerical simulations are presented which clarify the relations between the probability distributions and the behavior of expected values for unranked and ranked random variables. This analysis is performed, in particular, for the evolutionary model presented in our previous papers which leads to Zipf's law and reveals the underlying mechanism of this phenomenon in terms of a system with interdependent and interacting components as opposed to the ``ideal gas'' models suggested by previous researchers. The ranking procedure applied to this model leads to a new, unexpected phenomenon: a characteristic ``staircase'' behavior of the mean values of the ranked variables (ranked occupation numbers). This result is due to the broadness of the probability distributions for the occupation numbers and does not follow from the ``ideal gas'' model. Thus, it provides an opportunity, by comparison with empirical data, to obtain evidence as to which model relates to reality.", acknowledgement = ack-nhfb, classmath = "60A99 (Foundations of probability theory)", fjournal = "International Journal of Theoretical Physics", journal-URL = "http://link.springer.com/journal/10773", keywords = "numerical simulations; ranking procedures; Zipf's law", } @Article{Guo:2007:DIM, author = "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao and Xiaodong Zhang", title = "Does {Internet} media traffic really follow {Zipf}-like distribution?", journal = j-SIGMETRICS, volume = "35", number = "1", pages = "359--360", month = jun, year = "2007", CODEN = "????", DOI = "http://doi.acm.org/10.1145/1254882.1254929", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Fri Jun 27 09:42:48 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "It is commonly agreed that Web traffic follows the Zipf-like distribution, which is an analytical foundation for improving Web access performance by client-server based proxy caching systems on the Internet. However, some recent studies have observed non-Zipf-like distributions of Internet media traffic in different content delivery systems. Due to the variety of media delivery systems and the diversity of media content, existing studies on media traffic are largely workload specific, and the observed access patterns are often different from or even conflict with each other. For Web media systems, study [3] reports that the access pattern of streaming media is Zipf-like in a university campus network, while study [2] finds that it is not Zipf-like in an enterprise media server.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "media; stretched exponential; Zipf-like", } @Article{Gupta:2007:IMS, author = "Arjun K. Gupta and Saralees Nadarajah", title = "Information matrices for some bivariate {Pareto} distributions", journal = j-APPL-MATH-COMP, volume = "184", number = "2", pages = "1069--1079", day = "15", month = jan, year = "2007", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Sat Jul 12 09:03:01 MDT 2008", bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/00963003", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @InProceedings{Haferkorn:2013:HVA, author = "Martin Haferkorn", editor = "Fethi Rabhi and Peter Gomber", booktitle = "{Enterprise applications and services in the finance industry: 6th International Workshop, FinanceCom 2012, Barcelona, Spain, June 10, 2012. Revised papers}", title = "Humans vs. Algorithms --- Who Follows {Newcomb--Benford's Law} Better with Their Order Volume?", chapter = "4", publisher = pub-SV, address = pub-SV:adr, pages = "61--70", year = "2013", DOI = "http://dx.doi.org/10.1007/978-3-642-36219-4_4", ISBN = "3-642-36219-2", ISBN-13 = "978-3-642-36219-4", LCCN = "HG173 .I58 2012", bibdate = "Wed Feb 13 19:15:28 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4_4", acknowledgement = ack-nhfb, book-URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4", remark = "This may be the first publication to reference this bibliography. It examines trading patterns of several days on the German Stock Exchange (Deutsche B{\"o}rse), with a total volume of almost 10 million trades, split almost equally between human and algorithmic traders. It finds that the algorithmic trades follow Benford's Law closely, but the human trades do not. It points out that algorithmic trading could be manipulated to make it look more like human trades, so as not to alert competitors to its actions.", subject = "Financial services industry; Information technology; Congresses; Data processing", } @Unpublished{Hafner:1969:CSR, author = "Everett M. Hafner", title = "Circular slide roulette", year = "1969", bibdate = "Mon Nov 14 10:00:25 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Unpublished but dated 1969. Presented in 1975 in an address at Hampshire College, Amherst, MA, USA", acknowledgement = ack-nhfb, } @Article{Haight:1969:TPD, author = "F. A. Haight", title = "Two probability distributions connected with {Zipf}'s rank-size conjecture", journal = j-ZASTOS-MAT, volume = "10", pages = "225--228", year = "1969", CODEN = "ZAMTAK", ISSN = "0044-1899", ISSN-L = "0044-1899", MRclass = "62.31", MRnumber = "0246425 (39 \#7729)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Polska Akademia Nauk. Instytut Matematyczny. Zastosowania Matematyki", } @Article{Hales:2009:TBL, author = "Douglas N. Hales and Satya S. Chakravorty and V. Sridharan", title = "Testing {Benford's Law} for improving supply chain decision-making: a field experiment", journal = j-INT-J-PROD-ECON, volume = "122", number = "2", pages = "606--618", month = dec, year = "2009", CODEN = "JPCEYE", DOI = "http://dx.doi.org/10.1016/j.ijpe.2009.06.017", ISSN = "0925-5273 (print), 1873-7579 (electronic)", ISSN-L = "0925-5273", bibdate = "Wed Nov 23 18:41:54 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163", acknowledgement = ack-nhfb, ajournal = "Int. j. prod. econ.", fjournal = "International Journal of Production Economics", } @Book{Hamming:1962:NMS, author = "R. W. (Richard Wesley) Hamming", title = "Numerical methods for scientists and engineers", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "411", year = "1962", LCCN = "QA297 .H28", bibdate = "Fri Aug 20 09:12:08 MDT 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "International series in pure and applied mathematics", acknowledgement = ack-nhfb, remark = "Cited in \cite{Sterbenz:1974:FPC}.", subject = "Numerical analysis; Electronic digital computers", } @Article{Hamming:1965:NLB, author = "R. W. Hamming and W. L. Mammel", title = "A Note on the Location of the Binary Point in a Computing Machine", journal = j-IEEE-TRANS-ELEC-COMPUT, volume = "EC-14", number = "2", pages = "260--261", month = apr, year = "1965", CODEN = "IEECA8", DOI = "http://dx.doi.org/10.1109/PGEC.1965.264258", ISSN = "0367-7508", ISSN-L = "0367-7508", bibdate = "Thu Jul 14 06:26:22 MDT 2011", bibsource = "http://www.computer.org/tc/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electronic Computers", remark = "The authors consider the low-level multiplication circuit efficiency of placing the binary point before or after the first bit. If the leading bit is equally likely to be a 0 or a 1, then their analysis shows that it is better to place the point before the leading bit. However, they report that a more likely distribution is logarithmic (as predicted by Benford's Law, although the Newcomb / Benford work is neither mentioned nor cited), in which case there is no advantage for either choice of placement of the binary point. They conclude that it would be humane to place it after the leading digit, by analogy with how people learn decimal arithmetic.", } @Article{Hamming:1970:DN, author = "R. W. Hamming", title = "On the Distribution of Numbers", journal = j-BELL-SYST-TECH-J, volume = "49", number = "8", pages = "1609--1625", month = oct, year = "1970", CODEN = "BSTJAN", ISSN = "0005-8580", ISSN-L = "0005-8580", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html; http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf; http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf", abstract = "This paper examines the distribution of the mantissas of floating-point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distribution $$ r(x) = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where $b$ is the base of the number system). The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is include.", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Hand:2007:DDD, author = "David Hand", title = "Deception and Dishonesty with Data: Fraud in Science", journal = j-SIGNIF, volume = "4", number = "1", pages = "22--25", month = mar, year = "2007", CODEN = "????", DOI = "http://dx.doi.org/10.1111/j.1740-9713.2007.00215.x", ISSN = "1740-9705 (print), 1740-9713 (electronic)", ISSN-L = "1740-9705", bibdate = "Thu Nov 17 19:17:58 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Significance ({Oxford, England})", } @Article{Handurukande:2006:PSB, author = "S. B. Handurukande and A.-M. Kermarrec and F. {Le Fessant} and L. Massouli{\'e} and S. Patarin", title = "Peer sharing behaviour in the {eDonkey} network, and implications for the design of server-less file sharing systems", journal = j-OPER-SYS-REV, volume = "40", number = "4", pages = "359--371", month = oct, year = "2006", CODEN = "OSRED8", DOI = "http://doi.acm.org/10.1145/1218063.1217970", ISSN = "0163-5980 (print), 1943-586X (electronic)", ISSN-L = "0163-5980", bibdate = "Fri Jun 20 17:14:10 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "In this paper we present an empirical study of a workload gathered by crawling the eDonkey network --- a dominant peer-to-peer file sharing system --- for over 50 days. We first confirm the presence of some known features, in particular the prevalence of free-riding and the Zipf-like distribution of file popularity. We also analyze the evolution of document popularity. We then provide an in-depth analysis of several clustering properties of such workloads. We measure the geographical clustering of peers offering a given file. We find that most files are offered mostly by peers of a single country, although popular files don't have such a clear home country. We then analyze the overlap between contents offered by different peers. We find that peer contents are highly clustered according to several metrics of interest. We propose to leverage this property by allowing peers to search for content without server support, by querying suitably identified semantic neighbours. We find via trace-driven simulations that this approach is generally effective, and is even more effective for rare files. If we further allow peers to query both their semantic neighbours, and in turn their neighbours' neighbours, we attain hit rates as high as over 55\% for neighbour lists of size 20.", acknowledgement = ack-nhfb, fjournal = "ACM SIGOPS Operating Systems Review", keywords = "file sharing; peer-to-peer; simulation; trace", } @Book{Hardy:1949:DS, author = "G. H. (Godfrey Harold) Hardy", title = "Divergent series", publisher = pub-CLARENDON, address = pub-CLARENDON:adr, pages = "xvi + 396", year = "1949", LCCN = "QA295 .H29", bibdate = "Wed Nov 16 08:14:50 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1877--1947", } @Book{Hardy:1975:ITN, author = "Godfrey H. Hardy and Edward M. Wright", title = "An Introduction to the Theory of Numbers", publisher = pub-CLARENDON, address = pub-CLARENDON:adr, edition = "Fourth", pages = "421", year = "1975", ISBN = "0-19-853310-1", ISBN-13 = "978-0-19-853310-8", LCCN = "????", bibdate = "Fri Jun 24 12:32:14 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Hardy:1991:DS, author = "G. H. (Godfrey Harold) Hardy", title = "Divergent series", publisher = "Chelsea Pub. Co.", address = "New York, NY, USA", edition = "Second", pages = "xvi + 396", year = "1991", ISBN = "0-8284-0334-1", ISBN-13 = "978-0-8284-0334-4", LCCN = "QA295 .H29 1991", bibdate = "Wed Nov 16 08:17:27 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1877--1947", remark = "Unaltered reprint of \cite{Hardy:1949:DS}, despite label of second edition.", subject = "Divergent series", } @Article{Harremoes:2001:MEF, author = "Peter Harremo{\"e}s and Flemming Tops{\o}e", title = "Maximum Entropy Fundamentals", journal = j-ENTROPY, volume = "3", number = "3", pages = "191--226", month = sep, year = "2001", CODEN = "ENTRFG", DOI = "http://dx.doi.org/10.3390/e3030191", ISSN = "1099-4300", ISSN-L = "1099-4300", bibdate = "Thu Feb 28 10:55:45 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.mdpi.com/1099-4300/3/3/191", acknowledgement = ack-nhfb, fjournal = "Entropy", keywords = "continuity of entropy; entropy loss; exponential family; game theoretical equilibrium; hyperbolic distributions; information topology; maximum entropy; minimum risk; Nash equilibrium code; partition function; Zipf's law", remark = "Open access journal.", } @Article{Harremoes:2005:ZLHa, author = "Peter Harremo{\"e}s and Flemming Topsoe", title = "{Zipf}'s law, hyperbolic distributions and entropy loss", journal = j-PHYSICA-A, volume = "328", number = "3--4", pages = "315--318", day = "1", month = aug, year = "2005", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.endm.2005.07.075", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1571065305051450", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @InCollection{Harremoes:2005:ZLHb, author = "Peter Harremo{\"e}s and Flemming Topsoe", editor = "Rudolf Ahlswede and others", booktitle = "General theory of information transfer and combinatorics.", title = "{Zipf}'s law, hyperbolic distributions and entropy loss", volume = "21", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "315--318", year = "2005", DOI = "http://dx.doi.org/10.1016/j.endm.2005.07.075", bibdate = "Sat Nov 12 11:07:14 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Electronic Notes in Discrete Mathematics", ZMnumber = "1158.91482", abstract = "Zipf's law --- or Estoup-Zipf's law --- is an empirical fact of computational linguistics which relates rank and frequency of words in natural languages. The law suggests modelling by distributions of ``hyperbolic type''. We present a satisfactory general definition and an information-theoretical characterization of the resulting hyperbolic distributions. When applied to linguistics this leads to a property of stability and flexibility, explaining that a language can develop towards higher and higher expressive powers without changing its basic structure.", acknowledgement = ack-nhfb, classmath = "91F20 (Linguistics) 94A15 (General topics of information theory) 94A17 (Measures of information)", keywords = "entropy loss; hyperbolic distributions; Zipf's law", } @InCollection{Harremoes:2006:ZLH, author = "P. Harremo{\"e}s and F. Topsoe", editor = "Rudolf Ahlswede and others", booktitle = "General theory of information transfer and combinatorics", title = "{Zipf}'s law, hyperbolic distributions and entropy loss", volume = "4123", publisher = pub-SV, address = pub-SV:adr, pages = "788--792", year = "2006", DOI = "http://dx.doi.org/10.1007/11889342_50", bibdate = "Sat Nov 12 11:15:28 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, ZMnumber = "1158.91481", abstract = "Zipf's law --- or Estoup-Zipf's law --- is an empirical fact of computational linguistics which relates rank and frequency of words in natural languages. The law suggests modelling by distributions of ``hyperbolic type''. We present a satisfactory general definition and an information-theoretical characterization of the resulting hyperbolic distributions. When applied to linguistics this leads to a property of stability and flexibility, explaining that a language can develop towards higher and higher expressive powers without changing its basic structure.", acknowledgement = ack-nhfb, classmath = "91F20 (Linguistics) 94A15 (General topics of information theory) 94A17 (Measures of information)", keywords = "entropy loss; hyperbolic distributions; Zipf's law", } @Article{Hartshorn:2009:BRB, author = "Kevin Hartshorn", title = "Book Review: {{\booktitle{The fabulous Fibonacci numbers}} by Alfred Posamentier and Ingmar Lehmann}", journal = j-J-MATH-ARTS, volume = "3", number = "2", pages = "113--116", month = "????", year = "2009", CODEN = "????", DOI = "http://dx.doi.org/10.1080/17513470902897569", ISSN = "1751-3472 (print), 1751-3480 (electronic)", ISSN-L = "1751-3480", bibdate = "Sat Jan 07 09:43:47 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematics and the Arts", onlinedate = "05 Jun 2009", } @Article{Hasan:2002:ADA, author = "Bassam Hasan", title = "Assessing data authenticity with {Benford}'s law", journal = "Information Systems Control Journal", volume = "6", pages = "??--??", year = "2002", CODEN = "ISYJFS", ISSN = "1526-7407", bibdate = "Sat Feb 16 17:45:21 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx", acknowledgement = ack-nhfb, journal-URL = "http://www.isaca.org/", remark = "Journal publication ceased at volume 6 in 2008, according to one library catalog, but volumes up to 2013 are available at journal Web site.", } @Article{Hassan:2003:EDA, author = "Bassam Hassan", title = "Examining data accuracy and authenticity with leading digit frequency analysis", journal = "Industrial Management + Data Systems", volume = "103", number = "2", pages = "121--125", month = "????", year = "2003", CODEN = "MDSD8F", ISSN = "0263-5577 (print), 1758-5783 (electronic)", ISSN-L = "0263-5577", bibdate = "Fri Nov 25 11:07:59 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hasumi:2007:ITS, author = "Tomohiro Hasumi", title = "Interoccurrence time statistics in the two-dimensional {Burridge--Knopoff} earthquake model", journal = j-PHYS-REV-E, volume = "76", number = "??", pages = "026117", day = "29", month = aug, year = "2007", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.76.026117", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.026117", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf--Mandelbrot law", } @Book{Havil:2003:GEE, author = "Julian Havil", title = "{Gamma}: Exploring {Euler}'s Constant", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xxiii + 266", year = "2003", ISBN = "0-691-09983-9", ISBN-13 = "978-0-691-09983-5", LCCN = "QA41 .H23 2003", bibdate = "Thu Sep 25 16:52:46 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/master.bib", note = "Benford's Law is the subject of Section 14.2, pages 145--155.", price = "US\$29.95", URL = "http://www.loc.gov/catdir/description/prin031/2002192453.html", acknowledgement = ack-nhfb, } @Article{Havlin:1995:DBZ, author = "Shlomo Havlin", title = "The distance between {Zipf} plots", journal = j-PHYSICA-A, volume = "216", number = "1--2", pages = "148--150", day = "1", month = jun, year = "1995", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/0378-4371(95)00069-J", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/037843719500069J", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Book{Heaps:1978:IRC, author = "Harold Stanley Heaps", title = "Information retrieval, computational and theoretical aspects", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xii + 344", year = "1978", ISBN = "0-12-335750-0", ISBN-13 = "978-0-12-335750-2", LCCN = "Z699 .H38", bibdate = "Sat Nov 12 11:36:39 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Library and information science", acknowledgement = ack-nhfb, remark = "Heaps's Law is given on pp. 206--208.", subject = "Information storage and retrieval systems", } @Article{Hefeeda:2008:TMP, author = "Mohamed Hefeeda and Osama Saleh", title = "Traffic modeling and proportional partial caching for peer-to-peer systems", journal = j-IEEE-TRANS-NETWORKING, volume = "16", number = "6", pages = "1447--1460", month = dec, year = "2008", CODEN = "IEANEP", DOI = "http://dx.doi.org/10.1109/TNET.2008.918081", ISSN = "1063-6692 (print), 1558-2566 (electronic)", ISSN-L = "1063-6692", bibdate = "Fri Mar 6 16:31:04 MST 2009", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib", abstract = "Peer-to-peer (P2P) file sharing systems generate a major portion of the Internet traffic, and this portion is expected to increase in the future. We explore the potential of deploying proxy caches in different Autonomous Systems (ASes) with the goal of reducing the cost incurred by Internet service providers and alleviating the load on the Internet backbone. We conduct an eight-month measurement study to analyze the P2P traffic characteristics that are relevant to caching, such as object popularity, popularity dynamics, and object size. Our study shows that the popularity of P2P objects can be modeled by a Mandelbrot-Zipf distribution, and that several workloads exist in P2P traffic. Guided by our findings, we develop a novel caching algorithm for P2P traffic that is based on object segmentation, and proportional partial admission and eviction of objects. Our trace-based simulations show that with a relatively small cache size, a byte hit rate of up to 35\% can be achieved by our algorithm, which is close to the byte hit rate achieved by an off-line optimal algorithm with complete knowledge of future requests. Our results also show that our algorithm achieves a byte hit rate that is at least 40\% more, and at most triple, the byte hit rate of the common web caching algorithms. Furthermore, our algorithm is robust in face of aborted downloads, which is a common case in P2P systems.", acknowledgement = ack-nhfb, fjournal = "IEEE\slash ACM Transactions on Networking", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771", keywords = "internet measurement; network protocols; peer-to-peer systems; traffic analysis; traffic modeling", } @Book{Henriques:2011:WLB, author = "Diana B. Henriques", title = "The wizard of lies: {Bernie Madoff} and the death of trust", publisher = "Times Books/Henry Holt", address = "New York, NY, USA", pages = "xxiv + 419", year = "2011", ISBN = "0-8050-9134-3", ISBN-13 = "978-0-8050-9134-2", LCCN = "HV6692.M33 H46 2011", bibdate = "Fri Mar 22 08:51:50 MDT 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Madoff, Bernard L; Swindlers and swindling; United States; Biography; Ponzi schemes; Commercial crimes", tableofcontents = "An earthquake on Wall Street \\ Becoming bernie \\ The hunger for yield \\ The big four \\ The cash spigot \\ What they wanted to believe \\ Warning signs \\ A near-death experience \\ Madoff's world \\ The year of living dangerously \\ Waking up in the rubble \\ Reckoning the damage \\ Net winners and net losers \\ The sins of the father \\ The wheels of justice \\ Hope, lost and found", } @Article{Herman:1998:TRI, author = "Tom Herman", title = "Tax report: An {IRS} blooper startles thousands of taxpayers", journal = j-WALL-ST-J, volume = "??", number = "??", pages = "1--1", day = "18", month = feb, year = "1998", CODEN = "WSJOAF", ISSN = "0099-9660", bibdate = "Fri Mar 22 09:17:50 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://online.wsj.com/article/SB887753996209804500.html", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Wall Street Journal", keywords = "Benford's Law", remark = "From the article: ``[a taxpayer] was expecting a \$513 tax refund. Instead, he recently received a letter from the Internal Revenue Service informing him that he owes the government \$300,000,007.57. \ldots{} about 3,000 other people around the nation got similar erroneous notices, each showing a balance due of `three hundred million dollars and change.'