On the discrepancy of powers of random variables

Nicolas Chenavier (1) , Dominique Schneider (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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

Mots clés: Benford’s law; discrepancy; mantissa

Domaines: Probabilités [math.PR]

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⟩