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Further Results on Hesselager's Recursive Procedure for Calculation of some Compound Distributions*

Published online by Cambridge University Press:  29 August 2014

Shaun Wang  and
Monica Sobrero
Shaun Wang*
Affiliation:
University of Waterloo, Canada
Monica Sobrero*
Affiliation:
University of Waterloo, Canada
*
Dept. of Statistics & Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
Dipartimento di Scienze Attuariali e Matematica, Facoltà di Economia e Commercio, Università “La Sapienza”, Roma, Italia
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Abstract

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The recursive algorithm of Hesselager (1994) is extended to a more general class of counting distributions, which includes Sundt's (1992) class as well as all the mixed Poisson distributions discussed by Willmot (1993).

Keywords

Compound distributionsrecursionsmixed PoissonsSichelBetaGeneralized ParetoInverse Gamma
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 2 , November 1994 , pp. 161 - 166
Copyright
Copyright © International Actuarial Association 1994

Footnotes

*

The authors are grateful to the editor and the referees for their helpful comments.

References

Hesselager, O. (1994) A recursive procedure for calculation of some compound distributions. ASTIN Bulletin, to appear.Google Scholar
Ord, J.K. (1972) Families Of Frequency Distributions. Griffin, London.Google Scholar
Panjer, H.H. (1981) Recursive evaluation of a family of compund distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
Sundt, B. (1992) On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.CrossRefGoogle Scholar
Willmot, G.E. (1993) On recursive evaluation of mixed Poisson probabilities and related quantities. Scandinavian Actuarial Journal, to appear.Google Scholar
Willmot, G.E. and Panjer, H.H. (1987) Difference equation approaches in evaluation of compound distributions. Insurance: Mathematics and Economics 6, 43–56.Google Scholar