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