On Mixed and Compound Mixed Poisson Distributions

Abstract

Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented.

Keywords:

• Mixed Poisson distribution
• compound distribution
• t-th order cumulative distribution function
• t-th order tail probability
• recursion
• stop-loss transform
• moments

Notes

Antzoulakos DL, Chadjiconstantinidis S. On mixed and compound mixed Poisson distributions. Scand. Actuarial J. 2004; 3: 161–188.

Additional information

Notes on contributors

Demetrios L. Antzoulakos

Antzoulakos DL, Chadjiconstantinidis S. On mixed and compound mixed Poisson distributions. Scand. Actuarial J. 2004; 3: 161–188.