Products of random variables and the first digit phenomenon

Nicolas Chenavier, Bruno Massé and Dominique Schneider

Stochastic Processes and their Applications, 2018, vol. 128, issue 5, 1615-1634

Abstract: 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.

Keywords: Benford’s law; Density; Mantissa; Weak convergence (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:5:p:1615-1634

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DOI: 10.1016/j.spa.2017.08.003

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