A characterization of Benford’s law through generalized scale-invariance

Michał Ryszard Wójcik

Mathematical Social Sciences, 2014, vol. 71, issue C, 1-5

Abstract: If X is uniformly distributed modulo 1 and Y is independent of X then Y+X is also uniformly distributed modulo 1. We prove a converse for any continuous random variable Y (or a reasonable approximation to a continuous random variable) so that if X and Y+X are equally distributed modulo 1 and Y is independent of X then X is uniformly distributed modulo 1 (or approximates the uniform distribution equally reasonably). This translates into a characterization of Benford’s law through a generalization of scale-invariance: from multiplication by a constant to multiplication by an independent random variable.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:71:y:2014:i:c:p:1-5

DOI: 10.1016/j.mathsocsci.2014.03.006

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