N De Pril

Some results on moments and cumulants

Abstract In the present paper we discuss various results related to moments and cumulants of probability distributions and approximations to probability distributions. As the approximations are not necessarily probability distributions themselves, we shall apply the concept of moments and cumulants to more general functions. Recursions are deduced for moments and cumulants of functions in the form Rk [a, b] as defined by Dhaene & Sundt (1996). We deduce a simple relation between the De Pril transform and the cumulants of a function. This relation is applied to some classes of approximations to probability distributions, in particular the approximations of Hipp and De Pril.

On a class of generalized Γ-convolutions (Part I)

Abstract In this paper a set of sufficient conditions is given in order that a distribution function should be a generalized Γ-convolution. The method mainly consists of a generalization of Thorins result on the Pareto distribution. The main key of our method consists in the use of some rather recent developments of Laplace transforms in the neighbourhood of the origin.