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Journal Articles Statistics and Probability Letters Year : 2018

On the discrepancy of powers of random variables

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 (Xdnn ) 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

Dates and versions

hal-03611351 , version 1 (17-03-2022)

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Nicolas Chenavier, Dominique Schneider. On the discrepancy of powers of random variables. Statistics and Probability Letters, 2018, 134, pp.5-14. ⟨10.1016/j.spl.2017.10.006⟩. ⟨hal-03611351⟩
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