Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-25T07:12:45.084Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursions for certain bivariate counting distributions and their compound distributions

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager
Ole Hesselager*
Affiliation:
Laboratory of Actuarial Mathematics, University of Copenhagen
*
Laboratory of Actuarial Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø
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.

We consider three classes of bivariate counting distributions and the corresponding compound distributions. For each class we derive a recursive algorithm for calculating the bivariate compound distribution.

Keywords

Bivariate counting distributionsCompound distributionsRecursionsBivariate mixed Poisson
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 35 - 52
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

De Pril, N. (1986) Moments of a class of compound distributions. Scand. Actuarial J., 1986, 117–120.CrossRefGoogle Scholar
Guldberg, A. (1934) On discontinuous frequency functions of two variables. Skandinavisk Aktuarietidskrift, 1934, 89–117.Google Scholar
Hesselager, O. (1993) A recursive procedure for calculation of some mixed compound Poisson distributions. Working paper, 115, Laboratory of Actuarial Math., Copenhagen. (To appear in Scand. Actuarial J.).Google Scholar
Hesselager, O. (1994) A recursive procedure for calculation of some compound distributions. AST1N Bulletin, 24, 19–32.Google Scholar
Holgate, P. (1954) Estimation for the bivariate Poisson distribution. Biometrika, 51, 241–245.CrossRefGoogle Scholar
Johnson, N.L. and Kotz, S. (1969) Distributions in Statistics: Discrete distributions. Wiley, New York.Google Scholar
Kocherlakota, S. and Kocherlakota, K. (1992) Bivariate Discrete Distributions. Marcel Dekker, New York.Google Scholar
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin, 12, 22–26.CrossRefGoogle Scholar
Panier, H.H. and Willmot, G. (1982) Recursions for compound distributions. ASTIN Bulletin. 13, 1–11.Google Scholar
Panjer, H.H. and Willmot, G. (1992) Insurance Risk Models. Society of Actuaries, Schaumburg.Google Scholar
Papageorgiou, H. (1984) On recursive formulas for aggregate claims. Scand. Actuarial J., 1984, 102–104.CrossRefGoogle Scholar
Schröter, K.J. (1990) On a class of counting distributions and recursions for related compound distributions. Scand. Actuarial J., 1990, 161–175.CrossRefGoogle Scholar
Sundt, B. (1992) On some extensions of Panjer's class of counting distributions. ASTIN Bulletin, 22, 61–80.CrossRefGoogle Scholar
Teicher, H. (1954) On the multivariate Poisson distribution. Skandinavisk Aktuarietidskrift, 1954, 1–9.Google Scholar
Wang, S. and Sobrero, M. (1994) Further results on Hesselager's recursive procedure for calculation of some compound distributions. ASTIN Bulletin, 24, 160–166.CrossRefGoogle Scholar
Willmot, G. (1993) On recursive evaluation of mixed Poisson probabilities and related quantities. Scand. Actuarial J., 1993, 114–133.Google Scholar