\,''", } @Article{Hernando:2009:ZLF, author = "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas and C. Vesperinas and A. Plastino", title = "{Zipf}'s law from a {Fisher} variational-principle", journal = j-PHYS-LET-A, volume = "374", number = "1", pages = "18--21", day = "14", month = dec, year = "2009", CODEN = "PYLAAG", DOI = "http://dx.doi.org/10.1016/j.physleta.2009.10.027", ISSN = "0375-9601 (print), 1873-2429 (electronic)", ISSN-L = "0375-9601", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0375960109012894", acknowledgement = ack-nhfb, fjournal = "Physics Letters A", journal-URL = "http://www.sciencedirect.com/science/journal/03759601", keywords = "Zipf's Law", } @Article{Herzel:1957:SDD, author = "Amato Herzel", title = "Sulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]", journal = "{Atti dell XV e XVII Riunione, Societa Italiana di Statistica}", volume = "??", number = "??", pages = "205--228", year = "1957", CODEN = "????", ISSN = "????", bibdate = "Sun Sep 18 12:00:07 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", language = "Italian", } @Article{Hickman:2010:DAC, author = "Matthew Hickman and Stephen Rice", title = "Digital Analysis of Crime Statistics: Does Crime Conform to {Benford's Law}?", journal = j-J-QUANT-CRIMINOL, volume = "26", number = "3", pages = "333--349", month = sep, year = "2010", CODEN = "JQCRE6", DOI = "http://dx.doi.org/10.1007/s10940-010-9094-6", ISSN = "0748-4518 (print), 1573-7799 (electronic)", ISSN-L = "0748-4518", bibdate = "Fri Nov 25 10:30:30 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Quantitative Criminology", keywords = "Benford distribution; Benford's law; Crime data; Crime statistics; Data errors; Digital analysis; Fabricated data; First digit; Fraud detection; Uniform crime reports", } @Article{Hill:1970:ZLP, author = "Bruce M. Hill", title = "{Zipf}'s law and prior distributions for the composition of a population", journal = j-J-AM-STAT-ASSOC, volume = "65", number = "331", pages = "1220--1232", month = sep, year = "1970", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62.35", MRnumber = "0279936 (43 \#5657)", MRreviewer = "I. J. Good", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", URL = "http://www.jstor.org/stable/2284288", ZMnumber = "Zbl 0224.92011", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Hill:1974:RFF, author = "Bruce M. Hill", title = "The rank-frequency form of {Zipf}'s law", journal = j-J-AM-STAT-ASSOC, volume = "69", number = "348", pages = "1017--1026", month = dec, year = "1974", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62E15", MRnumber = "0426242 (54 \#14188)", MRreviewer = "S. M. Samuels", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", ZMnumber = "Zbl 0301.60011", acknowledgement = ack-nhfb, classification = "B0240 (Probability and statistics); C1140 (Probability and statistics)", corpsource = "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI, USA", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", keywords = "Bose--Einstein allocation; distribution; random processes; rank frequency form; statistics; Zipf's law", treatment = "T Theoretical or Mathematical", } @Article{Hill:1975:SFZ, author = "Bruce M. Hill and Michael Woodroofe", title = "Stronger forms of {Zipf}'s law", journal = j-J-AM-STAT-ASSOC, volume = "70", number = "349", pages = "212--219", month = mar, year = "1975", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62E15 (62D05)", MRnumber = "0440763 (55 \#13633)", MRreviewer = "I. J. Good", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", ZMnumber = "Zbl 0326.92014", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Hill:1988:RNG, author = "Theodore Hill", title = "Random number guessing and the first digit phenomenon", journal = j-PSYCHOL-REP, volume = "62", number = "3", pages = "967--971", month = jun, year = "1988", CODEN = "PYRTAZ", DOI = "http://dx.doi.org/10.2466/pr0.1988.62.3.967", ISSN = "0033-2941 (print), 1558-691X (electronic)", ISSN-L = "0033-2941", bibdate = "Fri Feb 15 06:41:31 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967", acknowledgement = ack-nhfb, ajournal = "Psychol. rep.", fjournal = "Psychological Reports", } @Article{Hill:1995:BII, author = "Theodore P. Hill", title = "Base-invariance implies {Benford's Law}", journal = j-PROC-AM-MATH-SOC, volume = "123", number = "3", pages = "887--895", month = mar, year = "1995", CODEN = "PAMYAR", DOI = "http://dx.doi.org/10.2307/2160815", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "60A10 (28D05)", MRnumber = "1233974 (95d:60006)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2160815", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", } @Article{Hill:1995:SDP, author = "Theodore P. Hill", title = "The significant-digit phenomenon", journal = j-AMER-MATH-MONTHLY, volume = "102", number = "4", pages = "322--327", month = apr, year = "1995", CODEN = "AMMYAE", DOI = "http://dx.doi.org/10.2307/2974952", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11K99 (60E99)", MRnumber = "96f:11101", MRreviewer = "Jean-Loup Mauclaire", bibdate = "Wed Dec 3 17:17:33 MST 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html", } @Article{Hill:1995:SDS, author = "Theodore P. Hill", title = "A statistical derivation of the significant-digit law", journal = j-STAT-SCI, volume = "10", number = "4", pages = "354--363", year = "1995", CODEN = "STSCEP", ISSN = "0883-4237", ISSN-L = "0883-4237", MRclass = "60E99 (60A10 62E99)", MRnumber = "1421567 (98a:60021)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 10:09:36 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "2-P&origin=MSN; http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO", ZMnumber = "Zbl 0955.60509", acknowledgement = ack-nhfb, fjournal = "Statistical Science. A Review Journal of the Institute of Mathematical Statistics", } @TechReport{Hill:1996:NDT, author = "Theodore P. Hill", title = "A note on distributions of true versus fabricated data", type = "Preprint", institution = "Department of Mathematics, Georgia Institute of Technology", address = "Atlanta, GA, USA", pages = "4", year = "1996", bibdate = "Sat Feb 16 17:47:27 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr", acknowledgement = ack-nhfb, } @InCollection{Hill:1997:BL, author = "Theodore Hill", editor = "Michiel Hazewinkel", booktitle = "Encyclopedia of Mathematics, Supplement {I}", title = "{Benford's Law}", volume = "1", publisher = pub-SV, address = pub-SV:adr, pages = "102--103", year = "1997", ISBN = "90-481-4896-0", ISBN-13 = "978-90-481-4896-7", LCCN = "????", bibdate = "Wed Nov 16 10:29:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hill:1998:FDP, author = "Theodore P. Hill", title = "The First Digit Phenomenon", journal = j-AM-SCI, volume = "86", number = "4", pages = "358--363", month = jul # "\slash " # aug, year = "1998", CODEN = "AMSCAC", DOI = "http://dx.doi.org/10.1511/1998.4.358", ISSN = "0003-0996 (print), 1545-2786 (electronic)", ISSN-L = "0003-0996", bibdate = "Sat Dec 10 11:54:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf; http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf", abstract = "A century ago, Simon Newcomb observed an unexpected pattern in the first digits of logarithm tables: The digit $1$ is significantly more likely to occur than $2$, $2$ than $3$, and so on. More than a half-century later, Frank Benford rediscovered the first-digit phenomenon and found that it applied to many tables of numerical data, including the stock market, census statistics and accounting figures. New mathematical insights establish the empirical law developed by Newcomb and Benford as part of modern probability theory, and recent applications include testing of mathematical models, design of computers and detection of fraud in accounting.", acknowledgement = ack-nhfb, fjournal = "American Scientist", journal-URL = "http://www.americanscientist.org/issues/past.aspx", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Hill:1999:DFD, author = "Theodore P. Hill", title = "The Difficulty of Faking Data", journal = j-CHANCE, volume = "12", number = "3", pages = "27--31", month = "????", year = "1999", CODEN = "CNDCE4", DOI = "http://dx.doi.org/10.1080/09332480.1999.10542154", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Tue Nov 22 18:54:44 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/", keywords = "Benford's Law", xxnote = "Check: Hurlimann bibliography says v26 pp. 8--13??; that is wrong!", } @Article{Hill:1999:PCS, author = "Theodore P. Hill", title = "Le premier chiffre significatif fait sa loi. ({French}) [{The} first significant digit makes its law]", journal = "La Recherche: L'actualit{\'e} des sciences", volume = "2", number = "316", pages = "72--76", month = jan, year = "1999", CODEN = "RCCHBV", ISSN = "0029-5671 (print), 1625-9955 (electronic)", ISSN-L = "0029-5671", bibdate = "Sat Feb 16 17:51:25 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970", acknowledgement = ack-nhfb, language = "French", xxjournal = "La Recherche Hors S{\'e}rie", } @InProceedings{Hill:2002:RAB, author = "T. P. Hill", editor = "????", booktitle = "Conference, Leiden University", title = "Recent applications of {Benford}'s law", publisher = "????", address = "????", pages = "??--??", year = "2002", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:55:46 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hill:2005:RDS, author = "Theodore P. Hill and Klaus Sch{\"u}rger", title = "Regularity of digits and significant digits of random variables", journal = j-STOCH-PROC-APPL, volume = "115", number = "10", pages = "1723--1743", month = oct, year = "2005", CODEN = "STOPB7", DOI = "http://dx.doi.org/10.1016/j.spa.2005.05.003", ISSN = "0304-4149 (print), 1879-209X (electronic)", ISSN-L = "0304-4149", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0304414905000657", acknowledgement = ack-nhfb, fjournal = "Stochastic Processes and Their Applications", keywords = "Benford's Law; digit-regular random variable; floating-point numbers; law of least significant digits; nonleading digits; normal numbers; significant digits; significant-digit-regular random variable; trailing digits", } @Article{Hill:2011:LEB, author = "Theodore P. Hill", title = "Letter to the Editor: {Benford's Law} Blunders", journal = j-AMER-STAT, volume = "65", number = "2", pages = "141--141", month = may, year = "2011", CODEN = "ASTAAJ", DOI = "http://dx.doi.org/10.1198/tast.2011.10179", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Mon Feb 18 18:34:43 2013", bibsource = "http://www.amstat.org/publications/tas/; http://www.math.utah.edu/pub/tex/bib/amstat2010.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/pdf/10.1198/tast.2011.11011", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", remark = "Brief comment on a error in Feller's derivation of Benford's Law, with pointer to a corrected proof in \cite{Berger:2011:BLS}.", } @Article{Hisano:2011:PVD, author = "Ryohei Hisano and Didier Sornette and Takayuki Mizuno", title = "Predicted and verified deviations from {Zipf}'s law in ecology of competing products", journal = j-PHYS-REV-E, volume = "84", number = "2", pages = "026117", day = "24", month = aug, year = "2011", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.84.026117", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.84.026117", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "8", } @InProceedings{Hjorland:2005:BLS, author = "Birger Hj{\o}rland and Jeppe Nicolaisen", editor = "Fabio Crestani and Ian Ruthven", booktitle = "Context: nature, impact, and role: {5th International Conference on Conceptions of Library and Information Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005; proceedings}", title = "{Bradford}'s law of scattering: ambiguities in the concept of ``subject''", volume = "3507", publisher = pub-SV, address = pub-SV:adr, pages = "96--106", year = "2005", ISBN = "3-540-26178-8", ISBN-13 = "978-3-540-26178-0", LCCN = "Z672.5 .I5616 2005", bibdate = "Fri Nov 25 11:52:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, bookpages = "xiii + 250", } @Article{Hoare:1986:DFS, author = "G. T. Q. Hoare and E. Wright", title = "The distribution of first significant digits", journal = j-MATH-GAZ, volume = "70", number = "451", pages = "34--37", month = mar, year = "1986", CODEN = "MAGAAS", ISSN = "0025-5572", ISSN-L = "0025-5572", bibdate = "Sat Feb 16 17:57:52 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3615826", acknowledgement = ack-nhfb, fjournal = "Mathematical Gazette", journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620", } @Article{Hobza:2001:NBL, author = "Tom{\'a}{\v{s}} Hobza and Igor Vajda", title = "On the {Newcomb--Benford} law in models of statistical data", journal = "Revista Matem{\'a}tica Complutense", volume = "14", number = "2", pages = "407--420", year = "2001", CODEN = "????", ISSN = "1139-1138, 1696-8220, 1988-2807", ISSN-L = "1139-1138", MRclass = "62E10", MRnumber = "1871305 (2002j:62015)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Rev. Mat. Complut.", fjournal = "Revista Matem{\'a}tica Complutense", } @InCollection{Horgan:2009:BL, author = "Jane M. Horgan", title = "{Benford's Law}", crossref = "Horgan:2009:PRI", chapter = "9.4", pages = "142--144", year = "2009", bibdate = "Mon Feb 18 18:46:16 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hosking:1987:PQE, author = "J. R. M. Hosking and J. R. Wallis", title = "Parameter and Quantile Estimation for the Generalized {Pareto} Distribution", journal = j-TECHNOMETRICS, volume = "29", number = "3", pages = "339--349", month = "????", year = "1987", CODEN = "TCMTA2", ISSN = "0040-1706 (print), 1537-2723 (electronic)", ISSN-L = "0040-1706", bibdate = "Fri Nov 25 16:39:38 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Technometrics", } @Article{Hoyle:2002:MSM, author = "David C. Hoyle and Magnus Rattray and Ray Jupp and Andrew Brass", title = "Making sense of microarray data distributions", journal = j-BIOINFORMATICS, volume = "18", number = "4", pages = "576--584", month = apr, year = "2002", ISSN = "1367-4803 (print), 1367-4811 (electronic)", ISSN-L = "1367-4803", bibdate = "Fri Nov 25 11:16:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Bioinformatics", keywords = "Benford's Law; mRNA transcription data", } @Article{Hsu:1948:ESM, author = "E. H. Hs{\"u}", title = "An Experimental Study on ``Mental Numbers'' and a New Application", journal = j-J-GEN-PSYCH, volume = "38", number = "1", pages = "57--67", month = "????", year = "1948", CODEN = "JGPSAY", DOI = "http://dx.doi.org/10.1080/00221309.1948.9711768", ISSN = "0022-1309 (print), 1940-0888 (electronic)", ISSN-L = "0022-1309", bibdate = "Sat Jan 07 09:29:53 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768", acknowledgement = ack-nhfb, fjournal = "The Journal of General Psychology", keywords = "Benford's Law", onlinedate = "06 Jul 2010", } @Article{Huang:2001:PLE, author = "Z. F. Huang and S. Solomon", title = "Power, {L{\'e}vy}, exponential and {Gaussian}-like regimes in autocatalytic financial systems", journal = j-EUR-PHYS-J-B, volume = "20", number = "4", pages = "601--607", month = apr, year = "2001", CODEN = "EPJBFY", DOI = "http://dx.doi.org/10.1007/PL00011114", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Thu Feb 28 10:26:53 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/PL00011114", acknowledgement = ack-nhfb, fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", keywords = "power law; scale invariance; Zipf's law", } @Article{Huang:2008:IZL, author = "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and Jing-Shiuan Hua", title = "An investigation of {Zipf's Law} for fraud detection {(DSS\# 06-10-1826R(2))}", journal = j-DEC-SUPP-SYS, volume = "46", number = "1", pages = "70--83", month = dec, year = "2008", CODEN = "DSSYDK", DOI = "http://dx.doi.org/10.1016/j.dss.2008.05.003", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167923608001073", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "Benford's Law; Zipf's Law", } @Article{Huberman:1999:IGD, author = "Bernardo A. Huberman and Lada A. Adamic", title = "{Internet}: Growth dynamics of the {World-Wide Web}", journal = j-NATURE, volume = "401", number = "6749", pages = "131--131", day = "9", month = sep, year = "1999", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/43604", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Tue Nov 15 09:52:36 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Zipf's Law", } @Article{Hui:2011:BLN, author = "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min", title = "{Benford's Law} in Nuclear Structure Physics", journal = j-CHIN-PHYS-LETT, volume = "28", number = "3", pages = "32101--32104", month = mar, year = "2011", CODEN = "CPLEEU", DOI = "http://dx.doi.org/10.1088/0256-307X/28/3/032101", ISSN = "0256-307X (print), 1741-3540 (electronic)", ISSN-L = "0256-307X", bibdate = "Fri Nov 25 10:37:25 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Chinese Physics Letters", } @TechReport{Humenberger:2006:BGV, author = "Hans Humenberger", title = "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on the distribution of the first digit of numbers]", type = "Report", institution = "Institut f{\"u}r Mathematik und Angewandte Statistik, Universit{\"a}t f{\"u}r Bodenkultur", address = "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria", month = aug, year = "2006", bibdate = "Sun Feb 17 09:37:40 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf", acknowledgement = ack-nhfb, language = "German", } @Article{Humenberger:2008:EBB, author = "H. Humenberger", title = "{Eine elementarmathematische Begr{\"u}ndung des Benford-Gesetzes}. ({German}) [{An} elementary mathematical derivation of the {Benford Law}]", journal = "Der Mathematikunterricht", volume = "54", number = "??", pages = "24--34", month = "????", year = "2008", CODEN = "????", ISSN = "0025-5807", ISSN-L = "0025-5807", bibdate = "Fri Nov 18 11:59:44 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf", acknowledgement = ack-nhfb, language = "German", } @TechReport{Hungerbuhler:2007:BGF, author = "Norbert H{\"u}ngerb{\"u}hler", title = "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie die Mathematik Steuers{\"u}ndern das F{\"u}rchten lehrt} [{Benford's Law} on leading digits. Mathematics teaches tax evaders to fear]", type = "Report", institution = "EducETH", address = "Z{\"u}rich, Switzerland", pages = "24", day = "2", month = mar, year = "2007", bibdate = "Fri Nov 18 12:02:21 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf", acknowledgement = ack-nhfb, language = "German", lastaccess = "18 November 2011", remark = "This report has several nice figures, including photographs of Newcomb, Benford, and worn pages of log tables, and an amazing plot of the agreement of 200,125,088 mathematical constants with Benford's Law.", } @Article{Hurlimann:2003:GBL, author = "Werner H{\"u}rlimann", title = "A generalized {Benford} law and its application", journal = j-ADV-APPL-STAT, volume = "3", number = "3", pages = "217--228", year = "2003", CODEN = "????", ISSN = "0972-3617", ISSN-L = "0972-3617", MRclass = "11K31 (11B73)", MRnumber = "2034405 (2004k:11125)", MRreviewer = "Vydas {\v{C}}ekanavi{\v{c}}ius", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Advances and Applications in Statistics", } @Article{Hurlimann:2004:IPB, author = "Werner H{\"u}rlimann", title = "Integer powers and {Benford}'s law", journal = j-INT-J-PURE-APPL-MATH, volume = "11", number = "1", pages = "39--46", year = "2004", CODEN = "????", ISSN = "1311-8080", ISSN-L = "1314-3395", MRclass = "62E15 (11B83 11K31 62E20)", MRnumber = "2033394 (2005c:62030)", MRreviewer = "I. N. Volodin", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Pure and Applied Mathematics", } @TechReport{Hurlimann:2006:BLB, author = "Werner H{\"u}rlimann", title = "{Benford's Law} from 1881 to 2006: a bibliography", type = "Report", address = "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland", pages = "15", day = "5", month = jul, year = "2006", bibdate = "Fri Mar 30 11:32:30 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/pdf/math.ST/0607168", abstract = "On the occasion of the 125-th anniversary of Newcomb's paper, a bibliography of academic work related to Benford's law from its year of origin 1881 to 2006 has been compiled.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "This bibliography lists 325 references on the title subject, with these (years) and counts: (1881) 1, (1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1, (1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1, (1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2, (1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1, (1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2, (1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3, (1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4, (1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1, (1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6, (1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4, (1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12, (2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29, (2005) 34, (2006) 18.", } @Article{Hurlimann:2006:GBL, author = "W. Hurlimann", title = "Generalizing {Benford}'s law using power laws: application to integer sequences", journal = "ArXiv Mathematics e-prints", month = jul, year = "2006", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006math......7166H", acknowledgement = ack-nhfb, eprint = "arXiv:math/0607166", keywords = "Mathematics - Statistics, Mathematics - Number Theory, 11B73, 11B83, 11K31, 62E15, 62E17", } @Article{Hurlimann:2009:GBL, author = "Werner H{\"u}rlimann", title = "Generalizing {Benford}'s law using power laws: application to integer sequences", journal = j-INT-J-MATH-MATH-SCI, pages = "10", year = "2009", CODEN = "????", ISSN = "0161-1712", ISSN-L = "0161-1712", MRclass = "60E05 (11B83 62E15)", MRnumber = "2533550 (2010h:60043)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Article ID 970284.", URL = "http://arxiv.org/abs/math/0607166", abstract = "A simple method to derive parametric analytical extensions of Benford's law for first digits of numerical data is proposed. Two generalized Benford distributions are considered, namely the two-sided power Benford distribution and the new Pareto Benford distribution. The fitting capabilities of these generalized Benford distributions are illustrated and compared at some interesting and important integer sequences.", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", } @Article{Ioannides:2003:ZLC, author = "Yannis M. Ioannides and Henry G. Overman", title = "{Zipf}'s law for cities: an empirical examination", journal = j-REG-SCI-URBAN-ECON, volume = "33", number = "2", pages = "127--137", day = "1", month = mar, year = "2003", CODEN = "RSUEDM", DOI = "http://dx.doi.org/10.1016/S0166-0462(02)00006-6", ISSN = "0166-0462 (print), 1879-2308 (electronic)", ISSN-L = "0166-0462", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0166046202000066", acknowledgement = ack-nhfb, fjournal = "Regional Science and Urban Economics", journal-URL = "http://www.sciencedirect.com/science/journal/01660462", keywords = "Zipf's Law", } @Article{Ioannidis:2005:WMP, author = "John P. A. Ioannidis", title = "Why Most Published Research Findings Are False", journal = j-PLOS-MED, volume = "2", number = "8", pages = "696--701", month = aug, year = "2005", CODEN = "PMLEAC", DOI = "http://dx.doi.org/10.1371/journal.pmed.0020124", ISSN = "1549-1277 (print), 1549-1676 (electronic)", ISSN-L = "1549-1277", bibdate = "Fri Nov 18 12:42:05 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124", abstract = "There is increasing concern that most current published research findings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater financial and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance. Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these problems for the conduct and interpretation of research.", acknowledgement = ack-nhfb, articleno = "e124", fjournal = "PLoS Medicine", remark = "This article does not discuss Benford's Law, but is related to the use of that law in the detection of fraud in research data. Ioannidis discusses the abuse of statistics for limited experimental data, a topic that receives book-length treatment in \cite{Ziliak:2008:CSS}.", } @Article{Ipeirotis:2008:CAH, author = "Panagiotis G. Ipeirotis and Luis Gravano", title = "Classification-aware hidden-web text database selection", journal = j-TOIS, volume = "26", number = "2", pages = "6:1--6:??", month = mar, year = "2008", CODEN = "ATISET", DOI = "http://doi.acm.org/10.1145/1344411.1344412", ISSN = "1046-8188", ISSN-L = "0734-2047", bibdate = "Thu Jun 12 16:52:34 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/tois/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Many valuable text databases on the web have noncrawlable contents that are ``hidden'' behind search interfaces. Metasearchers are helpful tools for searching over multiple such ``hidden-web'' text databases at once through a unified query interface. An important step in the metasearching process is database selection, or determining which databases are the most relevant for a given user query. The state-of-the-art database selection techniques rely on statistical summaries of the database contents, generally including the database vocabulary and associated word frequencies. Unfortunately, hidden-web text databases typically do not export such summaries, so previous research has developed algorithms for constructing approximate content summaries from document samples extracted from the databases via querying. We present a novel ``focused-probing'' sampling algorithm that detects the topics covered in a database and adaptively extracts documents that are representative of the topic coverage of the database. Our algorithm is the first to construct content summaries that include the frequencies of the words in the database. Unfortunately, Zipf's law practically guarantees that for any relatively large database, content summaries built from moderately sized document samples will fail to cover many low-frequency words; in turn, incomplete content summaries might negatively affect the database selection process, especially for short queries with infrequent words. To enhance the sparse document samples and improve the database selection decisions, we exploit the fact that topically similar databases tend to have similar vocabularies, so samples extracted from databases with a similar topical focus can complement each other. We have developed two database selection algorithms that exploit this observation. The first algorithm proceeds hierarchically and selects the best categories for a query, and then sends the query to the appropriate databases in the chosen categories. The second algorithm uses ``shrinkage,'' a statistical technique for improving parameter estimation in the face of sparse data, to enhance the database content summaries with category-specific words. We describe how to modify existing database selection algorithms to adaptively decide (at runtime) whether shrinkage is beneficial for a query. A thorough evaluation over a variety of databases, including 315 real web databases as well as TREC data, suggests that the proposed sampling methods generate high-quality content summaries and that the database selection algorithms produce significantly more relevant database selection decisions and overall search results than existing algorithms.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Information Systems (TOIS)", keywords = "database selection; Distributed information retrieval; web search", } @Article{Irmay:1997:RBZ, author = "Shragga Irmay", title = "The relationship between {Zipf}'s law and the distribution of first digits", journal = j-J-APPL-STAT, volume = "24", number = "4", pages = "383--393", day = "1", month = aug, year = "1997", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", MRclass = "62E15", MRnumber = "1491308 (98h:62015)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.catchword.co.uk/titles/carfax/02664763/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", URL = "http://www.tandfonline.com/doi/abs/10.1080/02664769723594", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", keywords = "Benford's Law; Zipf's Law", xxpages = "383--394", } @Article{Ismail:2004:SES, author = "Sanaa Isma{\"\i}l", title = "A Simple Estimator for the Shape Parameter of the {Pareto} Distribution with Economics and Medical Applications", journal = j-J-APPL-STAT, volume = "31", number = "1", pages = "3--13", month = jan, year = "2004", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Sat Dec 4 12:10:37 MST 2004", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Article{Israeloff:1996:CZD, author = "N. E. Israeloff and M. Kagalenko and K. Chan", title = "Can {Zipf} Distinguish Language From Noise in Noncoding {DNA}?", journal = j-PHYS-REV-LET, volume = "76", number = "??", pages = "1976--??", day = "11", month = mar, year = "1996", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.76.1976", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @MastersThesis{Iudica:2012:BLM, author = "Federico Iudica", title = "{Benford's Law}: Mathematical Properties and Forensic Accounting Applications", type = "{Master}'s Thesis", school = "Facolt{\`a} di Impresa e Management, Cattedra di Matematica, Luiss Guido Carli University", address = "Rome, Italy", pages = "iv + 56", year = "2012", bibdate = "Tue Feb 19 05:54:59 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://tesi.eprints.luiss.it/8189/1/iudica-tesi-2012.pdf", acknowledgement = ack-nhfb, advisor = "Marco Dall'Aglio", language = "English", } @Article{Iyengar:1983:SPL, author = "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R. Uppuluri", title = "String patterns of leading digits", journal = j-APPL-MATH-COMP, volume = "12", number = "4", pages = "321--337", month = jul, year = "1983", CODEN = "AMHCBQ", DOI = "http://dx.doi.org/10.1016/0096-3003(83)90045-0", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Sat Feb 16 18:02:26 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/00963003", URL = "http://www.sciencedirect.com/science/article/pii/0096300383900450", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @Article{Izsak:2006:MLE, author = "F. Izs{\'a}k", title = "Maximum likelihood estimation for constrained parameters of multinomial distributions --- Application to {Zipf--Mandelbrot} models", journal = j-COMPUT-STAT-DATA-ANAL, volume = "51", number = "3", pages = "1575--1583", day = "1", month = dec, year = "2006", CODEN = "CSDADW", DOI = "http://dx.doi.org/10.1016/j.csda.2006.05.008", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", MRnumber = "2307527", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S016794730600154X", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", keywords = "Zipf's Law", } @Article{Jager:2008:DAD, author = "Hendrik Jager and Pierre Liardet", title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs de convergents de fractions continues. ({French}) [Arithmetic distributions of the denominators of continued fractions]", journal = "Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, Indagationes mathematicae", volume = "91", number = "2", pages = "181--197", day = "20", month = jun, year = "2008", CODEN = "????", DOI = "http://dx.doi.org/10.1016/S1385-7258(88)80026-X", ISSN = "1385-7258 (print), 1878-5972 (electronic)", ISSN-L = "1385-7258", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S138572588880026X", acknowledgement = ack-nhfb, fjournal = "Indagationes Mathematicae (Proceedings)", keywords = "Benford's Law", language = "French", xxjournal = "Indagationes Mathematicae (Proceedings)", } @MastersThesis{Jamain:2001:BL, author = "Adrien Jamain", title = "{Benford's Law}", type = "{Master}'s thesis", school = "Department of Mathematics, Imperial College of London and ENSIMAG", address = "London, UK", pages = "????", year = "2001", bibdate = "Sat Feb 16 18:06:41 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Not found in Imperial College Library or COPAC catalogs on 16 February 2013. URL link is broken too.", URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf", acknowledgement = ack-nhfb, } @Article{Jang:2008:CDH, author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and S. J. Miller", title = "Chains of distributions, hierarchical {Bayesian} models and {Benford's Law}", journal = "ArXiv e-prints", month = may, year = "2008", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J; http://arxiv.org/abs/0805.4226", abstract = "Kossovsky recently conjectured that the distribution of leading digits of a chain of probability distributions converges to Benford's law as the length of the chain grows. We prove his conjecture in many cases, and provide an interpretation in terms of products of independent random variables and a central limit theorem. An interesting consequence is that in hierarchical Bayesian models priors tend to satisfy Benford's Law as the number of levels of the hierarchy increases, which allows us to develop some simple tests (based on Benford's law) to test proposed models. We give explicit formulas for the error terms as sums of Mellin transforms, which converges extremely rapidly as the number of terms in the chain grows. We may interpret our results as showing that certain Markov chain Monte Carlo processes are rapidly mixing to Benford's law.