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An empirical non-parametric likelihood family of data-based Benford-like distributions

  • Grendar, Marian
  • Judge, George
  • Schechter, Laura

A 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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Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 380 (2007)
Issue (Month): C ()
Pages: 429-438

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Handle: RePEc:eee:phsmap:v:380:y:2007:i:c:p:429-438
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