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Jasak, Z (2011)

Benford’s Law and Invariances

Journal of Mathematics and System Science, Volume 1, No.1 (Serial No.1).

ISSN/ISBN: 2159-5291 DOI: Not available at this time.

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Abstract: Benford’s law is logarithmic law for distribution of leading digits formulated by P[D = d] = log(1+1/d) where d is leading digit or group of digits. It's named by Frank Albert Benford (1938) who formulated mathematical model of this probability. Before him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number. The main characteristic properties of this law are base, scale, sum, inverse and product invariance. Base invariance means that logarithmic law is valid for any base. Inverse invariance means that logarithmic law for leading digits holds for inverse values in sample. Multiplication invariance means that if random variable X follows Benford’s law and Y is arbitrary random variable with continuous density then XY follows Benford’s law too. Sum invariance means that sums of significand are the same for any leading digit or group of digits. In this text method of testing sum invariance property is proposed.

@article {, AUTHOR = {Jasak, Zoran}, TITLE = {Benford’s Law and Invariances}, JOURNAL = {Journal of Mathematics and System Science}, YEAR = {2014}, VOLUME = {4}, NUMBER = {7}, PAGES = {457--462}, ISSN = {2159-5291}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Statistics