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0805.4226", keywords = "Mathematics - Probability, Mathematics - Statistics Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)", pagecount = "15", primaryclass = "math.PR", } @Article{Jang:2009:CDH, author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and S. J. Miller", title = "Chains of distributions, hierarchical {Bayesian} models and {Benford's Law}", journal = "Journal of Algebra, Number Theory: Advances and Applications", volume = "1", number = "1", pages = "37--60", month = mar, year = "2009", CODEN = "????", ISSN = "0972-5555", ISSN-L = "0972-5555", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0805.4226", keywords = "Mathematics - Probability, Mathematics - Statistics Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)", primaryclass = "math.PR", } @Article{Jansen:2001:RNP, author = "C. J. M. Jansen and M. M. W. Pollmann", title = "On Round Numbers: Pragmatic Aspects of Numerical Expressions", journal = j-J-QUANT-LINGUISTICS, volume = "8", number = "3", pages = "187--201", month = "????", year = "2001", DOI = "http://dx.doi.org/10.1076/jqul.8.3.187.4095", ISSN = "0929-6174 (print), 1744-5035 (electronic)", ISSN-L = "0929-6174", bibdate = "Sat Jan 07 09:51:05 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095", abstract = "This paper describes and explains some regularities in the frequency of numbers in text. An analysis of number frequencies in text corpora in Dutch, English, German, and French confirms the expectation that frequency is highly dependent on two factors: magnitude and roundness. Roundness (defined as number frequency in an approximation context) proves to be related to three arithmetical properties: `10-ness', `2-ness', and `5-ness'. In predicting the frequency of numbers irrespective of their context `$ 2 1 / 2 $-ness' should be added to these factors, as is suggested in the work of Sigurd (1988). The role of the four number characteristics found in this study can be explained by the preference of the language user for using base numbers, and for doubling and halving quantities.", acknowledgement = ack-nhfb, fjournal = "Journal of Quantitative Linguistics", onlinedate = "09 Aug 2010", } @Article{Janvresse:2004:UDB, author = "{\'E}lise Janvresse and Thierry de la Rue", title = "From uniform distributions to {Benford}'s law", journal = j-J-APPL-PROBAB, volume = "41", number = "4", pages = "1203--1210", year = "2004", CODEN = "JPRBAM", DOI = "http://dx.doi.org/10.1239/jap/1101840566", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "60J20 (60J10)", MRnumber = "2122815 (2006b:60161)", MRreviewer = "Michael Drmota", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566; http://www.jstor.org/stable/4141393; https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf", abstract = "We provide a new, probabilistic explanation for the appearance of Benford's law in everyday-life numbers, by showing that it arises naturally when we consider mixtures of uniform distributions. Then we connect our result to a result of Flehinger, for which we provide a shorter proof, and the speed of convergence.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", } @Article{Janvresse:2009:BL, author = "Elise Janvresse and Thierry de la Rue", title = "{Benford}'s law", journal = "Butl. Soc. Catalana Mat.", volume = "24", number = "1", pages = "5--12", year = "2009", CODEN = "????", ISSN = "0214-316X", ISSN-L = "0214-316X", MRclass = "62-01", MRnumber = "2567485", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Translated by Frederic Utzet", acknowledgement = ack-nhfb, fjournal = "Butllet{\'\i}n de la Societat Catalana de Matem{\`a}tiques", } @Article{Janvresse:2011:AAU, author = "{\'E}lise Janvresse and Thierry {De La Rue}", title = "Averaging along Uniform Random Integers", journal = "ArXiv e-prints", year = "2011", bibdate = "Mon Nov 21 07:06:41 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1103.1719", abstract = "Motivated by giving a meaning to ``The probability that a random integer has initial digit d'', we define a URI-set as a random set E of natural integers such that each n>0 belongs to E with probability 1/n, independently of other integers. This enables us to introduce two notions of densities on natural numbers: The URI-density, obtained by averaging along the elements of $E$, and the local URI-density, which we get by considering the $k$-th element of $E$ and letting $k$ go to infinity. We prove that the elements of $E$ satisfy Benford's law, both in the sense of URI-density and in the sense of local URI-density. Moreover, if $ b_1 $ and $ b_2 $ are two multiplicatively independent integers, then the mantissae of a natural number in base $ b_1 $ and in base $ b_2 $ are independent. Connections of URI-density and local URI-density with other well-known notions of densities are established: Both are stronger than the natural density, and URI-density is equivalent to log-density. We also give a stochastic interpretation, in terms of URI-set, of the $ H_\infty $-density.", acknowledgement = ack-nhfb, } @Article{Janvresse:2012:AAU, author = "{\'E}lise Janvresse and Thierry {De La Rue}", title = "Averaging along Uniform Random Integers", journal = "Uniform Distribution Theory", volume = "7", number = "2", pages = "35--60", month = "????", year = "2012", DOI = "????", ISSN = "1336-913X", ISSN-L = "1336-913X", bibdate = "Tue Feb 19 05:56:13 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.boku.ac.at/MATH/udt/vol07/no2/03JanRue16-11.pdf", acknowledgement = ack-nhfb, journal-URL = "http://www.boku.ac.at/MATH/udt/", keywords = "Benford's Law", } @PhdThesis{Janvresse:2012:QCP, author = "{\'E}lise Janvresse", title = "Quelques contributions aux probabilit{\'e}s et {\`a} la th{\'e}orie ergodique. ({French}) [Some contributions to probability theory and ergodic theory]", type = "Document de synth{\`e}se pr{\'e}sent{\'e} pour l'{Habilitation {\`a} Diriger des Recherches}", school = "l'Universit{\'e} de Rouen", address = "Rouen, France", pages = "67", day = "17", month = feb, year = "2012", bibdate = "Tue Feb 19 05:57:33 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.univ-rouen.fr/LMRS/Persopage/Janvresse/hdr_Janvresse.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", language = "French", } @MastersThesis{Jasak:2010:BZR, author = "Zoran Jasak", title = "Benfordov zakon i reinforcement u{\v{c}}enje. ({Bosnian}) [{Benford's Law} and reinforcement learning]", type = "{Magistarski Rad} ({M.Sc.} Thesis)", school = "Prirodno-Matematicki Fakultet, Odsjek za matematiku, Ju Univerzitet u Tuzla", address = "Tuzla, Bosnia and Herzegovina", pages = "124", month = dec, year = "2010", bibdate = "Mon Feb 18 17:48:33 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf", acknowledgement = ack-nhfb, keywords = "action; Adaptive Benford's method; Adaptivna Benfordova metoda; akcija; Benford's law; Benfordov zakon; confidence intervals; contamination level; intervali povjerenja; koli{\v{c}}nik; nivo kontaminacije; Q learning; Q u{\v{c}}enje; quotient; reinforcement learning; reinforcement u{\v{c}}enje; Sarsa; stanje; state", language = "Bosnian", } @Article{Jech:1992:LDL, author = "Thomas Jech", title = "The logarithmic distribution of leading digits and finitely additive measures", journal = j-DISCRETE-MATH, volume = "108", number = "1--3", pages = "53--57", month = "????", year = "1992", CODEN = "DSMHA4", ISSN = "0012-365X (print), 1872-681X (electronic)", ISSN-L = "0012-365X", bibdate = "Fri Nov 18 12:12:57 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Discrete Mathematics", } @Article{Jelenkovic:2008:CMS, author = "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang", title = "Characterizing the miss sequence of the {LRU} cache", journal = j-SIGMETRICS, volume = "36", number = "2", pages = "119--121", month = sep, year = "2008", CODEN = "????", DOI = "http://doi.acm.org/10.1145/1453175.1453203", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Wed Aug 25 07:31:09 MDT 2010", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "Renewed interest in caching systems stems from their wide-spread use for reducing the document download latency over the Internet. Since caches are usually organized in a hierarchical manner, it is important to study the performance properties of tandem caches. The first step in understanding this problem is to characterize the miss stream from one single cache since it represents the input to the next level cache. In this regard, we discover that the miss stream from one single cache is approximated well by the superposition of a number of asymptotically independent renewal processes. Interestingly, when this weakly correlated miss sequence is fed into another cache, this barely observable correlation can lead to measurably different caching performance when compared to the independent reference model. This result is likely to enable the development of a rigorous analysis of the tandem cache performance.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "average-case analysis; cache fault probability; hierarchical caching; least-recently-used caching; web caching; Zipf's law", } @Article{Jiang:2010:NMS, author = "Weina Jiang and Anthony T. S. Ho and Helen Treharne and Yun Q. Shi", title = "A Novel Multi-size Block {Benford's Law} Scheme for Printer Identification", journal = j-LECT-NOTES-COMP-SCI, volume = "6297", pages = "643--652", year = "2010", CODEN = "LNCSD9", DOI = "http://dx.doi.org/10.1007/978-3-642-15702-8_59", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:47:23 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59", acknowledgement = ack-nhfb, book-DOI = "http://dx.doi.org/10.1007/978-3-642-15702-8", book-URL = "http://www.springerlink.com/content/978-3-642-15702-8", fjournal = "Lecture Notes in Computer Science", } @Article{Jiang:2011:BLN, author = "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao", title = "{Benford}'s law in nuclear structure physics", journal = j-CHIN-PHYS-LETT, volume = "28", number = "3", pages = "032101", month = "????", year = "2011", CODEN = "CPLEEU", DOI = "http://dx.doi.org/10.1088/0256-307X/28/3/032101", ISSN = "0256-307X (print), 1741-3540 (electronic)", ISSN-L = "0256-307X", bibdate = "Mon Nov 14 16:16:10 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Chin. Phys. Lett.", fjournal = "Chinese Physics Letters", pagecount = "4", } @Article{Jin:2009:AUR, author = "Jang C. Jin", title = "{Asian} University Rankings in International and Development Economics: An Application of {Zipf's Law}", journal = j-REV-INT-ECON, volume = "17", number = "1", pages = "137--143", year = "2009", DOI = "http://dx.doi.org/10.1111/j.1467-9396.2008.00790.x", ISSN = "0965-7576 (print), 1467-9396 (electronic)", ISSN-L = "0965-7576", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Review of International Economics", } @Article{Jin:2009:PME, author = "Jang C. Jin", title = "Publications in mathematical economics and econometrics: ranking of {Asian} universities and an application of {Zipf's Law}", journal = "{Asian-Pacific} Economic Literature", volume = "23", number = "2", pages = "116--122", year = "2009", DOI = "http://dx.doi.org/10.1111/j.1467-8411.2009.01233.x", ISSN = "0818-9935 (print), 1467-8411 (electronic)", ISSN-L = "0818-9935", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291467-8411", } @Article{Jolion:2001:IBL, author = "Jean-Michel Jolion", title = "Images and {Benford}'s law", journal = j-J-MATH-IMAG-VIS, volume = "14", number = "1", pages = "73--81", year = "2001", CODEN = "JMIVEK", DOI = "http://dx.doi.org/10.1023/A:1008363415314", ISSN = "0924-9907 (print), 1573-7683 (electronic)", ISSN-L = "0924-9907", MRclass = "94A08 (68U10)", MRnumber = "1818436 (2001m:94007)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Imaging and Vision: JMIV", } @Article{Jolissaint:2005:LBR, author = "Paul Jolissaint", title = "Loi de {Benford}, relations de r{\'e}currence et suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s Law, recurrence relations, and equidistributed sequences]", journal = j-ELEM-MATH, volume = "60", number = "1", pages = "10--18", year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.4171/EM/2", ISSN = "0013-6018 (print), 1420-8962 (electronic)", ISSN-L = "0013-6018", MRclass = "11K36 (37A45 60E99)", MRnumber = "2188341 (2006j:11109)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elemente der Mathematik", language = "French", } @Article{Jolissaint:2009:LBR, author = "Paul Jolissaint", title = "Loi de {Benford}, relations de r{\'e}currence et suites {\'e}quidistribu{\'e}es. {II}. ({French}) [{Benford}'s Law, recurrence relations, and equidistributed sequences. {II}]", journal = j-ELEM-MATH, volume = "64", number = "1", pages = "21--36", year = "2009", CODEN = "????", DOI = "http://dx.doi.org/10.4171/EM/112", ISSN = "0013-6018 (print), 1420-8962 (electronic)", ISSN-L = "0013-6018", MRclass = "62E10 (11A63 37A45)", MRnumber = "2471593 (2010f:62032)", MRreviewer = "Denys Pommeret", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elemente der Mathematik", language = "French", } @Article{Jones:2002:LDR, author = "B. K. Jones", title = "Logarithmic distributions in reliability analysis", journal = j-MICROELECT-RELIABILITY, volume = "42", number = "4--5", pages = "779--786", month = apr # "\slash " # may, year = "2002", CODEN = "MCRLAS", DOI = "http://dx.doi.org/10.1016/S0026-2714(02)00031-8", ISSN = "0026-2714 (print), 1872-941X (electronic)", ISSN-L = "0026-2714", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0026271402000318", acknowledgement = ack-nhfb, fjournal = "Microelectronics and Reliability", keywords = "Benford's Law; Pareto distribution; Zipf's Law", } @TechReport{Judge:2006:DPS, author = "George Judge and Laura Schechter", title = "Detecting problems in survey data using {Benford}'s law", type = "Preprint", institution = "University of California at Berkeley and University of Wisconsin at Madison", address = "Berkeley, CA, USA and Madison, WI, USA", pages = "30", day = "1", month = nov, year = "2006", bibdate = "Sat Feb 16 18:12:29 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.aae.wisc.edu/lschechter/benford.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Judge:2009:DPS, author = "G. Judge and L. Schechter", title = "Detecting Problems in Survey Data using {Benford's Law}", journal = j-J-HUM-RESOUR, volume = "44", number = "1", pages = "1--24", month = "Winter", year = "2009", CODEN = "JHREA9", DOI = "http://dx.doi.org/10.3368/jhr.44.1.1", ISSN = "0022-166X (print), 1548-8004 (electronic)", ISSN-L = "0022-166X", bibdate = "Tue Nov 22 18:55:52 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jhr.uwpress.org/content/44/1/1.abstract; http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm", acknowledgement = ack-nhfb, fjournal = "Journal of Human Resources", } @Article{Kafri:2008:SIS, author = "Oded Kafri", title = "Sociological Inequality and the {Second Law}", journal = "ArXiv e-prints", year = "2008", bibdate = "Mon Nov 21 06:41:29 2011", bibsource = "http://dblp.uni-trier.de; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/0805.3206", abstract = "There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power law distribution function yields an uneven distribution of particles in boxes. It is shown that the obtained distribution fits well to sociological phenomena, such as the distribution of votes in polls and the distribution of wealth and Benford's law.", acknowledgement = ack-nhfb, } @Article{Kafri:2009:DNE, author = "Oded Kafri", title = "The Distributions in Nature and Entropy Principle", journal = "ArXiv e-prints", day = "28", month = jul, year = "2009", bibdate = "Mon Nov 21 07:26:11 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/0907.4852", abstract = "The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a ``bell-like'' distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is low, and the second one when the ratio is high. The obtained long tail distribution yields correctly the empirical Zipf law, Pareto's 20:80 rule and Benford's law. Therefore, it is concluded that the long tail and the ``bell-like'' distributions are outcomes of the tendency of statistical systems to maximize entropy.", acknowledgement = ack-nhfb, pagecount = "19", } @Article{Kafri:2009:EPD, author = "Oded Kafri", title = "Entropy Principle in Direct Derivation of {Benford's Law}", journal = "ArXiv e-prints", month = jan, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K; http://arxiv.org/abs/0901.3047", abstract = "The uneven distribution of digits in numerical data, known as Benford's law, was discovered in 1881. Since then, this law has been shown to be correct in copious numerical data relating to economics, physics and even prime numbers. Although it attracts considerable attention, there is no a priori probabilistic criterion when a data set should or should not obey the law. Here a general criterion is suggested, namely that any file of digits in the Shannon limit (namely, having maximum entropy) has a Benford's law distribution of digits.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0901.3047", keywords = "Computer Science - Discrete Mathematics, Physics - Data Analysis, Statistics and Probability", primaryclass = "cs.DM", } @InCollection{Kanemitsu:1988:BLF, author = "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard Rauzy and Jau-Shyong Shiue", booktitle = "Probability theory and mathematical statistics ({Kyoto}, 1986)", title = "On {Benford}'s law: the first digit problem", volume = "1299", publisher = pub-SV, address = pub-SV:adr, pages = "158--169", year = "1988", DOI = "http://dx.doi.org/10.1007/BFb0078471", MRclass = "11K06 (60E99)", MRnumber = "935987 (89d:11059)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes in Math.", acknowledgement = ack-nhfb, } @Article{Kanter:1995:MPL, author = "I. Kanter and D. A. Kessler", title = "{Markov} Processes: Linguistics and {Zipf's Law}", journal = j-PHYS-REV-LET, volume = "74", number = "??", pages = "4559--??", day = "29", month = may, year = "1995", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.74.4559", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Katsikas:1990:CDG, author = "A. A. Katsikas and J. S. Nicolis", title = "Chaotic dynamics of generating {Markov} partitions and linguistic sequences mimicking {Zipf}'s law", journal = "Nuovo Cimento D (1)", volume = "12", number = "2", pages = "177--195", year = "1990", CODEN = "NCSDDN", DOI = "http://dx.doi.org/10.1007/BF02450454", ISSN = "0392-6737 (print), 1826-9893 (electronic)", ISSN-L = "0392-6737", MRclass = "92A90 (58F13 92A08 94A15)", MRnumber = "1049338 (90m:92114)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D. Serie 1", } @Article{Katsikas:1991:CDG, author = "A. A. Katsikas and J. S. Nicolis", title = "Chaotic Dynamics of Generating {Markov} Partitions, and Linguistic Sequences Mimicking {Zipf}'s Law", journal = j-LECT-NOTES-COMP-SCI, volume = "565", pages = "335--??", year = "1991", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon May 13 08:51:55 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", } @Article{Katz:1986:FDP, author = "Talbot M. Katz and Daniel I. A. Cohen", title = "The First Digit Property for Exponential Sequences is Independent of the Underlying Distribution", journal = j-FIB-QUART, volume = "24", number = "1", pages = "2--7", month = feb, year = "1986", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:00:45 MDT 2011", bibsource = "http://www.fq.math.ca/24-1.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/24-1/katz.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Kawamura:2002:UZL, author = "Kenji Kawamura and Naomichi Hatano", title = "Universality of {Zipf}'s law", journal = j-J-PHYS-SOC-JAP, volume = "71", number = "5", pages = "1211--1213", year = "2002", CODEN = "JUPSAU", DOI = "http://dx.doi.org/10.1143/JPSJ.71.1211", ISSN = "0031-9015 (print), 1347-4073 (electronic)", ISSN-L = "0031-9015", bibdate = "Sat Nov 12 11:00:54 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jpsj.ipap.jp/", ZMnumber = "1063.60114", abstract = "The aim of the present paper is to propose and simulate a simple and generic model that reproduces Zipf's law. In the proposed model, the time evolution is considered to be a random walk in the logarithmic scale reflecting the company asset distribution and/or the evolution of city populations (e.g. Zipf's law for income distribution asserts that the size and number of companies are in inverse proportional relationship). The paper explains theoretically and shows by numerical simulation that the introduced model of Zipf's law has a very robust behaviour when applied to various natural and social phenomena. The authors do not investigate the famous case of Zipf's law application to the frequency of English words, but they speculate that this case might be also explained within the same time development of the proposed model.", acknowledgement = ack-nhfb, classmath = "60J60 (Diffusion processes) 60J70 (Appl. of diffusion theory) 76R50 (Diffusion) 82C24 (Interface problems (dynamic and non-equilibrium))", fjournal = "Journal of the Physical Society of Japan", keywords = "city population evolution; company asset distribution; diffusion; generic model of Zipf's law; natural and social phenomena; random walk in logarithmic scale", ZMreviewer = "Neculai Curteanu (Ia\c si)", } @Article{Kaynar:2010:FSM, author = "B. Kaynar and A. Berger and T. P. Hill and A. Ridder", title = "Finite-state {Markov} Chains obey {Benford's Law}", journal = "ArXiv e-prints", month = mar, year = "2010", CODEN = "????", ISSN = "????", MRclass = "60J22, 11K06, 15B51", bibdate = "Tue Nov 15 06:30:53 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K; http://arxiv.org/abs/1003.0562", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1003.0562", keywords = "Mathematics - Probability", primaryclass = "math.PR", } @Article{Kechedzhi:2005:RDW, author = "K. E. Kechedzhi and O. V. Usatenko and V. A. Yampol{\cprime}skii", title = "Rank distributions of words in correlated symbolic systems and the {Zipf} law", journal = j-PHYS-REV-E, volume = "72", number = "4", pages = "046138", day = "28", month = oct, year = "2005", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.72.046138", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", MRclass = "82C31", MRnumber = "2183723 (2006f:82069)", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.72.046138", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "6", } @Article{Kemperman:1975:BDM, author = "J. H. B. Kemperman", title = "Bounds on the discrepancy modulo $1$ of a real random variable", journal = j-BULL-INST-MATH-STAT, volume = "4", number = "??", pages = "138--??", month = "????", year = "1975", CODEN = "SMBCVA", ISSN = "0146-3942", ISSN-L = "0146-3942", bibdate = "Sat Nov 12 16:26:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Abstract no. 75t-47.", acknowledgement = ack-nhfb, fjournal = "Bulletin --- Institute of Mathematical Statistics", } @Article{Kennard:1981:MDF, author = "Robert W. Kennard and John E. Reith", title = "{M32}. On the distribution of first digits", journal = j-COMMUN-STAT-SIMUL-COMPUT, volume = "10", number = "1", pages = "97--98", month = "????", year = "1981", CODEN = "CSSCDB", DOI = "http://dx.doi.org/10.1080/03610918108812195", ISSN = "0361-0918", ISSN-L = "0361-0918", bibdate = "Sat Jan 07 09:27:42 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics: Simulation and Computation", keywords = "Benford's Law", onlinedate = "27 Jun 2007", } @InProceedings{Khosravani:2012:TIB, author = "A. Khosravani and C. Rasinariu", title = "Transformation invariance of {Benford} variables and their numerical modeling", crossref = "Niola:2012:RRA", pages = "57--61", year = "2012", bibdate = "Tue Feb 19 06:01:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.wseas.us/e-library/conferences/2012/SaintMalo/ACMIN/ACMIN-06.pdf", acknowledgement = ack-nhfb, } @Article{Kim:2011:ZAS, author = "SeongKi Kim and HaYoon Song and SangYong