EM Algorithm for Poisson-Lindley Distribution

Abstract

Mixed Poisson distributions have been used in scientific fields for modelling non-homogenous populations, (Karlis and xekalaki, 2005).. For example, in acturial applications, mixed Poisson distributions are used for modeling total claims in insurance. In this work, the concentration is mainly on the estimation of the parameters of Poisson- Lindley distribution using EM Algorithm which was first introduced by Dempster (1977). One-parameter, two-parameter and three-parameter Lindley distributions are compounded by the Poisson distribution to form the Poisson-Lindley distributions and then the parameters estimated. In order to carry out the EM Algorithm successfully, the posterior distribution is applied and the posterior expectation calculated. Various properties of each distribution are determined, for example, the rth moment, the cumulative distribution function (cdf), the moment generating function (mgf), the probability generating function (mgf) and the characteristic function.