Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T04:01:49.182Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive Formulae for Some Bivariate Counting Distributions Obtained by the Trivariate Reduction Method

Published online by Cambridge University Press:  29 August 2014

J.F. Walhin  and
J. Paris
J.F. Walhin*
Affiliation:
Université Catholique de Louvain SECURA Belgian Re Rue Montoyer 12 1000 Bruxelles
J. Paris*
Affiliation:
Université Catholique de Louvain
*
SECURA Belgian Re Rue Montoyer 12 1000 Bruxelles
SECURA Belgian Re Rue Montoyer 12 1000 Bruxelles
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study some bivariate counting distributions that are obtained by the trivariate reduction method. We work with Poisson compound distributions and we use their good properties in order to derive recursive algorithms for the bivariate distribution and bivariate aggregate claims distribution. A data set is also fitted.

Keywords

Bivariate counting distributionsPoisson compound distributionmixed Poisson distributionHofrnann distributionrecursive algorithmsfit
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 30 , Issue 1 , May 2000 , pp. 141 - 155
Copyright
Copyright © International Actuarial Association 2000

References

Ahmed, M.S. (1961) On a Locally Most Powerful Boundary Randomized Similar Test for the Independence of two Poisson Variables. Ann. Math. Statist. 32, 809–827.CrossRefGoogle Scholar
Hesselager, O. (1996) Recursions for Certain Bivariate Counting Distributions and their Compound Distributions. Astin Bulletin 26, 35–52.CrossRefGoogle Scholar
Hofmann, M. (1955) Uber zusammengesetzte Poisson-Prozesse und ihre Anwendungen in der Unfall versicherung. Bulletin of the Swiss Actuaries 55, 499–575.Google Scholar
Kestemont, R.M. and Paris, J. (1985) Sur l'Ajustement du Nombre de Sinistres. Bulletin of the Swiss Actuaries 85, 157–164.Google Scholar
LeMalre, J. (1995) Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Panjer, H.H. (1981) Recursive Evaluation of a Family of Compound Distributions. Astin Bulletin 12, 22–26.CrossRefGoogle Scholar
Panjer, H.H. and Willmot, G.E. (1992) Insurance Risk Models. Society of Actuaries.Google Scholar
Papageorgiou, H. and David, K.M. (1995) On a Class of Bivariate Compounded Poisson Distributions. Statistics & Probability Letters 23, 93–104.CrossRefGoogle Scholar
Walhin, J.F. and Paris, J. (2000a) Excess-of-Loss Reinsurance with Reinstatements and Ruin of the Cedent, submitted.CrossRefGoogle Scholar
Walhin, J.F. and Paris, J. (2000b) A Large Family of Discrete and Overdispersed Probability Laws, forthcoming.Google Scholar