Han", title = "{ZipfAllocation}: an algorithm for static allocation of movies in a cluster of video servers", journal = j-SPE, volume = "41", number = "6", pages = "695--716", month = may, year = "2011", CODEN = "SPEXBL", DOI = "http://dx.doi.org/10.1002/spe.1027", ISSN = "0038-0644 (print), 1097-024X (electronic)", ISSN-L = "0038-0644", bibdate = "Tue Jun 21 17:09:57 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Soft{\-}ware\emdash Prac{\-}tice and Experience", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X", onlinedate = "25 Nov 2010", } @Article{Kim:2012:BLN, author = "Sangrak Kim", title = "{Benford}'s law in non-equilibrium processes: Droplet collisions case", journal = j-PHYSICA-A, volume = "391", number = "20", pages = "4970--4975", day = "15", month = oct, year = "2012", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2012.05.043", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Thu Feb 14 05:56:39 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437112004141", acknowledgement = ack-nhfb, fjournal = "Physica A: Statistical Mechanics and its Applications", } @InProceedings{Kitsuregawa:1989:EBS, author = "Masaru Kitsuregawa and Masaya Nakayama and Mikio Takagi", title = "The Effect of Bucket Size Tuning in the Dynamic Hybrid {GRACE} Hash Join Method", crossref = "Apers:1989:VLD", pages = "257--266", month = aug, year = "1989", CODEN = "VLDBDP", bibdate = "Sat Jan 25 17:38:12 MST 1997", bibsource = "Compendex database; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/hash.bib", abstract = "In this paper, we show detailed analysis and performance evaluation of the Dynamic Hybrid GRACE Hash Join Method (DHGH Method) when the tuple distribution in buckets is unbalanced. The conventional Hash Join Methods specify the tuple distribution in buckets statically. However it may differ from estimation since join operations are applied with selection operations. When the tuple distribution in buckets is unbalanced, the processing cost of join operation becomes more costly than the ideal case when you use Hybrid Hash Join Method (HH Method). On the other hand, when you use the DHGH Method, the destaging buckets are selected dynamically, gives the same performance as the ideal case even if the tuple distribution in buckets is unbalanced such as Zipf-like distributions.", acknowledgement = ack-nhfb, affiliation = "Univ of Tokyo", affiliationaddress = "Tokyo, Jpn", classification = "723", journalabr = "Very Large Data Bases Int Conf Very Large Data Bases", keywords = "Computer Metatheory --- Programming Theory; Computer Programming --- Algorithms; Database Systems; Query Processing; Relational; Relational Algebra; VLDB", } @Article{Klar:2010:ZLL, author = "B. Klar and P. R. Parthasarathy and N. Henze", title = "{Zipf} and {Lerch} limit of birth and death processes", journal = j-PROB-ENG-INFO-SCI, volume = "24", number = "1", pages = "129--144", year = "2010", CODEN = "????", DOI = "http://dx.doi.org/10.1017/S0269964809990179", ISSN = "0269-9648 (print), 1469-8951 (electronic)", ISSN-L = "0269-9648", MRclass = "60J27 (91F20)", MRnumber = "2575846 (2010m:60254)", bibdate = "Sat Mar 23 12:53:04 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Probab. Engrg. Inform. Sci.", fjournal = "Probability in the Engineering and Informational Sciences", keywords = "Zipf's Law", } @Article{Knudsen:2001:ZLC, author = "Thorbj{\o}rn Knudsen", title = "{Zipf}'s law for cities and beyond: the case of {Denmark}", journal = j-AM-J-ECON-SOCIOL, volume = "60", number = "1", pages = "123--146", month = jan, year = "2001", CODEN = "AJESA3", DOI = "http://dx.doi.org/10.1111/1536-7150.00057", ISSN = "0002-9246 (print), 1536-7150 (electronic)", ISSN-L = "0002-9246", bibdate = "Sat Feb 16 18:14:02 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3487947", acknowledgement = ack-nhfb, fjournal = "The American Journal of Economics and Sociology", } @Book{Knuth:1969:SNM, author = "Donald E. Knuth", title = "Semi\-nu\-mer\-i\-cal Algorithms", volume = "2", publisher = pub-AW, address = pub-AW:adr, pages = "xi + 624", year = "1969", ISBN = "0-201-03802-1", ISBN-13 = "978-0-201-03802-6", LCCN = "QA76.5 .K57", bibdate = "Wed Dec 15 15:47:38 1993", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/master.bib", note = "Benford's Law is discussed on pp. 219--229.", price = "US\$19.75", series = "The Art of Computer Programming", } @Book{Knuth:1997:SA, author = "Donald E. Knuth", title = "Seminumerical Algorithms", volume = "2", publisher = pub-AW, address = pub-AW:adr, edition = "Third", pages = "xiii + 762", year = "1997", ISBN = "0-201-89684-2", ISBN-13 = "978-0-201-89684-8", LCCN = "QA76.6 .K64 1997", bibdate = "Fri Jul 11 15:41:22 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/master.bib", note = "See section 4.2.4V, The Fraction Parts, pages 254--262, for a discussion of Benford's Law.", price = "US\$52.75", series = "The Art of Computer Programming", acknowledgement = ack-nhfb, } @Article{Kohyama:1984:TIC, author = "Tamotsu Kohyama and Y{\=o}ji Aizawa", title = "Theory of the intermittent chaos. {$ 1 / f $} spectrum and the {Pareto--Zipf} law", journal = j-PROG-THEOR-PHYS, volume = "71", number = "5", pages = "917--929", year = "1984", CODEN = "PTPKAV", DOI = "http://dx.doi.org/10.1143/PTP.71.917", ISSN = "0033-068X (print), 1347-4081 (electronic)", ISSN-L = "0033-068X", MRclass = "58F13 (76F99)", MRnumber = "756214 (86a:58063)", MRreviewer = "Joseph Ford", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Progress of Theoretical Physics", } @TechReport{Kollath-Romano:2004:DSD, author = "P. Kollath-Romano", title = "On the distribution of significant digits in numbers", type = "Preprint", institution = "Rensselaer Polytechnic Institute", address = "Troy, NY, USA", year = "2004", bibdate = "Sat Feb 16 18:15:19 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Konheim:1965:MDT, author = "Alan G. Konheim", title = "Mantissa Distributions (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "19", number = "89", pages = "143--144", month = apr, year = "1965", CODEN = "MCMPAF", DOI = "http://dx.doi.org/10.2307/2004111", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Kontorovich:2005:BLV, author = "Alex V. Kontorovich and Steven J. Miller", title = "{Benford}'s law, values of {$L$}-functions and the {$ 3 x + 1 $} problem", journal = j-ACTA-ARITHMETICA, volume = "120", number = "3", pages = "269--297", year = "2005", CODEN = "AARIA9", DOI = "http://dx.doi.org/10.4064/aa120-3-4", ISSN = "0065-1036 (print), 1730-6264 (electronic)", ISSN-L = "0065-1036", MRclass = "11K06 (11B37 11M06 37A45)", MRnumber = "2188844 (2007c:11085)", MRreviewer = "J. C. Lagarias", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2005AcAri.120..269K; http://arxiv.org/abs/math/0412003", abstract = "We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the system. The other is a general technique of applying Poisson Summation to the limiting distribution. We show the distribution of values of $L$-functions near the central line and (in some sense) the iterates of the $ 3 x + 1 $ Problem are Benford.", acknowledgement = ack-nhfb, fjournal = "Acta Arithmetica", } @Article{Kossovsky:2006:TBU, author = "Alex Ely Kossovsky", title = "Towards a Better Understanding of the Leading Digits Phenomena", journal = "ArXiv Mathematics e-prints", year = "2006", bibdate = "Mon Nov 21 06:46:43 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math/0612627", abstract = "This article on leading digits (Benford's Law) contains the following: (i) An attempt at a comprehensive account on the leading digits phenomena, incorporating many of its existing explanations, proofs, and differing points of view. (ii) The finding that leading digits of random numbers derived from a chain of distributions that are linked via parameter selection are logarithmic in the limit as the number of sequences approaches infinity, and that empirically only around 5 or 6 sequences of such a distribution chain are needed to obtain results that are close enough to the logarithmic (i.e., rapid convergence). (iii) An outright exact logarithmic behavior for a 2-sequence chain whenever parametrical density is exactly logarithmic. (iv) An account on the existence of singularities in exponential growth rates with regards to the leading digits distributions of their series. (v) An account on several distributions that are intrinsically logarithmic or approximately so. (vi) A conceptual justification of Flehinger's iterated averaging scheme --- an algorithm that was presented without any clear motivation. (vii) A note on the close relationship of Flehinger's scheme and the chain of distribution to Hill's super distribution. (viii) A conceptual argument justifying the scale invariance principle --- a principle invoked in derivations of Benford's law. (ix) A note on the intimate connection between one-sided tail to the right in density distributions and logarithmic leading digit behavior.", acknowledgement = ack-nhfb, remark = "On 18 February 2013, the archive has 17 revisions of this article.", xxjournal = "CoRR", } @InCollection{Kotz:2004:FDP, author = "Samuel Kotz and N. Balakrishnan and Campbell B. Read and Brani Vidakovic", editor = "Samuel Kotz and N. Balakrishnan and Campbell B. Read and Brani Vidakovic", booktitle = "Encyclopedia of Statistical Sciences", title = "First-Digit Problem", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "??--??", year = "2004", DOI = "http://dx.doi.org/10.1002/0471667196.ess0783.pub2", ISBN = "0-471-66719-6 (e-book)", ISBN-13 = "978-0-471-66719-3 (e-book)", bibdate = "Sun Feb 24 10:49:25 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InProceedings{Krakar:2008:ABL, author = "Zdravko Krakar and Mario {\v{Z}}gela", editor = "Boris Aurer and Miroslav Ba{\'c}a", booktitle = "Proceedings of the 19th Central European Conference on Information and Intelligent Systems (CECIS 2008)", title = "Application of {Benford's Law} in Payment System Auditing", publisher = "Fakultet organizacije i informatike", address = "Vara{\v{z}}din, Croatia", pages = "187--193", year = "2008", bibdate = "Sun Nov 13 11:14:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InProceedings{Krakar:2008:EBL, author = "Zdravko Krakar and Mario {\v{Z}}gela", editor = "Mario Plenkovi{\'c}", booktitle = "Society and Technology 2008", title = "Evaluation of {Benford's Law}: application in stock prices and stock turnover", publisher = "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo", address = "Zagreb, Croatia", pages = "57--71", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sun Nov 13 11:18:37 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, remark = "International Federation of Communication Studies, Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u Zagrebu.", } @Article{Krakar:2009:ABL, author = "Mario {\v{Z}}gela and Zdravko Krakar", title = "Application of {Benford's Law} in Payment System Auditing", journal = j-J-INFO-ORG-SCI, volume = "33", number = "1", pages = "39--51", month = "????", year = "2009", CODEN = "????", ISSN = "1846-3312 (print), 1846-9418 (electronic)", ISSN-L = "1846-3312", bibdate = "Sun Nov 13 11:12:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf; http://jios.foi.hr/index.php/jios/article/view/108/66; http://jios.foi.hr/index.php/jios/issue/view/13", acknowledgement = ack-nhfb, fjournal = "Journal of Informational and Organizational Sciences", journal-URL = "http://jios.foi.hr/index.php/jios/index", xxjournal = "Journal of Information Ethics and Organisational Science (wrong!)", } @Article{Kreifelts:1973:OBG, author = "Thomas Kreifelts", title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik}. 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Kreiner", title = "First digit law", type = "Preprint", institution = "Abteilung Chemische Physik, Arbeitsgruppe Laseranwendungen, Universit{\"a}t Ulm", address = "Ulm, Germany", pages = "7", day = "3", month = may, year = "2002", bibdate = "Sat Feb 16 18:18:49 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law; First Digit Law; Newcomb; Statistisches Fraktal", language = "German", } @Article{Kreiner:2003:NBL, author = "W. A. Kreiner", title = "On the {Newcomb--Benford} law", journal = j-Z-NATURFORSCH, volume = "58a", number = "11", pages = "618--622", month = "????", year = "2003", CODEN = "ZNTFA2", ISSN = "0372-9516", ISSN-L = "0372-9516", bibdate = "Sat Feb 16 18:19:41 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Naturforschung}", } @Article{Krevitt:1972:CSZ, author = "Beth Krevitt and Belver C. Griffith", title = "A comparison of several {Zipf}-type distributions in their goodness of fit to language data", journal = j-J-AM-SOC-INF-SCI, volume = "23", number = "3", pages = "220--221", year = "1972", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/asi.4630230310", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", } @Article{Kriel:2010:DDM, author = "Eckhardt Kriel", title = "Discussion of {``Data mining journal entries for fraud detection: An exploratory study''}", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "11", number = "3", pages = "186--188", month = sep, year = "2010", CODEN = "IJAIA7", DOI = "http://dx.doi.org/10.1016/j.accinf.2010.07.009", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.", URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000400", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Benford's Law", } @Article{Kristiansen:2004:BTZ, author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T. Skjeltorp", title = "Braid theory and {Zipf} relation used in dynamics of magnetic microparticles", journal = j-ECONOM-LETT, volume = "30", number = "1", pages = "2387--2388", day = "1", month = may, year = "2004", CODEN = "ECLEDS", DOI = "http://dx.doi.org/10.1016/j.jmmm.2003.12.1288", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0304885303019127", acknowledgement = ack-nhfb, fjournal = "Economics Letters", keywords = "Zipf's Law", } @Article{Kristiansen:2004:EOZ, author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T. Skjeltorp", title = "Experimental observation of {Zipf--Mandelbrot} relation", journal = j-PHYSICA-A, volume = "335", number = "3--4", pages = "413--420", day = "15", month = apr, year = "2004", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2003.12.024", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "82D10 (76T99 82-05)", MRnumber = "2044153", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011804", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Kristiansen:2006:BTZ, author = "K. de Lange Kristiansen and G. Helgesen and A. T. Skjeltorp", title = "Braid theory and {Zipf--Mandelbrot} relation used in microparticle dynamics", journal = j-EUR-PHYS-J-B, volume = "51", number = "3", pages = "363--371", month = jun, year = "2006", CODEN = "EPJBFY", DOI = "http://dx.doi.org/10.1140/epjb/e2006-00241-7", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Sat Sep 8 18:31:14 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", } @Article{Krugman:1996:CMU, author = "Paul Krugman", title = "Confronting the Mystery of Urban Hierarchy", journal = j-J-JPN-INT-ECON, volume = "10", number = "4", pages = "399--418", month = dec, year = "1996", CODEN = "JJIEBD", DOI = "http://dx.doi.org/10.1006/jjie.1996.0023", ISSN = "0889-1583 (print), 1095-8681 (electronic)", ISSN-L = "0889-1583", bibdate = "Wed Feb 27 06:15:55 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0889158396900234", acknowledgement = ack-nhfb, fjournal = "Journal of the {Japanese} and International Economies", keywords = "Zipf's Law", } @Book{Krugman:1996:SOE, author = "Paul R. Krugman", title = "The Self-Organizing Economy", publisher = "Blackwell Publishers", address = "Cambridge, MA, USA", pages = "vi + 122", year = "1996", ISBN = "1-55786-699-6 (paperback)", ISBN-13 = "978-1-55786-699-8 (paperback)", LCCN = "HB199 .K75 1996", bibdate = "Wed Feb 27 07:08:14 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, keywords = "Zipf's Law", subject = "Economics; Self-organizing systems", } @Article{Kuipers:1969:RPR, author = "L. Kuipers", title = "Remark on a Paper by {R. L. Duncan} Concerning the Uniform Distribution Mod $1$ of the Sequence of the Logarithms of the {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "7", number = "5", pages = "465--466", month = dec, year = "1969", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:21 MDT 2011", bibsource = "http://www.fq.math.ca/7-5.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Kuipers:1973:RPD, author = "L. Kuipers and Jau-shyong Shiue", title = "Remark on a Paper by {Duncan} and {Brown} on the Sequence of Logarithms of Certain Recursive Sequences", journal = j-FIB-QUART, volume = "11", number = "3", pages = "292--293", month = oct, year = "1973", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:58:42 MDT 2011", bibsource = "http://www.fq.math.ca/11-3.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", note = "See \cite{Brown:1970:MOU}.", URL = "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. 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A. Kulikova and Yu. V. Prokhorov", title = "One-sided stable distributions and {Benford}'s law", journal = "Teor. Veroyatn. Primen.", volume = "49", number = "1", pages = "178--184", year = "2004", CODEN = "????", DOI = "http://dx.doi.org/10.1137/S0040585X97980944", ISSN = "0040-361X", ISSN-L = "0040-361X", MRclass = "60E07 (60F05)", MRnumber = "2141338 (2005m:60028)", MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya Veroyatnoste{\u\i} i ee Primeneniya", } @Article{Kulikova:2005:CAS, author = "A. A. Kulikova and Yu. V. Prokhorov", title = "Completely Asymmetric Stable Laws and {Benford's Law}", journal = j-THEORY-PROBAB-APPL, volume = "49", number = "1", pages = "163--169", month = mar, year = "2005", CODEN = "TPRBAU", DOI = "http://dx.doi.org/10.1137/S0040585X97980944", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Thu Jul 7 19:15:48 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/98094", acknowledgement = ack-nhfb, fjournal = "Theory of probability and its applications", journal-URL = "http://epubs.siam.org/tvp", keywords = "Benford's Law; Zipf's Law", } @Article{Kulikova:2005:HFD, author = "A. A. Kulikova and Yu. V. Prokhorov and V. I. Khokhlov", title = "{H. F. D.} ({$H$}-function distribution) and the {Benford} law. {I}", journal = "Teor. Veroyatn. Primen.", volume = "50", number = "2", pages = "366--371", year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.1137/S0040585X97981706", ISSN = "0040-361X", ISSN-L = "0040-361X", MRclass = "60E07 (60F05)", MRnumber = "2221718 (2007b:60029)", MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya Veroyatnoste{\u\i} i ee Primeneniya", } @Article{Kulikova:2006:HFD, author = "A. A. Kulikova and Yu. V. Prokhorov and V. I. Khokhlov", title = "{H.F.D.} ({$H$}-function Distribution) and {Benford's Law}. {I}", journal = j-THEORY-PROBAB-APPL, volume = "50", number = "2", pages = "311--315", month = jan, year = "2006", CODEN = "TPRBAU", DOI = "http://dx.doi.org/10.1137/S0040585X97981706", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Wed May 19 18:14:51 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1", acknowledgement = ack-nhfb, fjournal = "Theory of probability and its applications", journal-URL = "http://epubs.siam.org/tvp", } @InCollection{Kumar:2003:BLA, author = "Kuldeep Kumar and Sukanto Bhattacharya", editor = "Cheng-Few Lee", booktitle = "Advances in Financial Planning and Forecasting", title = "{Benford}'s law and its application in financial fraud detection", volume = "11", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "57--70", year = "2003", ISBN = "0-7623-1016-2", ISBN-13 = "978-0-7623-1016-6", ISSN = "1046-5847", LCCN = "????", bibdate = "Wed Nov 23 16:45:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, bookpages = "ix + 177", } @Article{Kumar:2007:DDD, author = "Kuldeep Kumar and Sukanto Bhattacharya", title = "Detecting the dubious digits: {Benford}'s law in forensic accounting", journal = j-SIGNIF, volume = "4", number = "2", pages = "81--83", month = jun, year = "2007", CODEN = "????", DOI = "http://dx.doi.org/10.1111/j.1740-9713.2007.00234.x", ISSN = "1740-9705 (print), 1740-9713 (electronic)", ISSN-L = "1740-9705", MRnumber = "2380610", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://onlinelibrary.wiley.com/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Significance ({Oxford, England})", onlinedate = "7 Jun 2007", } @Article{Kunoff:1987:FDP, author = "Sharon Kunoff", title = "{$ N! $} has the First Digit Property", journal = j-FIB-QUART, volume = "25", number = "4", pages = "365--367", month = nov, year = "1987", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:01:00 MDT 2011", bibsource = "http://www.fq.math.ca/25-4.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. 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Weiss", title = "The $ 3 x + 1 $ Problem: Two Stochastic Models", journal = j-ANN-APPL-PROBAB, volume = "2", number = "1", pages = "229--261", month = feb, year = "1992", CODEN = "????", ISSN = "1050-5164", ISSN-L = "1050-5164", bibdate = "Fri Jun 6 11:35:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/annapplprobab.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.aoap/1177005779", acknowledgement = ack-nhfb, fjournal = "Annals of Applied Probability", journal-URL = "http://projecteuclid.org/all/euclid.aoap/; http://www.jstor.org/journals/10505164.html;", } @Article{Lagarias:2005:BLF, author = "J. C. Lagarias and K. Soundararajan", title = "{Benford}'s law for the $ 3 x + 1 $ function", journal = "ArXiv Mathematics e-prints", month = sep, year = "2005", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2005math......9175L; http://arxiv.org/abs/math/0509175", acknowledgement = ack-nhfb, eprint = "arXiv:math/0509175", keywords = "Mathematics - Number Theory, Mathematics - Probability", } @Article{Lagarias:2006:BLF, author = "Jeffrey C. Lagarias and K. Soundararajan", title = "{Benford}'s law for the $ 3 x + 1 $ function", journal = "J. London Math. Soc. (2)", volume = "74", number = "2", pages = "289--303", year = "2006", CODEN = "JLMSAK", DOI = "http://dx.doi.org/10.1112/S0024610706023131", ISSN = "0024-6107 (print), 1469-7750 (electronic)", ISSN-L = "0024-6107", MRclass = "37A45", MRnumber = "2269630 (2007h:37007)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the London Mathematical Society. Second Series", } @Article{Lang:1989:UAB, author = "Sheau-Dong Lang and James R. Driscoll and Jiann H. Jou", title = "A Unified Analysis of Batched Searching of Sequential and Tree-Structured Files", journal = j-TODS, volume = "14", number = "4", pages = "604--618", month = dec, year = "1989", CODEN = "ATDSD3", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", MRclass = "68P10 (68P20)", MRnumber = "1 073 204", bibdate = "Sat Apr 14 10:34:48 MDT 2001", bibsource = "Database/Graefe.bib; Database/Wiederhold.bib; http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf; http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/; http://www.acm.org/pubs/toc/Abstracts/tods/76908.html", abstract = "A direct and unified approach is used to analyze the efficiency of batched searching of sequential and tree-structured files. The analysis is applicable to arbitrary search distributions, and closed-form expressions are obtained for the expected batched searching cost and savings. In particular, we consider a search distribution satisfying Zipf's law for sequential files and four types of uniform (random) search distribution for sequential and tree-structured files. These results unify and extend earlier research on batched searching and estimating block accesses for database systems.", acknowledgement = ack-nhfb, affiliation = "Central Florida Univ., Orlando, FL, USA", annote = "closed-form expressions for the number of accesses needed given arbitrary search distributions.", fjournal = "ACM Transactions on Database Systems", generalterms = "Algorithms; Design; Performance; Theory", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", keywords = "algorithms; design; performance; theory", subject = "{\bf H.3.3}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Search and Retrieval, Search process. {\bf H.3.2}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Storage, File organization. {\bf H.2.2}: Information Systems, DATABASE MANAGEMENT, Physical Design, Access methods.", } @Article{Lansey:2009:ISR, author = "Jonathan C. Lansey and Bruce Bukiet", title = "{Internet} Search Result Probabilities: {Heaps' Law} and Word Associativity", journal = j-J-QUANT-LINGUISTICS, volume = "16", number = "1", pages = "40--66", month = "????", year = "2009", CODEN = "????", DOI = "http://dx.doi.org/10.1080/09296170802514153", ISSN = "0929-6174 (print), 1744-5035 (electronic)", ISSN-L = "0929-6174", bibdate = "Sat Jan 07 09:36:17 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153", abstract = "We study the number of internet search results returned from multi-word queries based on the number of results returned when each word is searched for individually. We derive a model to describe search result values for multi-word queries using the total number of pages indexed by Google and by applying the Zipf power law to the words per page distribution on the internet and Heaps' law for unique word counts. Based on data from 351 word pairs each with exactly one hit when searched for together, and a Zipf law coefficient determined in other studies, we approximate the Heaps' law coefficient for the indexed worldwide web (about 8 billion pages) to be $ \beta = 0.52 $. Previous studies used under 20,000 pages. We demonstrate through examples how the model can be used to analyse automatically the relatedness of word pairs assigning each a value we call ``strength of associativity''. We demonstrate the validity of our method with word triplets and through two experiments conducted 8 months apart. We then use our model to compare the index sizes of competing search giants Yahoo and Google.", acknowledgement = ack-nhfb, fjournal = "Journal of Quantitative Linguistics", keywords = "Benford's Law; Heaps' Law; Zipf's Law", onlinedate = "25 Feb 2009", remark = "From page 65: ``We mention that tests we have conducted show that internet searches for random numbers return approximately log-normally distributed results and sorting by first digits yields results that follow Benford's law (1938).''", } @Article{Lanza:2000:UDA, author = "R. B. Lanza", title = "Using digital analysis to detect fraud: Review of the {DATAS\reg} statistical analysis tool", journal = j-J-FORENSIC-ACCOUNT, volume = "1", number = "??", pages = "291--296", month = "????", year = "2000", CODEN = "????", ISSN = "1524-5586", bibdate = "Tue Nov 22 10:47:45 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.rtedwards.com/journals/JFA/", acknowledgement = ack-nhfb, fjournal = "Journal of Forensic Accounting", } @Article{Lanza:2003:FSP, author = "Richard B. Lanza", title = "Fear Not the Software: Proactively Detecting Occupational Fraud Using Computer Audit Reports", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = sep # "\slash " # feb, year = "2003", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:14:47 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294967868", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", keywords = "Benford's Law", } @Article{Lanza:2004:CBS, author = "Richard B. Lanza", title = "Comparing Best Software for Fraud Examinations: Fraud Data Interrogation Tools", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = nov # "\slash" # dec, year = "2004", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:17:02 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294967837", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", keywords = "Benford's Law", } @Article{Lee:2010:SAR, author = "Joanne Lee and Wendy K. Tam Cho and George G. Judge", title = "{Stigler}'s approach to recovering the distribution of first significant digits in natural data sets", journal = j-STAT-PROB-LETT, volume = "80", number = "2", pages = "82--88", day = "15", month = jan, year = "2010", CODEN = "SPLTDC", DOI = "http://dx.doi.org/10.1016/j.spl.2009.09.015", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715209003563", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", keywords = "Benford's Law", } @Article{Leemis:2000:SDS, author = "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L. Evans", title = "Survival Distributions Satisfying {Benford's Law}", journal = j-AMER-STAT, volume = "54", number = "4", pages = "236--241", month = nov, year = "2000", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRclass = "62E15 (62N05)", MRnumber = "1803620", bibdate = "Fri Jan 27 18:16:34 MST 2012", bibsource = "http://www.amstat.org/publications/tas/; http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326510; http://www.math.utah.edu/pub/tex/bib/amstat.bib; http://www.math.utah.edu/pub/tex/bib/amstat2000.