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Grendar, M, Judge, G and Schechter, L (2007)

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

Physica A: Statistical Mechanics and its Applications 380, pp. 429-438.

ISSN/ISBN: 0378-4371 DOI: 10.1016/j.physa.2007.02.062

Abstract: 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.

@article{, title = "An empirical non-parametric likelihood family of data-based Benford-like distributions", journal = "Physica A: Statistical Mechanics and its Applications", volume = "380", pages = "429--438", year = "2007", issn = "0378-4371", doi = "10.1016/j.physa.2007.02.062", url = "", author = "Marian Grendar and George Judge and Laura Schechter", }

Reference Type: Journal Article

Subject Area(s): Statistics