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

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  • Wójcik, Michał Ryszard

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.

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  • Wójcik, Michał Ryszard, 2014. "A characterization of Benford’s law through generalized scale-invariance," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 1-5.
    • Handle: RePEc:eee:matsoc:v:71:y:2014:i:c:p:1-5
    DOI: 10.1016/j.mathsocsci.2014.03.006
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    1. Bernhard Rauch & Max Göttsche & Gernot Brähler & Stefan Engel, 2011. "Fact and Fiction in EU‐Governmental Economic Data," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 243-255, August.
    2. Tam Cho, Wendy K. & Gaines, Brian J., 2007. "Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance," The American Statistician, American Statistical Association, vol. 61, pages 218-223, August.
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