Mixed Poisson Distributions in terms of Special Functions

Abstract

Mixed Poisson distributions can be expressed in explicit, recursive and expectation forms. It can also be expressed in terms of special functions. This paper expresses mixed Poisson distributions and their proba- bility generating functions in terms of Con uent Hypergeometric func- tions and modi ed Bessel function of the third kind. Keywords: Mixed Poisson; Con uent Hypergeometric; Bessel fun- tion; Probability generating functio