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.amstat.org/publications/tas/Leemis.htm; http://www.jstor.org/stable/2685773", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Lefort:1982:LOA, author = "B. Lefort", title = "{L}'Emploi des Outils au Cours de Taches d'Entretien et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of Tools in Maintenance Tasks and the {Zipf--Mandelbrot Law}]", journal = j-TRAV-HUM, volume = "45", number = "2", pages = "307--316", month = "????", year = "1982", CODEN = "TRHUAH", ISSN = "0041-1868 (print), 2104-3663 (electronic)", ISSN-L = "0041-1868", bibdate = "Mon Sep 10 07:17:32 MDT 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/40657805", acknowledgement = ack-nhfb, fjournal = "Le Travail Humain", language = "French", } @Article{Lehner:2004:DVG, author = "B. Lehner and P. Doll", title = "Development and validation of a global database of lakes", journal = j-J-HYDROL, volume = "296", number = "1--4", pages = "1--22", day = "20", month = aug, year = "2004", CODEN = "JHYDA7", DOI = "http://dx.doi.org/10.1016/j.jhydrol.2004.03.028", ISSN = "0022-1694 (print), 1879-2707 (electronic)", ISSN-L = "0022-1694", bibdate = "Fri Mar 22 08:54:27 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022169404001404", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Journal of Hydrology", keywords = "Benford's Law", } @InProceedings{Lei:2000:EIN, author = "Skylar Lei and Michael Smith and Giancarlo Succi", title = "Empirical investigation of a novel approach to check the integrity of software engineering measuring processes", crossref = "ACM:2000:PIC", pages = "773--773", year = "2000", DOI = "http://dx.doi.org/10.1145/337180.337629", bibdate = "Sat Feb 16 18:28:12 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Leimkuhler:1980:EFB, author = "Ferdinand F. Leimkuhler", title = "An Exact Formulation of {Bradford's Law}", journal = j-J-DOC, volume = "36", number = "4", pages = "285--292", month = "????", year = "1980", CODEN = "JDOCAS", DOI = "http://dx.doi.org/10.1108/eb026699", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:14:04 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "An exact, discrete formulation of Bradford's law describing the distribution of articles in journals is derived by showing that Bradford's law is a special case of the Zipf--Mandelbrot `rank frequency' law. A relatively simple method is presented for fitting the model to empirical data and estimating the number of journals and articles in a subject collection. This method is demonstrated with an example application.", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", } @Article{Leinicke:2006:FFN, author = "Linda M. Leinicke and Joyce A. Ostrosky and W. Max Rexroad", title = "Fighting fraud by the numbers: Digital analysis primer", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2006", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:13:02 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294967620", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", keywords = "Benford's Law", } @Article{Lemons:1986:NTD, author = "Don S. Lemons", title = "On the number of things and the distribution of first digits", journal = j-AMER-J-PHYSICS, volume = "54", number = "9", pages = "816--817", month = sep, year = "1986", CODEN = "AJPIAS", DOI = "http://dx.doi.org/10.1119/1.14453", ISSN = "0002-9505 (print), 1943-2909 (electronic)", ISSN-L = "0002-9505", bibdate = "Wed Nov 23 12:03:08 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ajp.aapt.org/", acknowledgement = ack-nhfb, fjournal = "American Journal of Physics", keywords = "Benford's Law", remark = "Lemons gives a derivation of Benford's Law that does not assume scale invariance, unlike other widely-cited derivations \cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.", } @Article{Levene:2001:ZLW, author = "Mark Levene and Jos{\'e} Borges and George Loizou", title = "{Zipf}'s law for {Web} surfers", journal = j-KNOWL-INFO-SYS, volume = "3", number = "1", pages = "120--129", year = "2001", CODEN = "KISNCR", DOI = "http://dx.doi.org/10.1007/PL00011657", ISSN = "0219-1377", bibdate = "Sat Nov 12 11:00:30 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0991.68622", abstract = "One of the main activities of Web users, known as `surfing', is to follow links. Lengthy navigation often leads to disorientation when users lose track of the context in which they are navigating and are unsure how to proceed in terms of the goal of their original query. Studying navigation patterns of Web users is thus important, since it can lead us to a better understanding of the problems users face when they are surfing. We derive Zipf's rank frequency law (i.e., an inverse power law) from an absorbing Markov chain model of surfers' behavior assuming that less probable navigation trails are, on average, longer than more probable ones. In our model the probability of a trail is interpreted as the relevance (or `value') of the trail. We apply our model to two scenarios: in the first the probability of a user terminating the navigation session is independent of the number of links he has followed so far, and in the second the probability of a user terminating the navigation session increases by a constant each time the user follows a link. We analyze these scenarios using two sets of experimental data sets showing that, although the first scenario is only a rough approximation of surfers' behavior, the data is consistent with the second scenario and can thus provide an explanation of surfers' behavior.", acknowledgement = ack-nhfb, classmath = "68U99 (Computing methodologies) 68P15 (Database theory) 68P20 (Information storage and retrieval)", fjournal = "Knowledge and Information Systems", keywords = "Markov chain; Web navigation; Zipf's law", } @Article{Ley:1994:TPB, author = "Eduadro Ley and Hal R. Varian", title = "Are there psychological barriers in the {Dow--Jones} index?", journal = j-APPL-FINANC-ECON, volume = "4", number = "3", pages = "217--224", month = "????", year = "1994", CODEN = "????", DOI = "http://dx.doi.org/10.1080/758526902", ISSN = "0960-3107 (print), 1466-4305 (electronic)", ISSN-L = "0960-3107", bibdate = "Sat Feb 16 18:29:52 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/758526902", acknowledgement = ack-nhfb, fjournal = "Applied Financial Economics", } @Article{Ley:1996:PDU, author = "Eduardo Ley", title = "On the Peculiar Distribution of the {U.S.} Stock Indexes' Digits", journal = j-AMER-STAT, volume = "50", number = "4", pages = "311--313", month = nov, year = "1996", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Mon Nov 14 15:09:04 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/amstat.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.jstor.org/stable/2684926", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Leydesdorff:2006:CPL, author = "Loet Leydesdorff and Stephen Bensman", title = "Classification and power laws: the logarithmic transformation", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "57", number = "11", pages = "1470--1486", month = sep, year = "2006", CODEN = "JASIEF", DOI = "http://dx.doi.org/10.1002/asi.20467", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Sat Feb 16 18:31:04 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", keywords = "Benford's Law", } @Article{Li:1992:RTE, author = "W. Li", title = "Random texts exhibit {Zipf}'s-law-like word frequency distribution", journal = j-IEEE-TRANS-INF-THEORY, volume = "38", number = "6", pages = "1842--1845", month = "????", year = "1992", CODEN = "IETTAW", DOI = "http://dx.doi.org/10.1109/18.165464", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", bibdate = "Fri Nov 18 12:32:19 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Information Theory", } @Article{Li:2002:ZLI, author = "Wentian Li and Yaning Yang", title = "{Zipf's Law} in Importance of Genes for Cancer Classification Using Microarray Data", journal = j-J-THEOR-BIOL, volume = "219", number = "4", pages = "539--551", day = "21", month = dec, year = "2002", CODEN = "JTBIAP", DOI = "http://dx.doi.org/10.1006/jtbi.2002.3145", ISSN = "0022-5193 (print), 1095-8541 (electronic)", ISSN-L = "0022-5193", MRclass = "92C40 (92D10)", MRnumber = "2044066", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022519302931450", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Biology", journal-URL = "http://www.sciencedirect.com/science/journal/00225193", keywords = "Zipf's Law", } @Article{Li:2004:DBL, author = "Zhi-peng Li and Lin Cong and Hua-jia Wang", title = "Discussion on {Benford's Law} and its Application", journal = "ArXiv e-prints", pages = "1--13", year = "2004", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 16:17:04 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2004math......8057L; http://arxiv.org/abs/math/0408057", abstract = "The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law $ {\rm Prob} (d) = \log_{10} (1 + {\displaystyle {1 \over d}}), d = 1, 2, \ldots, 9 $. Illustrations of Benford's Law from both theoretical and real-life sources on both science and social science areas are shown in detail with some novel ideas and generalizations developed solely by the authors of this paper. Three tests, Chi-Square test, total variation distance, and maximum deviations are adopted to examine the fitness of the datasets to Benford's distribution. Finally, applications of Benford's Law are summarized and explored to reveal the power of this mathematical principle.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "math/0408057", } @Article{Li:2005:ZLP, author = "Yujian Li and Chuangbai Xiao", title = "{Zipf}'s law probably existing in protein sequences", journal = "J. Beijing Univ. Technol.", volume = "31", number = "4", pages = "366--368", year = "2005", CODEN = "????", ISSN = "????", bibdate = "Sat Nov 12 11:10:06 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1084.92019", abstract = "In order to analyze whether Zipf's law in linguistics exists in protein sequences, this paper uses $ 1.735 \, 7 \times 10^4 $ protein sequences labeled with secondary structures which are selected from the DSSP database. The segments of successive amino acid residues with a same code of secondary structure are defined as words. The results show that the distribution of words emerging frequency follows Zipf's law with the exponent $ 0.981 $.", acknowledgement = ack-nhfb, classmath = "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics to biology): 92D20 (Protein sequences, DNA sequences)", language = "Chinese. English summary", xxremark = "Which journal is this? Beijing gong ye da xue xue bao = Journal of Beijing Polytechnic University (ISSN 0254-0037), or Beijing ke ji da xue xue bao = Journal of University of Science and Technology, Beijing (ISSN 1001-053X), or something different?", } @Misc{Li:2011:ZLB, author = "Wentian Li", title = "{Zipf's Law} bibliography", howpublished = "Web site.", month = aug, year = "2011", bibdate = "Fri Nov 25 08:58:21 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The site holds 870 references (in untagged reference-list form) up to 11 August 2011.", URL = "http://www.nslij-genetics.org/wli/zipf/", acknowledgement = ack-nhfb, lastaccess = "25 November 2011", } @Article{LimKaiJie:2012:CES, author = "Shawn {Lim Kai Jie} and Mohandas Kalaichelvan", title = "A Critical Evaluation of the Significance of Round Numbers in {European} Equity Markets in Light of the Predictions from {Benford's Law}", journal = "International Research Journal of Finance and Economics", volume = "95", number = "??", pages = "196--210", day = "28", month = aug, year = "2012", DOI = "????", ISSN = "1450-2887", bibdate = "Tue Feb 19 06:04:47 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://mpra.ub.uni-muenchen.de/40960/; http://mpra.ub.uni-muenchen.de/40960/1/IRJFE_95_15.pdf", acknowledgement = ack-nhfb, } @Article{Lindsay:2004:DFD, author = "D. H. Lindsay and P. S. Foote and A. Campbell and D. R. Reilly", title = "Detecting fraud in the data using automatic intervention detection", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2004", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sat Feb 16 18:32:22 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", } @Book{Lines:1986:NYT, author = "Malcolm E. Lines", title = "A number for your thoughts: facts and speculations about numbers from {Euclid} to the latest computers", publisher = pub-ADAM-HILGER, address = pub-ADAM-HILGER:adr, pages = "vi + 214", year = "1986", ISBN = "0-85274-495-1 (paperback)", ISBN-13 = "978-0-85274-495-6 (paperback)", LCCN = "QA241 .L617 1986", bibdate = "Wed Nov 23 11:34:02 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.gbv.de:20011/gvk", URL = "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html", acknowledgement = ack-nhfb, remark = "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law of Benford''.", subject = "number theory", } @Article{Lipovetsky:2009:PLD, author = "Stan Lipovetsky", title = "{Pareto} $ 80 / 20 $ law: derivation via random partitioning", journal = j-INT-J-MATH-EDU-SCI-TECH, volume = "40", number = "2", pages = "271--277", month = "????", year = "2009", CODEN = "IJMEBM", DOI = "http://dx.doi.org/10.1080/00207390802213609", ISSN = "0020-739X (print), 1464-5211 (electronic)", ISSN-L = "0020-739X", bibdate = "Sat Jan 07 09:22:31 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609", abstract = "The Pareto 80/20 Rule, also known as the Pareto principle or law, states that a small number of causes (20\%) is responsible for a large percentage (80\%) of the effect. Although widely recognized as a heuristic rule, this proportion has not been theoretically based. The article considers derivation of this 80/20 rule and some other standard quotients from the mean and its interval estimation for the total value defined by the product of two variables in the random partitioning model.", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematical Education in Science and Technology", onlinedate = "19 Feb 2009", } @Article{Liu:2008:MNS, author = "Cheng-Shi Liu", title = "Maximal non-symmetric entropy leads naturally to {Zipf}'s law", journal = j-FRACTALS, volume = "16", number = "1", pages = "99--101", year = "2008", CODEN = "FRACEG", DOI = "http://dx.doi.org/10.1142/S0218348X08003788", ISSN = "0218-348X", ISSN-L = "0218-348X", MRclass = "94A17 (94A15)", MRnumber = "2399875 (2009c:94027)", MRreviewer = "Yasuichi Horibe", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Fractals. Complex Geometry, Patterns, and Scaling in Nature and Society", } @Article{Liu:2010:CIE, author = "Hongyan Liu and Xiaoyu Wang and Yinghui Yang", title = "Comments on {``An integrated efficient solution for computing frequent and top-$k$ elements in data streams''}", journal = j-TODS, volume = "35", number = "2", pages = "15:1--15:??", month = apr, year = "2010", CODEN = "ATDSD3", DOI = "http://doi.acm.org/10.1145/1735886.1735894", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", bibdate = "Wed Apr 28 13:44:08 MDT 2010", bibsource = "http://www.acm.org/pubs/contents/journals/tods/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Metwally:2006:IES}.", abstract = "We investigate a well-known algorithm, {\em Space-Saving\/} [Metwally et al. 2006], which has been proven efficient and effective at mining frequent elements in data streams. We discovered an error in one of the theorems in Metwally et al. [2006]. Experiments are conducted to illustrate the error.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Database Systems", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", keywords = "approximate queries; data streams; frequent elements; top-$k$ elements; Zipfian distributions", } @Article{Liu:2011:BLC, author = "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren", title = "{Benford}'s law and cross-sections of {$ A(n, \alpha) B $} reactions", journal = j-EUR-PHYS-J-A, volume = "47", pages = "78", month = jun, year = "2011", CODEN = "EPJAFV", DOI = "http://dx.doi.org/10.1140/epja/i2011-11078-3", ISSN = "1434-6001 (print), 1434-601X (electronic)", ISSN-L = "1434-6001", bibdate = "Mon Nov 14 18:00:32 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011EPJA...47...78L", acknowledgement = ack-nhfb, fjournal = "European Physical Journal A: Hadrons and Nuclei", journal-URL = "http://www.springerlink.com/content/1434-6001", } @Book{Livio:2002:GRS, author = "Mario Livio", title = "The golden ratio: the story of phi, the world's most astonishing number", publisher = "Broadway Books", address = "New York, NY, USA", pages = "viii + 294", year = "2002", ISBN = "0-7679-0815-5", ISBN-13 = "978-0-7679-0815-3", LCCN = "QA466 .L58 2002", bibdate = "Tue Jul 08 12:29:44 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/master.bib", note = "Benford's Law is treated on pages 231--237.", price = "US\$24.95, CAN\$37.95", acknowledgement = ack-nhfb, } @Article{Logan:1978:FDP, author = "Jonothan L. Logan and Samuel A. Goudsmit", title = "The First Digit Phenomenon", journal = j-PROC-AMER-PHIL-SOC, volume = "122", number = "4", pages = "193--197", day = "18", month = aug, year = "1978", CODEN = "PAPCAA", ISSN = "0003-049X", ISSN-L = "0003-049X", bibdate = "Fri Mar 30 11:20:35 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper contains derivations of both Stigler's Law and Benford's Law, and receives strong criticism in \cite{Raimi:1985:FDP}. This paper contains an important historical note that is recorded in entry \cite{Benford:1938:LAN}.", URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C; http://www.jstor.org/stable/986530", abstract = "Forty years ago an article appeared in these Proceedings, which has since then attracted much attention of mathematicians and some physicists. It was written by Frank Benford, a physicist from the General Electric Company at Schenectady. He had examined a large number of numerical tables, the kind that are printed in almanacs, and in scientific and technical handbooks. He noticed a most unusual and unexpected property of many of these tables. Consider, for example, the numbers representing the populations of states or all the countries in the world, or their areas, their budgets, their numbers of hospital beds, etc. One would expect that on the average just as many of these entries would begin with the digit $1$ as with $2$ or $3$ or $4$, and so on. But Benford noticed that small values of the first digits occur far more often.", acknowledgement = ack-nhfb, author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)", fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed the concept of electron spin, a critical step forward in the quantum mechanics of many-electron systems. Surprisingly, that work did not get them the Nobel Prize, but it did spur Wolfgang Pauli to present his Exclusion Principle in 1925, for which he received the 1945 Nobel Prize in Physics. After World War II, Goudsmit was the scientific head of the Alsos mission to capture German nuclear scientists. In the 1950s, he founded the journal Physical Review Letters. During the 1960s and 1970s, he was Editor-in-Chief of the main American physics journal, the Physical Review.", } @Article{Lolbert:2008:NEG, author = "Tam{\'a}s Lolbert", title = "On the non-existence of a general {Benford}'s law", journal = "Mathematical Social Sciences", volume = "55", number = "2", pages = "103--106", month = mar, year = "2008", CODEN = "MSOSDD", DOI = "http://dx.doi.org/10.1016/j.mathsocsci.2007.09.001", ISSN = "0165-4896 (print), 1879-3118 (electronic)", ISSN-L = "0165-4896", MRclass = "60A10 (60E10)", MRnumber = "2391902", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165489607000935", abstract = "Benford's law states that in randomly collected numbers certain digits are more often leading digits than others. More formally: the general law states that the mantissae follow the logarithmic distribution in any base. Benford's law was recognized by many mathematicians so that several possible explanations have been derived, but several questions are still open. Applications are widespread, for example an auditing technique (the so-called digital analysis), which is employed around the world by internal revenue services to detect tax fraud, is based on this phenomenon.\par In this paper it will be shown that there exists no probability measure that would obey Benford's law for any base, but if the set of possible bases does not exceed a given upper limit, most real-life distributions obey, or can be transformed to obey Benford's law.", acknowledgement = ack-nhfb, fjournal = "Mathematical Social Sciences", } @Article{Losee:2001:TDB, author = "Robert M. Losee", title = "Term dependence: a basis for {Luhn} and {Zipf} models", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "52", number = "12", pages = "1019--1025", year = "2001", CODEN = "JASIEF", DOI = "http://dx.doi.org/10.1002/asi.1155", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", } @Article{Lotka:1926:FDS, author = "Alfred J. Lotka", title = "The Frequency Distribution of Scientific Productivity", journal = j-J-WASH-ACAD-SCI, volume = "16", number = "12", pages = "317--323", month = dec, year = "1926", CODEN = "JWASA3", ISSN = "0043-0439", ISSN-L = "0043-0439", bibdate = "Thu Nov 24 14:36:11 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This is the earliest known publication on the phenomenon known as Zipf's Law, here applied to publication counts of chemists and physicists. Lotka's Law (a term possibly first used in \cite{Zipf:1949:HBP}) says that the number of authors producing $n$ publications is about $ 1 / n^2 $ of the number producing only one. This `law' seems to have been misunderstood and misapplied in other fields; see \cite{Potter:1981:LLR}.", acknowledgement = ack-nhfb, fjournal = "Journal of the Washington Academy of Sciences", keywords = "Lotka's Law", } @TechReport{Lowe:1999:FDL, author = "Tomas Lowe and Sally Murphy and Justin Hayward", title = "The First Digit Law", type = "Report", number = "??", institution = "Department of Computing, Imperial College", address = "London, UK", month = jun, year = "1999", bibdate = "Wed Nov 23 16:59:50 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf; http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html", acknowledgement = ack-nhfb, lastaccess = "23 November 2011", } @Article{Lu:2005:CZL, author = "Tim Lu and Christine M. Costello and Peter J. P. Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl and Stefan Schreiber", title = "Can {Zipf}'s law be adapted to normalize microarrays?", journal = "BMC Bioinformatics", volume = "6", number = "??", pages = "37--49", month = "????", year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.1186/1471-2105-6-37", ISSN = "1471-2105", ISSN-L = "1471-2105", bibdate = "Sat Feb 16 18:38:50 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.biomedcentral.com/1471-2105/6/37", acknowledgement = ack-nhfb, } @InProceedings{Lu:2005:DFH, author = "Fletcher Lu and J. Efrim Boritz", title = "Detecting Fraud in Health Insurance Data: Learning to Model Incomplete {Benford's Law} Distributions", crossref = "Gama:2005:MLE", pages = "633--640", year = "2005", DOI = "http://dx.doi.org/10.1007/11564096_63", bibdate = "Tue Nov 15 08:55:45 2011", bibsource = "DBLP; http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @InCollection{Lu:2006:AFD, author = "Fletcher Lu and J. Efrim Boritz and Dominic Covvey", booktitle = "Advances in artificial intelligence", title = "Adaptive fraud detection using {Benford}'s law", volume = "4013", publisher = pub-SV, address = pub-SV:adr, pages = "347--358", year = "2006", DOI = "http://dx.doi.org/10.1007/11766247_30", MRnumber = "2280590", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @InProceedings{Lu:2006:BCF, author = "F. Lu and J. E. Boritz", editor = "????", booktitle = "{Uncertainty in Artificial Intelligence: Proceedings of the 22nd Conference}", title = "Building a case for fraud using {Benford}'s law with reinforcement learning", publisher = "????", address = "????", pages = "??