From Uniform Distributions to Benford's Law

Elise Janvresse (1) , Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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 the theorem of B. J. Flehinger (``On the probability that a random integer has initial digit A", {\em Amer. Math. Monthly}, 73:1056--1061, 1966), for which we provide a shorter proof and a speed of convergence.

Mots clés: Benford's law; first-digit law; mantissa; uniform distribution; coupling method

Domaines: Probabilités [math.PR]

Elise Janvresse, Thierry de La Rue. From Uniform Distributions to Benford's Law. Journal of Applied Probability, 2004, 41, pp.1203-1210. ⟨hal-00373367⟩