Products of random variables and the first digit phenomenon

Products of random variables and the first digit phenomenon

We provide conditions on dependent and on non-stationary random variables Xn ensuring that the mantissa of the sequence of products ∏1nXk is almost surely distributed following Benford’s law or converges in distribution to Benford’s law. This is achieved through proving new generalizations of Lévy’s...

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Veröffentlicht in:Stochastic processes and their applications 2018-05, Vol.128 (5), p.1615-1634
Hauptverfasser: Chenavier, Nicolas, Massé, Bruno, Schneider, Dominique
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Sprache:eng
Schlagworte:
Benford’s law
Density
Mantissa
Mathematics
Probability
Weak convergence
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container_title Stochastic processes and their applications
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creator Chenavier, Nicolas
Massé, Bruno
Schneider, Dominique
description We provide conditions on dependent and on non-stationary random variables Xn ensuring that the mantissa of the sequence of products ∏1nXk is almost surely distributed following Benford’s law or converges in distribution to Benford’s law. This is achieved through proving new generalizations of Lévy’s and Robbins’s results on distribution modulo 1 of sums of independent random variables.
doi_str_mv 10.1016/j.spa.2017.08.003
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source Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
subjects Benford’s law
Density
Mantissa
Mathematics
Probability
Weak convergence
title Products of random variables and the first digit phenomenon
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