Expansions in Appell polynomials of the convolutions of probability distributions

Abstract

We use the composition method to analyse the convolutions of probability distributions by emploing the Appell polynomials and Bergström identity. Our approximation is based on the probability distributions which have the inverse generalized measure of bounded variation. The idea to use the accompanying probability distribution e^λ(F−E),  λ > 0, was first proposed by B.V. Gnedenko [1].