On the construction of mixed poisson distributions

Abstract

Mixed poisson distributions are very significant in modeling non - homogeneous populations, for instance in Actuarial applications for modeling total claims in insurance. In this work the concentration is mainly on the construction of these Mixed poisson distributions.

The methods of construction used are: Direct integration, obtaining Recursive relations for the Mixed poisson distributions, using Laplace Transforms of the mixing distributions and use of Special Functions to express the Mixed poisson distributions. A number of Mixed poisson distributions are constructed using each of the mentioned methods of construction.