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 the moments and cumulants of functions in the form Rka,b as defined by Dhaene & Sundt (1994). We deduce a simple relation between the DePril transform and the cumulants of a function. This relation is appplied to some classes of approximations to probability distributions, in particular the approximations of Hipp and DePril.