On Mixed and Compound Mixed Poisson Distributions

Demetrios L. Antzoulakos and Stathis Chadjiconstantinidis

Scandinavian Actuarial Journal, 2004, vol. 2004, issue 3, 161-188

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.

Date: 2004
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DOI: 10.1080/03461230110106525

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