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Evaluating Compound Generalized Poisson Distributions Recursively

Published online by Cambridge University Press:  29 August 2014

M. J. Goovaerts  and
R. Kaas
M. J. Goovaerts
Affiliation:
Amsterdam/Leuven
R. Kaas*
Affiliation:
Amsterdam/Leuven
*
University of Amsterdam, Institute of Actuarial Science and Econometrics, Jodenbreestraat 23, 1011 NH Amsterdam, The Netherlands.
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Abstract

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In this paper we give a recursive scheme, involving Panjer's recursion, to compute the distribution of a compound sum of integer claims, when the number of summands follows a Generalized Poisson distribution. Also, an elegant derivation is given for some basic properties of this counting distribution.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 21 , Issue 2 , November 1991 , pp. 193 - 198
Copyright
Copyright © International Actuarial Association 1991

References

Abramowitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions. Dover Publications, New York.Google Scholar
Consul, P.C. (1989) Generalized Poisson distributions, properties and applications. Marcel Dekker Inc., New York, Basel.Google Scholar
Gerber, H.U. (1990) When does the surplus reach a given target? Insurance: Mathematics and Economics 9, 115–119.Google Scholar
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. AST1N Bulletin 12, 22–26.Google Scholar
Sundt, B. and Jewell, W. S. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 27–39.CrossRefGoogle Scholar