An empirical non-parametric likelihood family of data-based Benford-like distributions
AbstractA mathematical expression known as Benford's law provides an example of an unexpected relationship among randomly selected sequences of first significant digits (FSDs). Newcomb [Note on the frequency of use of the different digits in natural numbers, Am. J. Math. 4 (1881) 39–40], and later Benford [The law of anomalous numbers, Proc. Am. Philos. Soc. 78(4) (1938) 551–572], conjectured that FSDs would exhibit a weakly monotonic decreasing distribution and proposed a frequency proportional to the logarithmic rule. Unfortunately, the Benford FSD function does not hold for a wide range of scale-invariant multiplicative data. To confront this problem we use information-theoretic methods to develop a data-based family of alternative Benford-like exponential distributions that provide null hypotheses for testing purposes. Two data sets are used to illustrate the performance of generalized Benford-like distributions.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 380 (2007)
Issue (Month): C ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
Benford's law; First significant digit phenomenon; Relative frequencies; Information-theoretic method; Empirical likelihood; Minimum-divergence distance measure;
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- Lee, Joanne & Cho, Wendy K. Tam & Judge, George G., 2010. "Stigler's approach to recovering the distribution of first significant digits in natural data sets," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 82-88, January.
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