On a family of counting distributions and recursions for related compound distributions

1 May 1990

journal article
research article
Published by Taylor & Francis in Scandinavian Actuarial Journal

Vol. 1990 (2-3) , 161-175
https://doi.org/10.1080/03461238.1990.10413879

Abstract

This paper considers a family of counting distributions whose densities satisfy certain second order difference equations. Recursions for the evaluation of related compound distributions are developed in the case of severity distributions which are concentrated on the non-negative integers. From these a characterization of the considered counting distributions is obtained, and it is shown that most of these are compound Poisson distributions.

Keywords

This publication has 6 references indexed in Scilit:

On evaluation of the Delaporte distribution and related distributions
Scandinavian Actuarial Journal, 1989
Practical aspects of stop-loss calculations
Insurance: Mathematics and Economics, 1983
On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums
Insurance: Mathematics and Economics, 1982
Recursive Evaluation of a Family of Compound Distributions
ASTIN Bulletin, 1981
Further Results on Recursive Evaluation of Compound Distributions
ASTIN Bulletin, 1981
On a transformation of the weighted compound Poisson process
ASTIN Bulletin, 1971