On the discrepancy of powers of random variables

Nicolas Chenavier and Dominique Schneider

Statistics & Probability Letters, 2018, vol. 134, issue C, 5-14

Abstract: Let (dn) be a sequence of positive numbers and let (Xn) be a sequence of positive independent random variables. We provide an upper bound for the deviation between the distribution of the mantissaes of the first N terms of (Xndn) and the Benford’s law. If dn goes to infinity at a rate at most polynomial, this deviation converges a.s. to 0 as N goes to infinity.

Keywords: Benford’s law; Discrepancy; Mantissa (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2017.10.006

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