Recursive Route to Mixed Poisson Distributions using Integration by Parts

Abstract

Mixed Poisson distributions are very significant in modeling non-homogeneous populations; for instance in Actuarial applications for modeling total claims in insurance. However, the setback is in their use since the probability mass functions are difficult to evaluate, except for a few mixing distributions. One way of dealing with this problem is to express Mixed Poisson distributions in terms of recursive relations.

In this paper, recursive relations of some mixed Poisson distributions are obtained by use of integration by parts technique.

Keywords: mixtures; recursive relation; generating functions; moments