Bounds for moment generating functions and for extinction probabilities

1 June 1966

journal article
research article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 3 (01) , 171-178
https://doi.org/10.1017/s0021900200114032

Abstract

Suppose that we have a non-negative, real valued random variable x, whose distribution is governed by some unknown moment generating function M(t). Suppose further that we are given certain moments of x, then the question to be discussed in this paper is : can we find a sharp upper bounding function for the m.g.f.? It will be shown that this is usually possible both in the single variate case and in its natural extension to the multivariate case.

Keywords

This publication has 2 references indexed in Scilit:

On inequalities of the Tchebychev type
Mathematical Proceedings of the Cambridge Philosophical Society, 1963
On a method for generalizations of tchebycheff’s inequality
Annals of the Institute of Statistical Mathematics, 1959