Products of random variables and the first digit phenomenon

Nicolas Chenavier (1) , Bruno Massé (1) , Dominique Schneider (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We provide conditions on dependent and on non-stationary random variables Xn ensuring that the mantissa of the sequence of products (∏n1 Xk) is almost surely distributed following the Benford’s law or converges in distribution to the Benford’s law

Mots clés: Benford’s law; density; mantissa; weak convergence

Domaines: Probabilités [math.PR]

Nicolas Chenavier, Bruno Massé, Dominique Schneider. Products of random variables and the first digit phenomenon. Stochastic Processes and their Applications, 2018, 128 (5), pp.1615-1634. ⟨10.1016/j.spa.2017.08.003⟩. ⟨hal-03611355⟩