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Recursive Evaluation of Some Bivariate Compound Distributions

Published online by Cambridge University Press:  29 August 2014

Raluca Vernic
Raluca Vernic*
Affiliation:
“Ovidius” University of Constanta, Romania
*
Dept. of Mathematics and Informatics, “Ovidius”, University of Constanta, 124, Bd. Mamaia, 8700 Constanta, Romania
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Abstract

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In this paper we consider compound distributions where the counting distribution is a bivariate distribution with the probability function (Pn1,n2)n1,n2≥0 that satisfies a recursion in the form

We present an algorithm for recursive evaluation of the corresponding compound distributions and some examples of distributions in this class.

Keywords

Recursionscompound distributionsbivariate distributionsTrinomial distributionbivariate Negative Binomialbivariate Poisson
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 315 - 325
Copyright
Copyright © International Actuarial Association 1999

References

Ambagaspitiya, R.S. (1998). Compound bivariate Lagrangian Poisson distributions. Insurance: Mathematics and Economics 23, 21–31.Google Scholar
Hesselager, O. (1994). A recursive procedure for calculation of some compound distributions. ASTIN Bulletin 24, 19–32.CrossRefGoogle Scholar
Hesselager, O. (1996). Recursions for certain bivariate counting distributions and their compound distributions. ASTIN Bulletin 26, 26–35.CrossRefGoogle Scholar
Kocherlakota, S. & Kocherlakota, K. (1992). Bivariate discrete distributions. Marcel Dekker Inc.Google Scholar
Lemaire, J. (1985). Automobile insurance: Actuarial models. Kluwer Publ.CrossRefGoogle Scholar
Panjer, H.H. (1981). Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 12–22.CrossRefGoogle Scholar
Panjer, H.H. & Willmot, G.E. (1992). Insurance risk models. Society of Actuaries, Schaumburg, Illinois.Google Scholar
Partrat, C. (1993). Compound model for two dependent kinds of claim, XXIVthASTIN Colloquium, Cambridge.Google Scholar
Picard, P. (1976). Generalisation de l'étude sur la survenance des sinistres en assurance automobile. Bulletin de l'Institut des Actuaires Français, 297, 204–267.Google Scholar
Sundt, B. (1992). On some extension of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.CrossRefGoogle Scholar
Sundt, B. (1993). An introduction to non-life insurance mathematics. (3. ed.) Verlag Versicherungswirtschaft e.V., Karlsruhe.Google Scholar
Sundt, B. (1998a). The multivariate De Pril transform. Research paper 59, Centre for Actuarial Studies, University of Melbourne.Google Scholar
Sundt, B. (1998b). On error bounds for multivariate distributions. Research paper 60, Centre for Actuarial Studies, University of Melbourne.Google Scholar
Sundt, B. (1999a). On multivariate Panjer recursions. ASTIN Bulletin 29, 29–45.CrossRefGoogle Scholar
Sundt, B. (1999b). Multivariate compound Poisson distributions and infinite divisibility. Statistical report 33. Department of Mathematics, University of Bergen.Google Scholar
Willmot, G.E. (1986). Mixed compound Poisson distributions. ASTIN Bulletin 16, S59–S79.CrossRefGoogle Scholar
Willmot, G.E. (1993). On recursive evaluation of mixed Poisson probabilities and related quantities. Scandinavian Actuarial Journal, 114–133.Google Scholar
Willmot, G.E. & Panjer, H.H. (1987). Difference equation approaches in evaluation of compound distributions. Insurance: Mathematics and Economics 6, 6–43.Google Scholar