--??", year = "2006", bibdate = "Sat Feb 16 18:34:47 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Lu:2010:BLP, author = "Ocean Fan Lu and David E. Giles", title = "{Benford's Law} and psychological barriers in certain {eBay} auctions", journal = j-APPL-ECON-LETT, volume = "17", number = "10", pages = "1005--1008", month = "????", year = "2010", CODEN = "????", DOI = "http://dx.doi.org/10.1080/13504850802631814", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Sat Jan 07 09:10:23 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814", abstract = "Using generalizations of Benford's Law we test for the absence of psychological barriers at various price levels in eBay auctions for professional football tickets. Our empirical results indicate that this hypothesis cannot be rejected.", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", onlinedate = "16 Jun 2009", } @Article{Lu:2013:DZH, author = "Linyuan L{\"u} and Zi-Ke Zhang and Tao Zhou", title = "Deviation of {Zipf}'s and {Heaps' Laws} in Human Languages with Limited Dictionary Sizes", journal = j-SCI-REP, volume = "3", number = "??", pages = "1--7", month = "????", year = "2013", CODEN = "SRCEC3", DOI = "http://dx.doi.org/10.1038/srep01082", ISSN = "2045-2322", bibdate = "Tue Feb 26 07:39:15 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/srep/2013/130130/srep01082/full/srep01082.html", accepted = "21 December 2012", acknowledgement = ack-nhfb, articleno = "1082", fjournal = "Scientific Reports", onlinedate = "30 January 2013", received = "11 June 2012", } @Article{Luque:2008:FDF, author = "Bartolo Luque and Lucas Lacasa", title = "The first digit frequencies of primes and {Riemann} zeta zeros tend to uniformity following a size-dependent generalized {Benford}'s law", journal = "ArXiv e-prints", month = nov, year = "2008", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See published paper \cite {Luque:2009:FDF}.", URL = "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L; http://arxiv.org/abs/0811.3302", abstract = "Prime numbers seem to distribute among the natural numbers with no other law than that of chance, however its global distribution presents a quite remarkable smoothness. Such interplay between randomness and regularity has motivated scientists of all ages to search for local and global patterns in this distribution that eventually could shed light into the ultimate nature of primes. In this work we show that a generalization of the well known first-digit Benford's law, which addresses the rate of appearance of a given leading digit $d$ in data sets, describes with astonishing precision the statistical distribution of leading digits in the prime numbers sequence. Moreover, a reciprocal version of this pattern also takes place in the sequence of the nontrivial Riemann zeta zeros. We prove that the prime number theorem is, in the last analysis, the responsible of these patterns. Some new relations concerning the prime numbers distribution are also deduced, including a new approximation to the counting function $ \pi (n) $. Furthermore, some relations concerning the statistical conformance to this generalized Benford's law are derived. Some applications are finally discussed.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0811.3302", keywords = "Mathematics - Number Theory, Mathematics - Probability, Mathematics - Statistics", pagecount = "20", primaryclass = "math.NT", } @Article{Luque:2009:FDF, author = "Bartolo Luque and Lucas Lacasa", title = "The first digit frequencies of prime numbers and {Riemann} zeta zeros", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "465", number = "2107", pages = "2197--2216", day = "8", month = jul, year = "2009", CODEN = "PRLAAZ", DOI = "http://dx.doi.org/10.1098/rspa.2009.0126", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", bibdate = "Mon Feb 25 10:44:43 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, \& Engineering Sciences", keywords = "Benford's Law", onlinedate = "22 April 2009", } @InProceedings{Lyons:2011:NSF, author = "M. Lyons and E. Carl-Ludwig Siegel", booktitle = "APS March Meeting Abstracts", title = "{NON-Shor} Factorization via {BEQS BEC}: {Watkins} Number-Theory ``Pure''-Mathematics $ \cup $ with Statistical-Physics: {Benford} Log-Law Inversion to {ONLY} {BEQS} digit $ d = 0 $ {BEC}!!!", publisher = "American Physical Society", address = "????", pages = "K1142", month = mar, year = "2011", bibdate = "Mon Nov 14 18:08:39 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L", acknowledgement = ack-nhfb, } @Article{Ma:2005:CBL, author = "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel and J. Wang and T. Keutgen and Z. Majka and M. Murray and L. Qin and P. Smith and R. Alfaro and J. Cibor and M. Cinausero and Y. El Masri and D. Fabris and E. Fioretto and A. Keksis and M. Lunardon and A. Makeev and N. Marie and E. Martin and A. Martinez-Davalos and A. Menchaca-Rocha and G. Nebbia and G. Prete and V. Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis and P. Staszel and M. Veselsky and G. Viesti and E. M. Winchester and S. J. Yennello", title = "Critical behavior in light nuclear systems: Experimental aspects", journal = j-PHYS-REV-C, volume = "71", number = "5", pages = "054606", day = "26", month = may, year = "2005", CODEN = "PRVCAN", DOI = "http://dx.doi.org/10.1103/PhysRevC.71.054606", ISSN = "0556-2813 (print), 1089-490X, 1538-4497", ISSN-L = "0556-2813", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevC.71.054606", acknowledgement = ack-nhfb, fjournal = "Physical Review C (Nuclear Physics)", journal-URL = "http://prc.aps.org/browse", keywords = "Zipf's Law", } @InCollection{Macaulay:1922:PLG, author = "F. R. Macaulay", editor = "W. C. Mitchell", booktitle = "Income in the {United States}: Its Amount and Distribution: 1909--1919", title = "{Pareto}'s law and the general problem of mathematical describing the frequency of distribution of income", publisher = "National Bureau of Economic Research", address = "New York, NY, USA", pages = "??--??", year = "1922", LCCN = "????", bibdate = "Fri Nov 25 09:06:43 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Macon:1950:DFD, author = "N. Macon and L. Moser", title = "On the distribution of first digits of powers", journal = "Scripta Mathematica", volume = "16", number = "??", pages = "290--291", month = "????", year = "1950", CODEN = "????", ISSN = "0036-9713", ISSN-L = "0036-9713", bibdate = "Sat Nov 12 16:28:13 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Scripta Math.", fjournal = "Scripta Mathematica", } @Article{Mahdian:2010:BBM, author = "Babak Mahdian and Stanislav Saic", title = "A bibliography on blind methods for identifying image forgery", journal = j-SIGNAL-PROCESS-IMAGE-COMMUN, volume = "25", number = "6", pages = "389--399", month = jul, year = "2010", CODEN = "SPICEF", DOI = "http://dx.doi.org/10.1016/j.image.2010.05.003", ISSN = "0923-5965 (print), 1879-2677 (electronic)", ISSN-L = "0923-5965", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0923596510000536", acknowledgement = ack-nhfb, fjournal = "Signal Processing: Image Communication", keywords = "Benford's Law", } @Article{Maia:1984:UBL, author = "M. J. F. Maia and M. D. Maia", title = "On the Unity of {Bradford's Law}", journal = j-J-DOC, volume = "40", number = "3", pages = "206--216", month = "????", year = "1984", CODEN = "JDOCAS", DOI = "http://dx.doi.org/10.1108/eb026765", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:11:46 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", } @Article{Maillart:2008:ETZ, author = "T. Maillart and D. Sornette and S. Spaeth and G. von Krogh", title = "Empirical Tests of {Zipf's Law} Mechanism in Open Source {Linux} Distribution", journal = j-PHYS-REV-LET, volume = "101", number = "21", pages = "218701", day = "19", month = nov, year = "2008", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.101.218701", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/gnu.bib; http://www.math.utah.edu/pub/tex/bib/linux.bib; http://www.math.utah.edu/pub/tex/bib/unix.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", pagecount = "4", } @Article{Makse:1995:MUG, author = "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene Stanley", title = "Modelling urban growth patterns", journal = j-NATURE, volume = "377", number = "6550", pages = "608--612", day = "19", month = oct, year = "1995", CODEN = "NATUAS", DOI = "http://dx.doi.org/10.1038/377608a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Wed Feb 27 06:06:25 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Berlin (Germany) population; London (UK) population; Zipf's Law", } @Article{Malacarne:2001:QED, author = "L. C. Malacarne and R. S. Mendes and E. K. Lenzi", title = "$q$-exponential distribution in urban agglomeration", journal = j-PHYS-REV-E, volume = "65", number = "??", pages = "017106", day = "21", month = dec, year = "2001", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.65.017106", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.65.017106", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf--Mandelbrot law", } @Article{Malcai:1999:PLD, author = "Ofer Malcai and Ofer Biham and Sorin Solomon", title = "Power-law distributions and {L{\'e}vy}-stable intermittent fluctuations in stochastic systems of many autocatalytic elements", journal = j-PHYS-REV-E, volume = "60", number = "2", pages = "1299--1303", month = aug, year = "1999", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.60.1299", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:25:38 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.1299", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", } @Article{Malevergne:2011:TPA, author = "Yannick Malevergne and Vladilen Pisarenko and Didier Sornette", title = "Testing the {Pareto} against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities", journal = j-PHYS-REV-E, volume = "83", number = "3", pages = "036111", day = "22", month = mar, year = "2011", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.83.036111", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.83.036111", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Pareto distribution; Zipf's Law", pagecount = "11", } @InProceedings{Manaris:2002:PTR, author = "B. Manaris and T. Purewal and C. McCormick", editor = "{IEEE}", booktitle = "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002, Embassy Suites Hotel, Columbia, South Carolina, USA", title = "Progress Towards Recognizing and Classifying Beautiful Music with Computers: {MIDI}-Encoded Music and the {Zipf-Mandelbrot Law}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "52--57", year = "2002", DOI = "http://dx.doi.org/10.1109/.2002.995557", ISBN = "0-7803-7252-2", ISBN-13 = "978-0-7803-7252-8", LCCN = "TK7801 .I56 2002", bibdate = "Mon Feb 18 10:40:27 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7814", acknowledgement = ack-nhfb, bookpages = "xviii + 482", } @InProceedings{Manaris:2003:EMZ, author = "Bill Manaris and Dallas Vaughan and Christopher Wagner and Juan Romero and Robert B. Davis", title = "Evolutionary Music and the {Zipf--Mandelbrot Law}: Developing Fitness Functions for Pleasant Music", crossref = "Raidl:2003:AEC", pages = "522--534", year = "2003", bibdate = "Mon Feb 18 10:49:54 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Manaris:2005:ZLM, author = "Bill Manaris and Juan Romero and Penousal Machado and Dwight Krehbiel and Timothy Hirzel and Walter Pharr and Robert B. Davis", title = "{Zipf}'s law, music classification, and aesthetics", journal = j-COMP-MUSIC-J, volume = "29", number = "1", pages = "55--69", month = "Spring", year = "2005", CODEN = "CMUJDY", ISSN = "0148-9267 (print), 1531-5169 (electronic)", ISSN-L = "0148-9267", bibdate = "Sat Feb 16 18:40:14 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html; http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf", acknowledgement = ack-nhfb, fjournal = "Computer Music Journal", keywords = "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law", } @InProceedings{Manaris:2006:IES, author = "Bill Manaris and Luca Pellicoro and George Pothering and Harland Hodges", editor = "????", booktitle = "{2006 IASTED International Conference on Artificial Intelligence and Applications (AIA 2006), February 13--16, 2006, Innsbruck, Austria}", title = "Investigating {Esperanto}'s statistical proportions relative to other languages using neural networks and {Zipf}'s law", publisher = "Acta Press", address = "????", pages = "1--7", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 18:41:37 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mandelbrot:1953:ITS, author = "Beno{\^\i}t B. Mandelbrot", editor = "Willis Jackson", booktitle = "{Communication theory: papers read at a Symposium on ``Applications of Communication Theory'' held at the Institution of Electrical Engineers, London, September 22nd--26th 1952}", title = "An Informational Theory of the Statistical Structure of Languages", publisher = pub-BUTTERWORTHS, address = pub-BUTTERWORTHS:adr, pages = "486--502", year = "1953", LCCN = "Q350 .S92 1952", bibdate = "Wed Nov 16 09:37:30 2011", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://lccn.loc.gov/53004215; http://www.nytimes.com/2010/10/17/us/17mandelbrot.html", acknowledgement = ack-nhfb, bookpages = "xii + 532", remark = "The paper is incorrectly referenced as a book in \cite{Baek:2011:ZLU}. Mandelbrot got his Master of Science in Aeronautics at CalTech in 1948, and his Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in 1952 in Paris, so perhaps this is a translation of his thesis work.", } @Article{Mandelbrot:1959:NCS, author = "Beno{\^\i}t Mandelbrot", title = "A note on a class of skew distribution functions: analysis and critique of a paper by {H. A. Simon}", journal = j-INF-CONTROL, volume = "2", number = "??", pages = "90--99", month = apr, year = "1959", CODEN = "IFCNA4", DOI = "http://dx.doi.org/10.1016/S0019-9958(59)90098-1", ISSN = "0019-9958 (print), 1878-2981 (electronic)", ISSN-L = "0019-9958", bibdate = "Wed Nov 16 09:45:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Simon:1955:CSD}.", abstract = "This note is a discussion of H. A. Simon's model (1955) concerning the class of frequency distributions generally associated with the name of G. K. Zipf. The main purpose is to show that Simon's model is analytically circular in the case of the linguistic laws of Estoup--Zipf and Willis--Yule. Insofar as the economic law of Pareto is concerned, Simon has himself noted that his model is a particular case of that of Champernowne; this is correct, with some reservation. A simplified version of Simon's model is included.", acknowledgement = ack-nhfb, fjournal = "Information and Control", } @Article{Mandelbrot:1960:PLL, author = "Beno{\^\i}t Mandelbrot", title = "The {Pareto--Levy} law and the distribution of income", journal = j-INT-ECON-REV, volume = "1", number = "??", pages = "79--106", month = "????", year = "1960", CODEN = "INERAE", ISSN = "0020-6598 (print), 1468-2354 (electronic)", ISSN-L = "0020-6598", bibdate = "Wed Nov 23 11:07:01 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ingenta.com/journals/browse/bpl/iere", acknowledgement = ack-nhfb, fjournal = "International Economic Review", } @TechReport{Mandelbrot:1962:SNR, author = "Beno{\^\i}t Mandelbrot", title = "Statistics of natural resources and the law of {Pareto}", type = "Research Note", number = "NC-146", institution = "IBM", address = "Yorktown Heights, NY, USA", day = "29", month = jun, year = "1962", bibdate = "Mon Sep 10 17:35:59 2012", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Manin:2008:ZLA, author = "Dmitrii Y. Manin", title = "{Zipf's Law} and Avoidance of Excessive Synonymy", journal = j-COGN-SCI, volume = "32", number = "7", pages = "1075--1098", year = "2008", CODEN = "COGSD5", DOI = "http://dx.doi.org/10.1080/03640210802020003", ISSN = "0364-0213 (print), 1551-6709 (electronic)", ISSN-L = "0364-0213", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Cognitive Science", keywords = "Semantics; Synonymy; Word frequency; Word meaning; Zipf's law", } @Article{Manoochehrnia:2010:BLA, author = "P. Manoochehrnia and F. Rachidi and M. Rubinstein and W. Schulz and G. Diendorfer", title = "{Benford's Law} and Its Application to Lightning Data", journal = j-IEEE-TRANS-ELECTROMAGN-COMPAT, volume = "52", number = "4", pages = "956--961", month = nov, year = "2010", CODEN = "IEMCAE", DOI = "http://dx.doi.org/10.1109/TEMC.2010.2067218", ISSN = "0018-9375 (print), 1558-187X (electronic)", ISSN-L = "0018-9375", bibdate = "Mon Nov 21 22:24:43 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electromagnetic Compatibility", } @Article{Manrubia:1998:IMU, author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette", title = "Intermittency model for urban development", journal = j-PHYS-REV-E, volume = "58", number = "1", pages = "295--302", month = jul, year = "1998", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.58.295", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:42:23 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.295", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Article{Manrubia:1999:SMP, author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette", title = "Stochastic multiplicative processes with reset events", journal = j-PHYS-REV-E, volume = "59", number = "5", pages = "4945--4948", month = may, year = "1999", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.59.4945", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:25:24 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.59.4945", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", issue = "5", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's law", } @Article{Manrubia:1999:TDS, author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette and Ricard V. Sol{\'e}", title = "Transient Dynamics and Scaling Phenomena in Urban Growth", journal = j-FRACTALS, volume = "7", number = "1", pages = "1--8", month = mar, year = "1999", CODEN = "FRACEG", DOI = "http://dx.doi.org/10.1142/S0218348X99000025", ISSN = "0218-348X", ISSN-L = "0218-348X", bibdate = "Wed Feb 27 07:11:42 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025", acknowledgement = ack-nhfb, fjournal = "Fractals", keywords = "Zipf's Law", } @Article{Mansury:2007:EZL, author = "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s", title = "The emergence of {Zipf's Law} in a system of cities: an agent-based simulation approach", journal = j-J-ECON-DYN-CONTROL, volume = "31", number = "7", pages = "2438--2460", day = "15", month = jul, year = "2007", CODEN = "JEDCDH", DOI = "http://dx.doi.org/10.1016/j.jedc.2006.08.002", ISSN = "0165-1889 (print), 1879-1743 (electronic)", ISSN-L = "0165-1889", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165188906001527", ZMnumber = "1163.91504", abstract = "This paper develops a spatial agent-based model to generate a system of cities that exhibits the statistical properties of the Zipf's Law. The numerical results suggest that the combination of bounded rationality and maximum heterogeneity of agents can produce a generic power-law relationship in the size distribution of cities, but does not always generate the Zipf's Law. We found sufficient conditions on the probability distribution of spatial reach to generate the Zipf's Law associated with unit power coefficient. Our model also indicates that the Zipf's Law breaks down unless the extent of agglomeration economies overwhelms the negative disagglomerating forces.", acknowledgement = ack-nhfb, classmath = "91B72 (Spatial models)", fjournal = "Journal of Economic Dynamics and Control", keywords = "complex systems; power laws; spatial agent based models; Zipf's Law", } @Article{Mantegna:1994:LFN, author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger and S. Havlin and C. K. Peng and M. Simons and H. E. Stanley", title = "Linguistic Features of Noncoding {DNA} Sequences", journal = j-PHYS-REV-LET, volume = "73", number = "??", pages = "3169--??", day = "5", month = dec, year = "1994", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.73.3169", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Mantegna:1995:SAC, author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger and S. Havlin and C.-K. Peng and M. Simons and H. E. Stanley", title = "Systematic analysis of coding and noncoding {DNA} sequences using methods of statistical linguistics", journal = j-PHYS-REV-E, volume = "52", number = "??", pages = "2939--??", day = "1", month = sep, year = "1995", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.52.2939", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.2939", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Marchi:2006:AAS, author = "Scott Marchi and James Hamilton", title = "Assessing the Accuracy of Self-Reported Data: an Evaluation of the Toxics Release Inventory", journal = "Journal of Risk and Uncertainty", volume = "32", number = "1", pages = "57--76", month = jan, year = "2006", CODEN = "JRUNEN", DOI = "http://dx.doi.org/10.1007/s10797-006-6666-3", ISSN = "0895-5646 (print), 1573-0476 (electronic)", ISSN-L = "0895-5646", bibdate = "Fri Nov 25 11:25:49 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Marsili:1998:IIL, author = "Matteo Marsili and Yi-Cheng Zhang", title = "Interacting Individuals Leading to {Zipf's Law}", journal = j-PHYS-REV-LET, volume = "80", number = "??", pages = "2741--??", day = "23", month = mar, year = "1998", CODEN = "PRLTAO", DOI = "http://dx.doi.org/10.1103/PhysRevLett.80.2741", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Maslov:2005:GTS, author = "V. P. Maslov", title = "On a general theorem of set theory that leads to the {Gibbs}, {Bose--Einstein}, and {Pareto} distributions and to the {Zipf--Mandelbrot} law for the stock market", journal = j-MAT-ZAMETKI, volume = "78", number = "6", pages = "870--877", year = "2005", CODEN = "????", DOI = "http://dx.doi.org/10.1007/s11006-005-0186-9", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "91B28 (90C29)", MRnumber = "2249037 (2007b:91077)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", } @Article{Maslov:2005:RZLa, author = "V. P. Maslov", title = "Refining {Zipf}'s law for frequency dictionaries", journal = j-DOKL-AKAD-NAUK, volume = "405", number = "5", pages = "591--594", year = "2005", CODEN = "DANKAS", ISSN = "0869-5652", ISSN-L = "0869-5652", MRclass = "94A15 (60C05)", MRnumber = "2340762", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii Nauk", } @Article{Maslov:2005:RZLb, author = "V. P. Maslov", title = "Refinement of {Zipf}'s law for frequency dictionaries", journal = j-DOKL-MATH, volume = "72", number = "3", pages = "942--945", year = "2005", CODEN = "????", ISSN = "1064-5624 (print), 1531-8362 (electronic)", ISSN-L = "1064-5624", bibdate = "Sat Nov 12 11:05:14 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1206.82009", acknowledgement = ack-nhfb, classmath = "82B10 (Quantum equilibrium statistical mechanics (general)) 68T50 (Natural language processing) 68Q45 (Formal languages)", fjournal = "Doklady Mathematics", keywords = "Bose--Einstein statistics", language = "English. Russian original", } @Article{Maslov:2005:ZML, author = "V. P. Maslov", title = "The {Zipf--Mandelbrot} law: quantization and an application to the stock market", journal = j-RUSS-J-MATH-PHYS, volume = "12", number = "4", pages = "483--488", year = "2005", CODEN = "RJMPEL", ISSN = "1061-9208", ISSN-L = "1061-9208", MRclass = "91B28 (82B99)", MRnumber = "2201312 (2006i:91053)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Russian Journal of Mathematical Physics", } @Article{Maslov:2006:BGA, author = "V. P. Maslov", title = "{Bose} gas of anharmonic oscillators and a refinement of {Zipf}'s law", journal = j-TEORET-MATH-FIZ, volume = "148", number = "3", pages = "495--496", year = "2006", CODEN = "TMFZAL", DOI = "http://dx.doi.org/10.1007/s11232-006-0117-2", ISSN = "0564-6162", ISSN-L = "0564-6162", MRclass = "82B10", MRnumber = "2283664", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i Matematicheskaya Fizika", } @Article{Maslov:2006:NAD, author = "V. P. Maslov", title = "Negative asymptotic dimension, a new condensate, and their relation to the quantized {Zipf} law", journal = j-MAT-ZAMETKI, volume = "80", number = "6", pages = "856--863", year = "2006", CODEN = "????", DOI = "http://dx.doi.org/10.1007/s11006-006-0203-7", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "82B10 (20F69 53C23 81S10 91F20)", MRnumber = "2311613 (2008e:82005)", MRreviewer = "Artur E. Ruuge", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", } @Article{Maslov:2006:RZM, author = "V. P. Maslov", title = "A refinement of the {Zipf--Mandelbrot} law and lacunarity in an ideal gas", journal = j-TEORET-MATH-FIZ, volume = "147", number = "3", pages = "511--512", year = "2006", CODEN = "TMFZAL", DOI = "http://dx.doi.org/10.1007/s11232-006-0083-8", ISSN = "0564-6162", ISSN-L = "0564-6162", MRclass = "82B10", MRnumber = "2254729 (2007d:82007)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i Matematicheskaya Fizika", } @Article{Maslov:2006:ZLR, author = "V. P. Maslov and T. V. Maslova", title = "On {Zipf}'s law and rank distributions in linguistics and semiotics", journal = j-MAT-ZAMETKI, volume = "80", number = "5", pages = "718--732", year = "2006", CODEN = "????", DOI = "http://dx.doi.org/10.1007/s11006-006-0189-1", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "60C05 (62-07 62P99)", MRnumber = "2311586 (2008g:60027)", MRreviewer = "Konstantin E. Feldman", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "Zbl 1134.62086", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", } @Article{Maslov:2007:PTZ, author = "V. P. Maslov", title = "Phase transitions of the zeroth kind and the quantization of the {Zipf} law", journal = j-TEORET-MATH-FIZ, volume = "150", number = "1", pages = "118--142", year = "2007", CODEN = "TMFZAL", DOI = "http://dx.doi.org/10.1007/s11232-007-0008-1", ISSN = "0564-6162", ISSN-L = "0564-6162", MRclass = "82B26 (82B03)", MRnumber = "2325869 (2008g:82037)", MRreviewer = "N. N. Ganikhodjaev", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i Matematicheskaya Fizika", } @Article{Maslova:2006:ZLM, author = "T. V. Maslova", title = "{Zipf}'s law and {Maslov}'s formula as applied to semiotic systems", journal = j-DOKL-MATH, volume = "74", number = "3", pages = "917--920", year = "2006", CODEN = "????", DOI = "http://dx.doi.org/10.1134/S1064562406060330", ISSN = "1064-5624 (print), 1531-8362 (electronic)", ISSN-L = "1064-5624", bibdate = "Sat Nov 12 11:13:35 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "pre05824774", acknowledgement = ack-nhfb, classmath = "62E20 (Asymptotic distribution theory in statistics) 82B03 (Foundations of equilibrium statistical mechanics)", fjournal = "Doklady Mathematics", language = "English. Russian original", } @Article{Maslova:2006:ZLV, author = "T. V. Maslova", title = "On the {Zipf} law and the {V. P. Maslov} formula for semiotic systems", journal = j-DOKL-AKAD-NAUK, volume = "411", number = "6", pages = "754--757", year = "2006", CODEN = "DANKAS", ISSN = "0869-5652", ISSN-L = "0869-5652", MRclass = "62E20 (82B03)", MRnumber = "2451374", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii Nauk", } @Article{Masse:2011:SWD, author = "B. Mass{\'e} and D. Schneider", title = "A survey on weighted densities and their connection with the first digit phenomenon", journal = j-ROCKY-MOUNTAIN-J-MATH, volume = "41", number = "5", pages = "1395--1415", month = "????", year = "2011", CODEN = "RMJMAE", DOI = "http://dx.doi.org/10.1216/RMJ-2011-41-5-1395", ISSN = "0035-7596 (print), 1945-3795 (electronic)", ISSN-L = "0035-7596", bibdate = "Mon Feb 18 18:47:30 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rmmc.asu.edu/abstracts/rmj/vol41-5/surv-masspag1.pdf", acknowledgement = ack-nhfb, fjournal = "Rocky Mountain Journal of Mathematics", keywords = "Benford's law; first digit phenomenon; hierarchy; mantissa; weighted density", } @Article{Masse:2012:RNS, author = "Bruno Mass{\'e} and Dominique Schneider", title = "Random number sequences and the first digit phenomenon", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "86:1--86:17", year = "2012", CODEN = "????", DOI = "http://dx.doi.org/10.1214/EJP.v17-1900", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/ejp.