%0 Journal Article
%T A unifying probabilistic interpretation of Benford's Law
%A Rita Giuliano
%A ¨Ślise Janvresse
%J Uniform Distribution Theory
%D 2010
%I Mathematical Institute of the Slovak Academy of Sciences
%X We propose a probabilistic interpretation of Benford's law, which predicts the probability distribution of all digits in everyday-life numbers. Heuristically, our point of view consists in considering an everyday-life number as a continuous random variable taking value in an interval $[0, A]$, whose maximum $A$ is itself an everyday-life number. This approach can be linked to the characterization of Benford's law by scale-invariance,as well as to the convergence of a product of independent random variables to Benford's law. It also allows to generalize Flehinger's result about the convergence of iterations of Cesaro-averages to Benford's law.
%K BenfordĄŻs law
%K first-digit law
%K mantissa
%K Markov chain
%K exponential speed of con- vergence
%K averaging method
%U http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf