Benford’s law: A Poisson perspective

Iddo I. Eliazar

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 16, 3360-3373

Abstract: Benford’s law is a counterintuitive statistical law asserting that the distribution of leading digits, taken from a large ensemble of positive numerical values that range over many orders of scale, is logarithmic rather than uniform (as intuition suggests). In this paper we explore Benford’s law from a Poisson perspective, considering ensembles of positive numerical values governed by Poisson-process statistics. We show that this Poisson setting naturally accommodates Benford’s law and: (i) establish a Poisson characterization and a Poisson multidigit-extension of Benford’s law; (ii) study a system-invariant leading-digit distribution which generalizes Benford’s law, and establish a Poisson characterization and a Poisson multidigit-extension of this distribution; (iii) explore the universal emergence of the system-invariant leading-digit distribution, couple this universal emergence to the universal emergence of the Weibull and Fréchet extreme-value distributions, and distinguish the special role of Benford’s law in this universal emergence; (iv) study the continued-fractions counterpart of the system-invariant leading-digit distribution, and establish a Poisson characterization of this distribution; and (v) unveil the elemental connection between the system-invariant leading-digit distribution and its continued-fractions counterpart. This paper presents a panoramic Poisson approach to Benford’s law, to its system-invariant generalization, and to its continued-fractions counterpart.

Keywords: Power-laws; Invariance; Universality; Extreme-value statistics; Poisson limit theorems; Continued fractions (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:16:p:3360-3373

DOI: 10.1016/j.physa.2013.03.057

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