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On the non-existence of a general Benford's law

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  • Lolbert, Tamás

Abstract

Benford's law states that in randomly collected numbers certain digits are more often leading digits than others. More formally: the general law states that the mantissae follow the logarithmic distribution in any base. Benford's law was recognized by many mathematicians so that several possible explanations have been derived, but several questions are still open. Applications are widespread, for example an auditing technique (the so-called digital analysis), which is employed around the world by internal revenue services to detect tax fraud, is based on this phenomenon. In this paper it will be shown that there exists no probability measure that would obey Benford's law for any base, but if the set of possible bases does not exceed a given upper limit, most real-life distributions obey, or can be transformed to obey Benford's law.

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  • Lolbert, Tamás, 2008. "On the non-existence of a general Benford's law," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 103-106, March.
    • Handle: RePEc:eee:matsoc:v:55:y:2008:i:2:p:103-106
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    Cited by:

    1. Schräpler Jörg-Peter, 2011. "Benford’s Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(5-6), pages 685-718, October.
    2. Carrera, César, 2015. "Tracking exchange rate management in Latin America," Review of Financial Economics, Elsevier, vol. 25(C), pages 35-41.
    3. Wójcik, Michał Ryszard, 2013. "How fast increasing powers of a continuous random variable converge to Benford’s law," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2688-2692.

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