SUMS OF HAZARD FUNCTIONS OF EXPONENTIAL MIXTURES AND ASSOCIATED CONVOLUTIONS OF MIXED POISSON DISTRIBUTIONS

Abstract

A Sum of hazard functions of exponential mixtures characterizes a convolution of infinitely divisible mixed Poisson distributions which is also a convolution of compound Poisson distri- butions. For each sum of two special cases of Hofmann hazard function, the following have been ob- tained: • the probability generating function (pgf) of the convolution of the mixed Poisson distri- butions. • the pgf of the independent and identically distributed (iid) random variables for the convolution of the compound Poisson distributions. • the recursive form of the convolution of the compound Poisson distribution. We also wish to find out whether Panjer's recursive model holds for all cases.