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From uniform distributions to Benford's law

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Markov processes

Published online by Cambridge University Press:  14 July 2016

Élise Janvresse  and
Thierry de la Rue
Élise Janvresse*
Affiliation:
CNRS, Université de Rouen
Thierry de la Rue*
Affiliation:
CNRS, Université de Rouen
*
∗ Postal address: Université de Rouen, LMRS, UMR 6085 - CNRS, 76 821 Mont Saint Aignan, France
∗ Postal address: Université de Rouen, LMRS, UMR 6085 - CNRS, 76 821 Mont Saint Aignan, France
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Abstract

We provide a new probabilistic explanation for the appearance of Benford's law in everyday-life numbers, by showing that it arises naturally when we consider mixtures of uniform distributions. Then we connect our result to a result of Flehinger, for which we provide a shorter proof and the speed of convergence.

Keywords

Benford's lawfirst-digit lawmantissauniform distributioncoupling method

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 11K99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1203 - 1210
Copyright
Copyright © Applied Probability Trust 2004 

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