MIXED POISSON DISTRIBUTIONS ASSOCIATED WITH HAZARD FUNCTIONS OF EXPONENTIAL MIXTURES

Abstract

The hazard function of an exponential mixture characterizes an in- nitely divisible mixed Poisson distribution which is also a compound Poisson distribution. Given the hazard function, the probability generating functions (pgf) of the compound Poisson distribution and its independent and identically distributed (iid) random variables are derived.The recursive forms of the distributions are also given. Hofmann hazard function has been discussed and re-parameterized. The recursive form of the distribution of the iid random variables for the Hofmann distribution follows Panjer's model. Key words: Mixed Poisson distributions, Laplace transform, expo- nential mixtures, complete monotocity, in nite divisibility, compound Poisson distribution, Hofmann distributions, Panjer's model.