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ejp.ejpecp.org/article/view/1900", abstract = "The sequences of mantissa of positive integers and of prime numbers are known not to be distributed as Benford's law in the sense of the natural density. We show that we can correct this defect by selecting the integers or the primes by means of an adequate random process and we investigate the rate of convergence. Our main tools are uniform bounds for deterministic and random trigonometric polynomials. We then adapt the random process to prove the same result for logarithms and iterated logarithms of integers. Finally we show that, in many cases, the mantissa law of the $n$ th randomly selected term converges weakly to the Benford's law.", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Benford's law; density; mantissa; weak convergence", } @Article{Matthews:1999:PO, author = "Robert Matthews", title = "The Power of One", journal = j-NEW-SCIENTIST, volume = "163", number = "2194", pages = "27--30", day = "10", month = jul, year = "1999", CODEN = "NWSCAL", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Mon Nov 14 16:04:36 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fortunecity.com/emachines/e11/86/one.html; http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html", acknowledgement = ack-nhfb, fjournal = "New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", xxISSN = "0262-4079, 0028-6664", } @Article{McAllister:2003:ARE, author = "James W. McAllister", title = "Algorithmic randomness in empirical data", journal = j-STUD-HIST-PHILOS-SCI, volume = "34", number = "3", pages = "633--646", month = sep, year = "2003", CODEN = "SHPSB5", DOI = "http://dx.doi.org/10.1016/S0039-3681(03)00047-5", ISSN = "0039-3681 (print), 1879-2510 (electronic)", ISSN-L = "0039-3681", bibdate = "Mon Nov 7 12:11:57 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/shps-a.bib; http://www.sciencedirect.com/science/journal/00393681", note = "See replies \cite{Twardy:2005:EDS,McAllister:2005:ACE}.", URL = "http://www.sciencedirect.com/science/article/pii/S0039368103000475", acknowledgement = ack-nhfb, fjournal = "Studies in History and Philosophy of Science Part A", journal-URL = "http://www.sciencedirect.com/science/journal/00393681", } @Article{McAllister:2005:ACE, author = "James W. McAllister", title = "Algorithmic compression of empirical data: reply to {Twardy}, {Gardner}, and {Dowe}", journal = j-STUD-HIST-PHILOS-SCI, volume = "36", number = "2", pages = "403--410", month = jun, year = "2005", CODEN = "SHPSB5", DOI = "http://dx.doi.org/10.1016/j.shpsa.2005.04.005", ISSN = "0039-3681 (print), 1879-2510 (electronic)", ISSN-L = "0039-3681", bibdate = "Mon Nov 7 12:11:58 MST 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/shps-a.bib; http://www.sciencedirect.com/science/journal/00393681", note = "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.", URL = "http://www.sciencedirect.com/science/article/pii/S0039368105000221", acknowledgement = ack-nhfb, fjournal = "Studies in History and Philosophy of Science Part A", journal-URL = "http://www.sciencedirect.com/science/journal/00393681", } @Article{McCowan:2005:AUZ, author = "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F. Hanser", title = "The appropriate use of {Zipf}'s law in animal communication studies", journal = j-ANIM-BEHAV, volume = "69", number = "1", pages = "F1--F7", day = "20", month = jan, year = "2005", CODEN = "ANBEA8", DOI = "http://dx.doi.org/10.1016/j.anbehav.2004.09.002", ISSN = "0003-3472 (print), 1095-8282 (electronic)", ISSN-L = "0003-3472", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S000334720400346X", acknowledgement = ack-nhfb, fjournal = "Animal Behaviour", journal-URL = "http://www.sciencedirect.com/science/journal/00033472", keywords = "Zipf's Law", } @Book{McGrayne:2011:TWH, author = "Sharon Bertsch McGrayne", title = "The theory that would not die: how {Bayes}' rule cracked the {Enigma} code, hunted down {Russian} submarines, and emerged triumphant from two centuries of controversy", publisher = pub-YALE, address = pub-YALE:adr, pages = "xiii + 320", year = "2011", ISBN = "0-300-16969-8", ISBN-13 = "978-0-300-16969-0", LCCN = "QA279.5 .M415 2011", bibdate = "Wed May 11 14:42:54 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", abstract = "Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years --- at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany's Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.", acknowledgement = ack-nhfb, remark = "This book has important comments on the battles among Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl Pearson, supplementing the extensive discussion of those conflicts in \cite{Ziliak:2008:CSS}.", subject = "Bayesian statistical decision theory; history; science / history; mathematics / history and philosophy", } @Article{McKee:1980:POR, author = "Arnold F. McKee", title = "The {Pareto} Optimum: Reconcilable with Social Thought?", journal = "International Journal of Social Economics", volume = "7", number = "7", pages = "366--375", month = "????", year = "1980", CODEN = "ISLEBC", DOI = "http://dx.doi.org/10.1108/eb013878", ISSN = "0306-8293 (print), 1758-6712 (electronic)", ISSN-L = "0306-8293", bibdate = "Fri Nov 25 07:01:57 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{McLaughlin:1984:DFI, author = "William I. McLaughlin and Sylvia A. Lundy", title = "Digit Functions of Integer Sequences", journal = j-FIB-QUART, volume = "22", number = "2", pages = "105--115", month = may, year = "1984", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:00:30 MDT 2011", bibsource = "http://www.fq.math.ca/22-2.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @InProceedings{Mebane:2006:DAE, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2006 Annual Meeting of the Midwest Political Science Association, April 20--23, Palmer House, Chicago}", title = "Detecting Attempted Election Theft: Vote Counts, Voting Machines and {Benford's Law}", publisher = "????", address = "????", pages = "i + 50", day = "19", month = apr, year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:14:14 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/mw06.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2006:EFS, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{Election Fraud Conference, Salt Lake City, Utah, September 29--30, 2006}", title = "Election Forensics: The Second-digit {Benford's Law} Test and Recent {American Presidential} Elections", publisher = "????", address = "????", pages = "??--??", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Feb 15 18:22:27 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www-personal.umich.edu/~wmebane/fraud06.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2006:EFV, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2006 Summer Meeting of the Political Methodology Society, UC-Davis, July 20--22, 2006}", title = "Election Forensics: Vote Counts and {Benford's Law}", publisher = "????", address = "????", pages = "ii + 48", day = "18", month = jul, year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:01:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/pm06.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2007:SD, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2007 Summer Meeting of the Political Methodology Society, Pennsylvania State University, July 18--21, 2007}", title = "Statistics for Digits", publisher = "????", address = "????", pages = "1--21", day = "2", month = jul, year = "2007", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:03:01 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/pm07.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InProceedings{Mebane:2008:EFO, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{The American Electoral Process conference, Center for the Study of Democratic Politics, Princeton University, May 1--3, 2008}", title = "Election Forensics: Outlier and Digit Tests in {America} and {Russia}", publisher = "????", address = "????", pages = "i + 26", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:08:23 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/aep2008.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2008:EFS, author = "Walter R. {Mebane, Jr.}", editor = "R. Michael Alvarez and Thad E. Hall and Susan D. Hyde", booktitle = "{The Art and Science of Studying Election Fraud: Detection, Prevention, and Consequences}", title = "Election Forensics: The Second-digit {Benford's Law} Test and Recent {American Presidential} Elections", publisher = "Brookings Institution", address = "Washington, DC, USA", pages = "ii + 30", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:04:22 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Preprint dated 3 November 2006.", URL = "http://www.umich.edu/~wmebane/fraud06.pdf", acknowledgement = ack-nhfb, remark = "An earlier version of this paper was presented at the Election Fraud Conference, Salt Lake City, Utah, September 29--30, 2006.", } @InProceedings{Mebane:2010:EFS, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2010 Summer Meeting of the Political Methodology Society, University of Iowa, July 22--24, 2010}", title = "Election Fraud or Strategic Voting? {Can} Second-digit Tests Tell the Difference?", publisher = "????", address = "????", pages = "1--49", year = "2010", ISBN = "????", ISBN-13 = "????", bibdate = "Sat Feb 16 11:56:47 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/pm10.pdf", acknowledgement = ack-nhfb, } @Article{Mebane:2010:FPE, author = "Walter R. {Mebane, Jr.}", title = "Fraud in the 2009 presidential election in {Iran}?", journal = j-CHANCE, volume = "23", number = "1", pages = "6--15", month = mar, year = "2010", CODEN = "CNDCE4", DOI = "http://dx.doi.org/10.1007/s00144-010-0003-4", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Mon Feb 18 17:50:18 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.springerlink.com/content/0337v415563q0753/abstract/", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/", xxnote = "Publisher archive at \path=http://amstat.tandfonline.com/loi/ucha20= is missing volumes 18 (2005)--24 (2011). Those volumes are available at \path=http://link.springer.com/journal/144=", } @TechReport{Mebane:2010:MSD, author = "Walter R. {Mebane, Jr.}", title = "Memo on second-digit tests done on precinct counts for {Democratic Senate} primary in {South Carolina}, 2010", type = "Report", institution = "University of Michigan", address = "Ann Arbor, MI, USA", day = "12", month = jun, year = "2010", bibdate = "Sat Feb 16 12:06:16 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf", acknowledgement = ack-nhfb, } @Article{Mebane:2011:CBL, author = "Walter R. {Mebane, Jr.}", title = "Comment on {Benford's Law} and the Detection of Election Fraud", journal = j-POLIT-ANAL, volume = "19", number = "3", pages = "269--272", day = "18", month = "Summer", year = "2011", CODEN = "????", DOI = "http://dx.doi.org/10.1093/pan/mpr024", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Fri Nov 25 11:00:46 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Deckert:2011:BLD}.", URL = "http://pan.oxfordjournals.org/content/19/3/269.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", } @Article{Mellor:2006:GKZ, author = "Andy Mellor", title = "Book Review: {G. K. Zipf, \booktitle The Psycho-biology of Language (1935) MIT Press, Cambridge, MA}", journal = j-SYSTEM, volume = "34", number = "3", pages = "455--457", day = "20", month = sep, year = "2006", CODEN = "????", DOI = "http://dx.doi.org/10.1016/j.system.2006.07.004", ISSN = "0346-251X (print), 1879-3282 (electronic)", ISSN-L = "0346-251X", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0346251X06000674", acknowledgement = ack-nhfb, fjournal = "System", journal-URL = "http://www.sciencedirect.com/science/journal/0346251X", keywords = "Zipf's Law", } @Article{Mercik:1999:SAI, author = "Szymon Mercik and Karina Weron and Zuzanna Siwy", title = "Statistical analysis of ionic current fluctuations in membrane channels", journal = j-PHYS-REV-E, volume = "60", number = "6", pages = "7343--7348", day = "1", month = dec, year = "1999", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.60.7343", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.7343", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Metwally:2006:IES, author = "Ahmed Metwally and Divyakant Agrawal and Amr {El Abbadi}", title = "An integrated efficient solution for computing frequent and top-$k$ elements in data streams", journal = j-TODS, volume = "31", number = "3", pages = "1095--1133", month = sep, year = "2006", CODEN = "ATDSD3", DOI = "http://doi.acm.org/10.1145/1166074.1166084", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", bibdate = "Tue Oct 17 05:41:01 MDT 2006", bibsource = "http://www.acm.org/pubs/contents/journals/tods/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See comments in \cite{Liu:2010:CIE}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Database Systems", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", } @Article{Michel:2011:QAC, author = "Jean-Baptiste Michel and Yuan Kui Shen and Aviva Presser Aiden and Adrian Veres and Matthew K. Gray and {The Google Books Team} and Joseph P. Pickett and Dale Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant and Steven Pinker and Martin A. Nowak and Erez Lieberman Aiden", title = "Quantitative Analysis of Culture Using Millions of Digitized Books", journal = j-SCIENCE, volume = "331", number = "6014", pages = "176--182", day = "14", month = jan, year = "2011", CODEN = "SCIEAS", DOI = "http://dx.doi.org/10.1126/science.1199644", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Fri Dec 09 11:06:28 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/331/6014/176.abstract", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "Zipf's law", remark = "This papers reports results from a large study of cultural phenomena, fame, and word usage from 4\% of all books ever printed. Among the findings is this quote from the first page: ``we estimated the number of words in the English lexicon as 544,000 in 1900, 597,000 in 1950, and 1,022,000 in 2000. The lexicon is enjoying a period of enormous growth: The addition of $ \approx 8500 $ words/year has increased the size of the language by over 70\% during the past 50 years.'' From page 177: ``Consistent with Zipf's famous law, a large fraction of the words in our lexicon (63\%) were in this lowest-frequency bin. As a result, we estimated that 52\% of the English lexicon --- the majority of the words used in English books --- consists of lexical `dark matter' undocumented in standard references (12).''", } @Article{Miller:1957:SEI, author = "George A. Miller", title = "Some Effects of Intermittent Silence", journal = j-AMER-J-PSYCHOLOGY, volume = "70", number = "2", pages = "311--314", month = jun, year = "1957", CODEN = "AJPCAA", ISSN = "0002-9556 (print), 1939-8298 (electronic)", ISSN-L = "0002-9556", bibdate = "Tue Nov 15 09:40:05 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/1419346", acknowledgement = ack-nhfb, fjournal = "The American Journal of Psychology", keywords = "Zipf's Law", } @TechReport{Miller:2004:STB, author = "Steven J. Miller", title = "Some thoughts on {Benford}'s law", type = "Preprint", institution = "Williams College", address = "Williamstown, MA 01267 USA", year = "2004", bibdate = "Sat Feb 16 18:43:46 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf", acknowledgement = ack-nhfb, remark = "URL not found on 17 February 2013; perhaps in ReCALL 2004 proceedings", } @Article{Miller:2005:BLV, author = "S. J. Miller and A. Kontorovich", title = "{Benford}'s law, values of {$L$}-functions and the $ 3 x + 1 $ problem", journal = j-ACTA-ARITHMETICA, volume = "120", number = "3", pages = "269--297", month = "????", year = "2005", CODEN = "AARIA9", DOI = "http://dx.doi.org/10.4064/aa120-3-4", ISSN = "0065-1036 (print), 1730-6264 (electronic)", ISSN-L = "0065-1036", MRclass = "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65, 46F12)", bibdate = "Tue Feb 26 06:11:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Acta Arithmetica", } @Book{Miller:2006:IMN, author = "Steven J. Miller and Ramin Takloo-Bighash", title = "An Invitation to Modern Number Theory", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xx + 503", year = "2006", ISBN = "0-691-12060-9 (hardcover)", ISBN-13 = "978-0-691-12060-7 (hardcover)", LCCN = "QA241 .M5344 2006", bibdate = "Fri Mar 22 08:57:57 MDT 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Number theory", tableofcontents = "Part 1. Basic Number Theory \\ 1. Mod p Arithmetic, Group Theory and Cryptography \\ 2. Arithmetic Functions \\ 3. Zeta and L-Functions \\ 4. Solutions to Diophantine Equations \\ Part 2. Continued Fractions and Approximations \\ 5. Algebraic and Transcendental Numbers \\ 6. The Proof of Roth's Theorem \\ 7. Introduction to Continued Fractions \\ Part 3. Probabilistic Methods and Equidistribution \\ 8. Introduction to Probability \\ 9. Applications of Probability: Benford's Law and Hypothesis Testing \\ 10. Distribution of Digits of Continued Fractions \\ 11. Introduction to Fourier Analysis \\ 12. f n k g and Poissonian Behavior \\ Part 4. The Circle Method \\ 13. Introduction to the Circle Method \\ 14. Circle Method: Heuristics for Germain Primes \\ Part 5. Random Matrix Theory and L-Functions \\ 15. From Nuclear Physics to L-Functions \\ 16. Random Matrix Theory: Eigenvalue Densities \\ 17. Random Matrix Theory: Spacings between Adjacent Eigenvalues \\ 18. The Explicit Formula and Density Conjectures \\ Appendix A. Analysis Review \\ Appendix B. Linear Algebra Review \\ Appendix C. Hints and Remarks on the Exercises \\ Appendix D. Concluding Remarks", } @Article{Miller:2006:MCL, author = "S. J. Miller and M. J. Nigrini", title = "The {Modulo 1 Central Limit Theorem} and {Benford's Law} for Products", journal = "International Journal of Algebra", volume = "3", number = "3", pages = "119--130", month = jul, year = "2006", CODEN = "????", ISSN = "1312-8868", ISSN-L = "1312-8868", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006math......7686M; http://arxiv.org/abs/math/0607686", abstract = "We derive a necessary and sufficient condition for the sum of $M$ independent continuous random variables modulo $1$ to converge to the uniform distribution in $ L^1 ([0, 1]) $, and discuss generalizations to discrete random variables. A consequence is that if $ X_1, \ldots {}, X_M $ are independent continuous random variables with densities $ f_1, \ldots {}, f_M $, for any base $B$ as $ M \to \infty $ for many choices of the densities the distribution of the digits of $ X_1 * \cdots {} * X_M $ converges to Benford's law base $B$. The rate of convergence can be quantified in terms of the Fourier coefficients of the densities, and provides an explanation for the prevalence of Benford behavior in many diverse systems.", acknowledgement = ack-nhfb, eprint = "arXiv:math/0607686", keywords = "Mathematics - Probability, Mathematics - Classical Analysis and ODEs, 60F05, 60F25, 11K06 (Primary), 42A10, 42A61, 62E15 (Secondary)", } @Article{Miller:2006:OSB, author = "S. J. Miller and M. J. Nigrini", title = "Order Statistics and {Benford's Law}", journal = "ArXiv Mathematics e-prints", month = jan, year = "2006", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006math......1344M", acknowledgement = ack-nhfb, eprint = "arXiv:math/0601344", keywords = "Mathematics - Probability, Mathematics - Number Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16 (Secondary)", } @Article{Miller:2008:MCL, author = "Steven J. Miller and Mark J. Nigrini", title = "The modulo $1$ central limit theorem and {Benford}'s law for products", journal = "International Journal of Algebra", volume = "2", number = "1--4", pages = "119--130", year = "2008", CODEN = "????", ISSN = "1312-8868", ISSN-L = "1312-8868", MRclass = "60F05 (11K06 42A10)", MRnumber = "2417189 (2009e:60053)", MRreviewer = "Gutti J. Babu", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Int. J. Algebra", fjournal = "International Journal of Algebra", } @Article{Miller:2008:OSB, author = "Steven J. Miller and Mark J. Nigrini", title = "Order statistics and {Benford}'s law", journal = j-INT-J-MATH-MATH-SCI, year = "2008", CODEN = "????", ISSN = "0161-1712", ISSN-L = "0161-1712", MRclass = "62G30 (62E10)", MRnumber = "2461421 (2010c:62168)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Article ID 382948.", URL = "http://arxiv.org/abs/math/0601344", abstract = "Fix a base $B$ and let zeta have the standard exponential distribution; the distribution of digits of zeta base $B$ is known to be very close to Benford's Law. If there exists a $C$ such that the distribution of digits of $C$ times the elements of some set is the same as that of zeta, we say that set exhibits shifted exponential behavior base $B$ (with a shift of $ \log_B C \bmod 1 $ ). Let $ X_1, \ldots {}, X_N $ be independent identically distributed random variables. If the $ X_i $'s are drawn from the uniform distribution on $ [0, L] $, then as $ N \to \infty $ the distribution of the digits of the differences between adjacent order statistics converges to shifted exponential behavior (with a shift of $ \log_B L / N \bmod 1 $ ). By differentiating the cumulative distribution function of the logarithms modulo 1, applying Poisson Summation and then integrating the resulting expression, we derive rapidly converging explicit formulas measuring the deviations from Benford's Law. Fix a delta in $ (0, 1) $ and choose $N$ independent random variables from any compactly supported distribution with uniformly bounded first and second derivatives and a second order Taylor series expansion at each point. The distribution of digits of any $ N^\delta $ consecutive differences {\em and\/} all $ N - 1 $ normalized differences of the order statistics exhibit shifted exponential behavior. We derive conditions on the probability density which determine whether or not the distribution of the digits of all the un-normalized differences converges to Benford's Law, shifted exponential behavior, or oscillates between the two, and show that the Pareto distribution leads to oscillating behavior.", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", pagecount = "19", } @Article{Mir:2011:LLD, author = "Tariq Ahmad Mir", title = "Law of the leading digits and the ideological struggle for numbers", journal = "ArXiv e-prints", pages = "11", year = "2011", bibdate = "Mon Nov 21 07:02:48 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1104.3948", abstract = "Benford's law states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger ones. We investigate here numerical data on the country-wise adherent distribution of seven major world religions i.e., Christianity, Islam, Buddhism, Hinduism, Sikhism, Judaism and Baha'ism to see if the proportion of the leading digits occurring in the distribution conforms to Benford's law. We find that the adherent data of all the religions, except Christianity, excellently does conform to Benford's law. Furthermore, unlike the adherent data on Christianity, the significant digit distribution of the three major Christian denominations i.e. Catholicism, Protestantism and Orthodoxy obeys the law. Thus in spite of their complexity general laws can be established for the evolution of the religious groups.", acknowledgement = ack-nhfb, } @Article{Mir:2012:LDD, author = "T. A. Mir", title = "The leading digit distribution of the worldwide illicit financial flows", journal = "ArXiv e-prints", year = "2012", bibdate = "Tue Feb 19 06:07:33 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1201.3432", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Mir:2012:LLD, author = "Tariq Ahmad Mir", title = "The law of the leading digits and the world religions", journal = j-PHYSICA-A, volume = "391", number = "3", pages = "792--798", day = "1", month = feb, year = "2012", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2011.09.001", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Mon Nov 21 07:04:12 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0378437111007175", acknowledgement = ack-nhfb, fjournal = "Physica A: Statistical Mechanics and its Applications", } @Article{Mitchell:2008:TST, author = "James G. Mitchell and Laurent Seuront", title = "Towards a seascape topology {II}: {Zipf} analysis of one-dimensional patterns", journal = j-J-MAR-SYST, volume = "69", number = "3--4", pages = "328--338", month = feb, year = "2008", CODEN = "JMASE5", DOI = "http://dx.doi.org/10.1016/j.jmarsys.2006.03.026", ISSN = "0924-7963 (print), 1879-1573 (electronic)", ISSN-L = "0924-7963", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000632", acknowledgement = ack-nhfb, fjournal = "Journal of Marine Systems", keywords = "Zipf's Law", } @Article{Mitzenmacher:2003:BHG, author = "Michael Mitzenmacher", title = "A Brief History of Generative Models for Power Law and Lognormal Distributions", journal = j-INTERNET-MATH, volume = "1", number = "2", pages = "226--251", month = dec, year = "2003", CODEN = "????", DOI = "http://dx.doi.org/10.1080/15427951.2004.10129088", ISSN = "1542-7951 (print), 1944-9488 (electronic)", ISSN-L = "1542-7951", bibdate = "Thu Nov 24 13:38:13 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.im/1089229510; http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf; http://www.tandfonline.com/toc/uinm20/1/2", acknowledgement = ack-nhfb, ajournal = "Internet Math.", fjournal = "Internet Mathematics", keywords = "Fibonacci sequence; lognormal distribution; monkeys typing randomly; Pareto distribution; power-law distribution; Yule distribution; Zipf's Law", remark = "This is a survey article with a six-page bibliography of earlier work, and a clear description of the differences between lognormal and power-law distributions, which otherwise look similar on log-log plots. Lognormal distributions have finite means and moments, while power-law distributions may have infinite means and/or moments, depending on the exponent. The preprint at author's Web site (last URL) contains additional material on the acrimonious debate between Beno{\^\i}t Mandelbrot and Herbert A. Simon (see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and other references in Mitzenmacher's paper) on the derivation and modeling of Zipf's Law distributions.", } @Article{Mizuno:2008:PLE, author = "Takayuki Mizuno and Masahiro Toriyama and Takao Terano and Misako Takayasu", title = "{Pareto} law of the expenditure of a person in convenience stores", journal = j-PHYSICA-A, volume = "387", number = "15", pages = "3931--3935", year = "2008", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/j.physa.2008.01.059", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B82", MRnumber = "2586890", bibdate = "Mon Feb 18 17:05:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", } @Article{Mochty:2002:AMI, author = "L. Mochty", title = "{Die Aufdeckung von Manipulationen im Rechnungswesen --- Was leistet das Benford's Law?