Modelling Dispersion Using Finite Mixture Of PoissoN

Abstract

The negative binomial distribution is a versatile distribution in describing dispersion. The negative binomial parameter k is considered as a dispersion parameter. The aim of this paper is to demonstrate that filnite mixture of Poisson can be used in modelling dispersion. The digamma ." function and the Sterling's expansion for the gamma function are used to construct a dispersion parameter in relation to the negative binomial parameter k. The construction is based on the hierarchical maximum likelihood estimation of the negative binomial parameter k. The method of moments estimates of