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.