}. ({German}) [{The} disclosure of accounting manipulations --- what does {Benford's Law} mean?]", journal = "Die Wirtschaftspr{\"u}fung", volume = "14", number = "??", pages = "725--736", month = "????", year = "2002", CODEN = "????", ISSN = "0043-6313", ISSN-L = "0043-6313", bibdate = "Thu Nov 17 19:20:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Mohanty:1979:MMQ, author = "Siba N. Mohanty", title = "Models and Measurements for Quality Assessment of Software", journal = j-COMP-SURV, volume = "11", number = "3", pages = "251--275", month = sep, year = "1979", CODEN = "CMSVAN", DOI = "http://doi.acm.org/10.1145/356778.356783", ISSN = "0010-4892", ISSN-L = "0360-0300", bibdate = "Thu Jun 19 09:25:12 MDT 2008", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib; http://www.acm.org/pubs/contents/journals/surveys/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.", acknowledgement = ack-nhfb, annote = "Several software quality assessment methods which span the software life cycle are discussed. The quality of a system design can be estimated by measuring the system entropy function or the system work function. The quality improvement due to reconfiguration can be determined by calculating system entropy loading measures. Software science and Zipf's law are shown to be useful for estimating program length and implementation time.", country = "USA", date = "11/10/79", descriptors = "Software; design; software engineering; reliability; measurement; model; fundamentals in statistics; performance evaluation;", enum = "2189", fjournal = "ACM Computing Surveys", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204", references = "65", } @Article{Mohanty:1980:SFW, author = "Siba Mohanty", title = "Surveyor's Forum: {Working} on Interpretations", journal = j-COMP-SURV, volume = "12", number = "2", pages = "256--256", month = jun, year = "1980", CODEN = "CMSVAN", DOI = "http://doi.acm.org/10.1145/356810.356818", ISSN = "0010-4892", ISSN-L = "0360-0300", bibdate = "Thu Jun 19 09:27:10 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/surveys/; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.", acknowledgement = ack-nhfb, fjournal = "ACM Computing Surveys", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204", } @Article{Molchanov:2004:BEL, author = "Stanislav Molchanov and Xian Wang", title = "On the {Benford}'s empirical law", journal = "Random Oper. Stochastic Equations", volume = "12", number = "3", pages = "201--210", year = "2004", CODEN = "????", DOI = "http://dx.doi.org/10.1163/1569397042222495", ISSN = "0926-6364 (print), 1569-397X (electronic)", ISSN-L = "0926-6364", MRclass = "11K16 (11B39 60B15)", MRnumber = "2084074 (2005h:11162)", MRreviewer = "A. N. Philippou", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Random Operators and Stochastic Equations", } @TechReport{Moller:2009:MQA, author = "M. M{\"o}ller", title = "Measuring the Quality of Auditing Services with the Help of {Benford's Law} -- An Empirical Analysis and Discussion of this Methodical Approach", type = "Report", number = "??", institution = "Institute for Accounting and Control, University of Z{\"u}rich", address = "Z{\"u}rich, Switzerland", pages = "25", day = "24", month = apr, year = "2009", bibdate = "Tue Nov 22 20:40:12 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ssrn.com/abstract=1529307", abstract = "The so-called Benford's Law describes regularity in the distribution of digits of randomly selected numbers, which states that the relative frequency of the leading digits reduces in a systematic manner from the digit 1 to the digit 9. This distribution hypothesis is being discussed in recent times as an audit instrument in order to gain insights into possible conscious and inadvertent errors in data records. The present paper analyses the closing accounts of 1,373 annual financial statements of companies listed on the German DAX and compares these with the Benford's distribution hypothesis. It can be seen in the process that data pertaining to financial accounts, which have not been audited by the so-called ``Big 4'' audit firms, but by smaller external auditors, deviate to a significant extent from the regularity of Benford's Law, which appears to make the use of Benford's Law suitable as a benchmark to assess the quality of the audit.", acknowledgement = ack-nhfb, } @Article{Montemurro:2001:BZM, author = "Marcelo A. Montemurro", title = "Beyond the {Zipf--Mandelbrot} law in quantitative linguistics", journal = j-PHYSICA-A, volume = "300", number = "3--4", pages = "567--578", day = "15", month = nov, year = "2001", CODEN = "PHYADX", DOI = "http://dx.doi.org/10.1016/S0378-4371(01)00355-7", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437101003557", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", keywords = "Zipf's Law", } @Article{Montroll:1983:NOD, author = "Elliott W. Montroll and Michael F. Shlesinger", title = "On $ 1 / f $ noise and other distributions with long tails", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "79", number = "10", pages = "3380--3383", day = "15", month = may, year = "1983", CODEN = "PNASA6", DOI = "http://dx.doi.org/10.1073/pnas.79.10.3380", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Thu Feb 28 11:03:24 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.pnas.org/content/79/10/3380.abstract", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/search", keywords = "power law; scale invariance; Zipf's law", } @Book{Moon:1936:SBI, author = "Parry Moon", title = "The Scientific Basis of Illuminating Engineering", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xi + 608", year = "1936", LCCN = "TH7703 .M65", bibdate = "Mon Nov 14 10:11:54 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", remark = "See pages 420ff.", } @Article{Moret:2006:NBL, author = "M. A. Moret and V. de Senna and M. G. Pereira and G. F. Zebende", title = "{Newcomb--Benford} Law in Astrophysical Sources", journal = j-INT-J-MOD-PHYS-C, volume = "17", number = "11", pages = "1597--1604", month = "????", year = "2006", CODEN = "IJMPEO", ISSN = "0129-1831 (print), 1793-6586 (electronic)", ISSN-L = "0129-1831", bibdate = "Mon Nov 14 17:37:59 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M", acknowledgement = ack-nhfb, fjournal = "International Journal of Modern Physics C [Physics and Computers]", journal-URL = "http://www.worldscientific.com/loi/ijmpc", } @Article{Moret:2009:GSA, author = "M. A. Moret and V. de Senna and M. C. Santana and G. F. Zebende", title = "Geometric Structural Aspects of Proteins and {Newcomb--Benford Law}", journal = j-INT-J-MOD-PHYS-C, volume = "20", number = "12", pages = "1981--1988", month = "????", year = "2009", CODEN = "IJMPEO", DOI = "http://dx.doi.org/10.1142/S0129183109014874", ISSN = "0129-1831 (print), 1793-6586 (electronic)", ISSN-L = "0129-1831", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M", acknowledgement = ack-nhfb, fjournal = "International Journal of Modern Physics C [Physics and Computers]", journal-URL = "http://www.worldscientific.com/loi/ijmpc", keywords = "Hydrophobicity, protein packing, complex systems, Time series analysis, Systems obeying scaling laws, Binary and multiple stars", } @Article{Morrison:2010:MG, author = "Kent E. Morrison", title = "The Multiplication Game", journal = j-MATH-MAG, volume = "83", number = "??", pages = "100--110", month = apr, year = "2010", CODEN = "MAMGA8", DOI = "????", ISSN = "0025-570X", ISSN-L = "0025-570X", bibdate = "Mon Feb 18 17:51:50 2013", bibsource = "http://www.maa.org/pubs/mag_apr10_toc.html; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics Magazine", journal-URL = "http://www.maa.org/pubs/mathmag.html", } @TechReport{Morrow:2006:BLF, author = "John Morrow", title = "{Benford's Law}, Families of Distributions and a Test Basis", type = "Report", institution = "University of Wisconsin--Madison", address = "Madison, WI, USA", month = "????", year = "2006", bibdate = "Tue Nov 22 20:44:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Revised draft of 9 October 2010.", URL = "http://www.johnmorrow.info/projects/benford/benfordMain.pdf", acknowledgement = ack-nhfb, lastaccess = "22 November 2011", } @PhdThesis{Morters:2001:BGV, author = "Peter M{\"o}rters", title = "{Benford's Gesetz {\"u}ber die Verteilung der Ziffern}. (German) [{Benford}'s law on the distribution of digits]", type = "{Habilitationsvorlesung}", school = "????", address = "Kaiserslauten, Germany, and Bath, UK", pages = "4", month = "????", year = "2001", bibdate = "Sat Feb 16 18:47:15 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://people.bath.ac.uk/maspm/benford.ps", acknowledgement = ack-nhfb, language = "German", } @Article{Mosimann:1995:DFC, author = "James E. Mosimann and Claire V. Wiseman and Ruth E. Edelman", title = "Data Fabrication: Can People Generate Random Digits?", journal = j-ACCOUNT-RES, volume = "4", number = "1", pages = "31--55", month = "????", year = "1995", CODEN = "ARQAEZ", ISSN = "0898-9621 (print), 1545-5815 (electronic)", ISSN-L = "0898-9621", bibdate = "Sat Dec 10 11:56:38 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866", acknowledgement = ack-nhfb, fjournal = "Accountability in Research", keywords = "Benford's Law", remark = "The abstract ends with: ``The difficulty that people have in creating random error digits supports the utility of examining such digits in investigations of scientific misconduct.''", } @Article{Mosteller:1967:DSR, author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn", title = "The Distribution of Sums of Rounded Percentages", journal = j-DEMOGRAPHY, volume = "4", number = "2", pages = "850--858", month = jun, year = "1967", CODEN = "????", ISSN = "0070-3370 (print), 1533-7790 (electronic)", ISSN-L = "0070-3370", bibdate = "Thu Nov 24 08:03:16 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "See \cite{Diaconis:1979:RP} for further work.", URL = "http://muse.jhu.edu/journals/dem/; http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html; http://www.jstor.org/stable/2060324", abstract = "When percentages are computed for counts in several categories or for several positive measurements0 each taken as a fraction of their sum, the rounded percentages often fail to add to 100 percent. We investigate how frequently this failure occurs and what the distributions of sums of rounded percentages are for (1) an empirical set of data, (2) the multinomial distribution in small samples, (3) spacings between points dropped on an interval --- the broken-stick model; and (4) for simulation for several categories. The several methods produce similar distributions.We find that the probability that the sum of rounded percentages adds to exactly 100 percent is certain for two categories, about three-fourths for three categories, about two-thirds for four categories, and about [Formula: see text] for larger numbers of categories, c, on the average when categories are not improbable.", acknowledgement = ack-nhfb, fjournal = "Demography", pubmedid = "21318695", } @Article{Moura:2006:ZLB, author = "Newton J. Moura Jr. and Marcelo B. Ribeiro", title = "{Zipf} law for {Brazilian} cities", journal = j-J-THEOR-BIOL, volume = "219", number = "4", pages = "441--448", day = "15", month = jul, year = "2006", CODEN = "JTBIAP", DOI = "http://dx.doi.org/10.1016/j.physa.2005.11.038", ISSN = "0022-5193 (print), 1095-8541 (electronic)", ISSN-L = "0022-5193", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437105012422", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Biology", journal-URL = "http://www.sciencedirect.com/science/journal/00225193", keywords = "Zipf's Law", } @PhdThesis{Muller:2003:AZP, author = "Mathias M{\"u}ller", title = "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}. ({German}) [Applications of the digit analysis in the audit practice with a focus on {Benford's Law}]", type = "{Diplomarbeit}", school = "Wirtschaftsuniversit{\"a}t Wien", address = "Wien, Austria", pages = "v + 75", month = "????", year = "2003", bibdate = "Sat Feb 16 18:44:50 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://permalink.obvsg.at/wuw/AC03895842", acknowledgement = ack-nhfb, language = "German", } @Article{Muller:2011:HAS, author = "Hans Christian M{\"u}ller", title = "How an arcane statistical law could have prevented the {Greek} disaster", journal = "Economics Intelligence", volume = "??", number = "??", pages = "??", day = "28", month = jul, year = "2011", CODEN = "????", ISSN = "????", bibdate = "Sun Nov 20 10:04:08 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/", abstract = "If we had known what we know today, Greece would not have been able to enter the Euro area. The macroeconomic data the country reported to Eurostat in Luxembourg were heavily tweaked. Unfortunately, however, this only became clear years after it was too late.", acknowledgement = ack-nhfb, } @Article{Murphy:1973:LLH, author = "Larry J. Murphy", title = "{Lotka's Law} in the Humanities?", journal = j-J-AM-SOC-INF-SCI, volume = "24", number = "6", pages = "461--462", month = nov # "\slash " # dec, year = "1973", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/asi.4630240607", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 08:09:40 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", } @Article{Nabeshima:2004:ZLP, author = "Terutaka Nabeshima and Yukio-Pegio Gunji", title = "{Zipf}'s law in phonograms and {Weibull} distribution in ideograms: comparison of {English} with {Japanese}", journal = j-BIOSYSTEMS, volume = "73", number = "2", pages = "131--139", day = "20", month = feb, year = "2004", CODEN = "BSYMBO", DOI = "http://dx.doi.org/10.1016/j.biosystems.2003.11.002", ISSN = "0303-2647 (print), 1872-8324 (electronic)", ISSN-L = "0303-2647", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0303264703002260", acknowledgement = ack-nhfb, fjournal = "Biosystems (A6E)", keywords = "Zipf's Law", } @Article{Nadarajah:2007:CPG, author = "Saralees Nadarajah and Samuel Kotz", title = "On the convolution of {Pareto} and gamma distributions", journal = j-COMP-NET-AMSTERDAM, volume = "51", number = "12", pages = "3650--3654", day = "22", month = aug, year = "2007", CODEN = "????", ISSN = "1389-1286 (print), 1872-7069 (electronic)", ISSN-L = "1389-1286", bibdate = "Sat Apr 2 08:42:20 MDT 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/13891286", acknowledgement = ack-nhfb, fjournal = "Computer Networks", journal-URL = "http://www.sciencedirect.com/science/journal/13891286", } @Article{Nagasaka:1984:BL, author = "Kenji Nagasaka", title = "On {Benford}'s law", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "36", number = "2", pages = "337--352", year = "1984", CODEN = "AISXAD", DOI = "http://dx.doi.org/10.1007/BF02481974", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", MRclass = "60F99 (11K06 11K36 62E99)", MRnumber = "758506 (86a:60052)", MRreviewer = "L. Kuipers", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Ann. Inst. Statist. Math.", fjournal = "Annals of the Institute of Statistical Mathematics (Tokyo)", } @Article{Nagasaka:1987:BLL, author = "Kenji Nagasaka and Jau-Shyong Shiue", title = "{Benford}'s law for linear recurrence sequences", journal = "Tsukuba J. Math.", volume = "11", number = "2", pages = "341--351", year = "1987", CODEN = "????", ISSN = "0387-4982", ISSN-L = "0387-4982", MRclass = "60E99 (11B37)", MRnumber = "926460 (88m:60047)", MRreviewer = "L. Kuipers", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Tsukuba Journal of Mathematics", } @InCollection{Nagasaka:1990:BLL, author = "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong Shiue", booktitle = "Number theory, {Vol}.\ {I} ({Budapest}, 1987)", title = "{Benford}'s law: the logarithmic law of first digit", volume = "51", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "361--391", year = "1990", MRclass = "11K06", MRnumber = "1058225 (92b:11048)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Colloq. Math. Soc. J{\'a}nos Bolyai", acknowledgement = ack-nhfb, } @InProceedings{Nagasaka:2005:BLD, author = "Kenji Nagasaka", editor = "G. Barat and H. Daud{\'e} and M. Laurent and P. Liardet and S. Louboutin and A. Thomas", booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July 4--8, 2005, Universit{\'e} de Provence and Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS Marseilles, France}", title = "{Benford}'s law with different basis", publisher = "????", address = "????", pages = "1--2", year = "2005", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 18:49:26 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://atlas-conferences.com/c/a/r/e/47.htm", acknowledgement = ack-nhfb, } @Article{Naldi:2003:CIZ, author = "M. Naldi", title = "Concentration indices and {Zipf}'s law", journal = j-ECONOM-LETT, volume = "78", number = "3", pages = "329--334", month = mar, year = "2003", CODEN = "ECLEDS", DOI = "http://dx.doi.org/10.1016/S0165-1765(02)00251-3", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", MRclass = "91B82", MRnumber = "1959355", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176502002513", acknowledgement = ack-nhfb, fjournal = "Economics Letters", keywords = "Zipf's Law", } @Article{Nebel:2012:DHG, author = "J.-C. Nebel and S. Pezzulli", title = "Distribution of Human Genes Observes {Zipf's Law}", journal = "Kingston University Research \& Innovation Reports (KURIR)", volume = "8", number = "??", pages = "1--9", month = "????", year = "2012", DOI = "????", ISSN = "1749-5652", ISSN-L = "1749-5652", bibdate = "Tue Feb 19 06:09:05 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://staffnet.kingston.ac.uk/~ku33185/Papers/PDFformat/Kurir12.pdf", acknowledgement = ack-nhfb, journal-URL = "http://kurir.kingston.ac.uk/", remark = "Kingston University, London, UK. Year 2012 volume is not yet online on 19 February 2013.", } @Book{Newbold:2010:SBE, author = "Paul Newbold and William L. Carlson and Betty Thorne", title = "Statistics for Business and Economics", publisher = "Pearson", address = "Boston, MA, USA", edition = "Seventh", pages = "986 + 16", year = "2010", ISBN = "0-13-507248-4", ISBN-13 = "978-0-13-507248-6", LCCN = "QA276.18 .N49 2010", bibdate = "Fri Mar 22 09:03:48 MDT 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @Book{Newbold:2013:SBE, author = "Paul Newbold and William L. (William Lee) Carlson and Betty Thorne", title = "Statistics for Business and Economics", publisher = "Pearson Education", address = "Harlow, Essex, UK", edition = "Eighth", pages = "792", year = "2013", ISBN = "0-273-76706-2", ISBN-13 = "978-0-273-76706-0", LCCN = "HF1017 .N48 2013", bibdate = "Fri Mar 22 09:03:53 MDT 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Commercial statistics; Economics; Statistical methods; Statistics", } @Article{Newcomb:1881:NFU, author = "Simon Newcomb", title = "Note on the frequency of use of the different digits in natural numbers", journal = j-AM-J-MATH, volume = "4", number = "1--4", pages = "39--40", year = "1881", CODEN = "AJMAAN", ISSN = "0002-9327 (print), 1080-6377 (electronic)", ISSN-L = "0002-9327", bibdate = "Thu Feb 15 16:35:24 2007", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.jstor.org/stable/2369148", abstract = "That the ten digits do not occur with equal frequency must be evident to any one making much use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones. The first significant figure is oftener 1 than any other digit, and the frequency diminishes up to 9.", acknowledgement = ack-nhfb, author-dates = "March 12, 1835--July 11, 1909", fjournal = "American Journal of Mathematics", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From p. 40: ``The law of probability of the occurrence of numbers is such that all mantissas of their logarithms are equally probable.''. The article contains no references to earlier work.", remark-2 = "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are the earliest citations of Newcomb's work that I have yet found in connection with Benford's Law.", xxURL = "http://en.wikipedia.org/wiki/Simon_Newcomb", } @Article{Newman:1996:ASC, author = "M. E. J. Newman and Kim Sneppen", title = "Avalanches, scaling, and coherent noise", journal = j-PHYS-REV-E, volume = "54", number = "6", pages = "6226--6231", month = dec, year = "1996", CODEN = "PLEEE8", DOI = "http://dx.doi.org/10.1103/PhysRevE.54.6226", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:44:51 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.6226", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Book{Newman:2002:ME, author = "M. E. J. (Mark E. J.) Newman and Richard G. Palmer", title = "Modeling extinction", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xii + 102", year = "2002", ISBN = "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)", ISBN-13 = "978-0-19-515946-2 (paperback), 978-0-19-515945-5 (hardcover)", LCCN = "QH78 .N48 2002", bibdate = "Thu Feb 28 10:36:25 MST 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; library.ox.ac.uk:210/ADVANCE", series = "Santa Fe Institute studies in the sciences of complexity", acknowledgement = ack-nhfb, keywords = "power law; Zipf's law", subject = "Extinction (Biology); Statistical methods; Mathematical models", } @Article{Newman:2005:PLP, author = "M. E. J. Newman", title = "Power laws, {Pareto} distributions and {Zipf}'s law", journal = j-CONTEMP-PHYS, volume = "46", number = "5", pages = "323--351", month = sep, year = "2005", CODEN = "CTPHAF", DOI = "http://dx.doi.org/10.1080/00107510500052444", ISSN = "0010-7514 (print), 1366-5812 (electronic)", ISSN-L = "0010-7514", bibdate = "Fri Jul 09 16:33:18 2010", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.", acknowledgement = ack-nhfb, fjournal = "Contemporary physics", keywords = "Benford's Law; critical phenomena; Legendre beta function; Pareto distribution; percolation; phase transitions; power-law distributions; random walks; Riemann zeta function; scale-free distributions; Yule process; Zipf's Law", remark = "This article is an excellent survey of continuous and discrete distributions that follow a power law, and some that do not. It is well worth reading.", subject = "astrophysics; atomic and nuclear physics; chemical physics; computational physics; condensed matter physics; environmental physics; experimental physics; general physics; particle and high energy physics; plasma physics; space science; theoretical physics", } @Article{Nguyen:2003:DPL, author = "H. T. Nguyen and V. Kreinovich and L. Longpre", title = "Dirty pages of logarithm tables, lifetime of the universe, and subjective (fuzzy) probabilities on finite and infinite intervals", journal = j-IEEE-TRANS-FUZZY-SYSTEMS, volume = "1", pages = "67--73", year = "2003", CODEN = "IEFSEV", DOI = "http://dx.doi.org/10.1109/FUZZ.2003.1209339", ISSN = "1063-6706 (print), 1941-0034 (electronic)", ISSN-L = "1063-6706", bibdate = "Sat Feb 16 18:51:15 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The 12th IEE International Conference on Fuzzy Systems. FUZZ'03", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Fuzzy Systems", xxnote = "Is this the listed journal, or a conference paper??", } @Article{Nguyen:2004:DPL, author = "Hung T. Nguyen and Vladik Kreinovich and Luc Longpr{\'e}", title = "Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals", journal = j-RELIABLE-COMPUTING, volume = "10", number = "2", pages = "83--106", month = apr, year = "2004", CODEN = "RCOMF8", DOI = "http://dx.doi.org/10.1023/B:REOM.0000015848.19449.12", ISSN = "1385-3139 (print), 1573-1340 (electronic)", ISSN-L = "1385-3139", bibdate = "Mon Feb 6 07:42:05 MST 2012", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2; http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/rc.bib", URL = "http://link.springer.com/article/10.1023/B%3AREOM.0000015848.19449.12/; http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83; http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83-106", acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk, fjournal = "Reliable Computing = Nadezhnye vychisleniia", journal-URL = "http://link.springer.com/journal/11155", } @Article{Ni:2008:BLH, author = "D. Ni and Z. Ren", title = "{Benford}'s law and half-lives of unstable nuclei", journal = j-EUR-PHYS-J-A, volume = "38", pages = "251--255", month = dec, year = "2008", CODEN = "EPJAFV", DOI = "http://dx.doi.org/10.1140/epja/i2008-10680-8", ISSN = "1434-6001 (print), 1434-601X (electronic)", ISSN-L = "1434-6001", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008EPJA...38..251N", acknowledgement = ack-nhfb, fjournal = "European Physical Journal A: Hadrons and Nuclei", journal-URL = "http://www.springerlink.com/content/1434-6001", } @Article{Ni:2009:BLD, author = "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren", title = "{Benford's Law} and $ \beta $-Decay Half-Lives", journal = j-COMM-THEOR-PHYS, volume = "51", number = "4", pages = "713--716", month = apr, year = "2009", CODEN = "CTPHDI", DOI = "http://dx.doi.org/10.1088/0253-6102/51/4/25", ISSN = "0253-6102", ISSN-L = "0253-6102", bibdate = "Sun Nov 13 11:01:52 2011", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N; http://stacks.iop.org/0253-6102/51/i=4/a=25", abstract = "The experimental values of 2059 $ \beta $-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford's law, which states that the frequency of occurrence of each figure, 1--9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford's logarithmic distribution of $ \beta $-decay half-lives can be explained in terms of Newcomb's justification of Benford's law and empirical exponential law of $ \beta $-decay half-lives. Moreover, we test the calculated values of 6721 $ \beta $-decay half-lives with the aid of Benford's law. This indicates that Benford's law is useful for theoretical physicists to test their methods for calculating $ \beta $-decay half-lives.", acknowledgement = ack-nhfb, fjournal = "Communications in theoretical physics", } @Article{Nicholls:1987:EZP, author = "Paul Travis Nicholls", title = "Estimation of {Zipf} parameters", journal = j-J-AM-SOC-INF-SCI, volume = "38", number = "6", pages = "443--445", year = "1987", CODEN = "AISJB6", DOI = "http://dx.doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO;2-E", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", } @Article{Nicolaisen:2007:PPB, author = "Jeppe Nicolaisen and Birger Hj{\o}rland", title = "Practical potentials of {Bradford}'s law: a critical examination of the received view", journal = j-J-DOC, volume = "63", number = "3", pages = "359--377", month =