Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T12:56:24.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Computational Aspects of Sundt's Generalized Class1

Published online by Cambridge University Press:  29 August 2014

Harry H. Panjer  and
Shaun Wang
Harry H. Panjer*
Affiliation:
University of Waterloo, Ontario, Canada
Shaun Wang*
Affiliation:
University of Waterloo, Ontario, Canada
*
University of Waterloo, Ontario, Canada.
University of Waterloo, Ontario, Canada.
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.

Some practical applications of Sundt's (1992) generalized class of counting distributions are discussed. The numerical stabilities of some recursive formulas in Sundt's class are investigated.

Keywords

Compound distributionsrecursive methodstability
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 25 , Issue 1 , May 1995 , pp. 5 - 17
Copyright
Copyright © International Actuarial Association 1995

Footnotes

1

The authors wish to thank the anonymous referees for numerous suggestions which improved the presentation and readability of the paper.

References

Bender, E. (1974) Asymptotic methods of enumeriation. SIAM Review 16, 485–515.CrossRefGoogle Scholar
Cash, J.R. (1979) Stable Recursions: with applications to the numerical solution of stiff systems. Academic Press, London.Google Scholar
De Pril, N. (1985) Recursions for convolutions of arithmetic distributions. ASTIN Bulletin 15, 135–139.CrossRefGoogle Scholar
Elvers, E. (1991) A note on the generalized Poisson distribution. ASTIN Bulletin 21, 167.Google Scholar
Evans, D.A. (1953) Experimental evidence concerning contagious distributions in ecology. Biometrika 40, 186–211.CrossRefGoogle Scholar
Goovaerts, M.J. and Kaas, R. (1991) Evaluating compound generalized Poisson distributions recursively. ASTIN Bulletin 21, 193–198.CrossRefGoogle Scholar
Islam, M.N. and Consul, P.C. (1992) A probability model for automobile claims. Journal of the Swiss Association of Actuaries, Heft 1, 83–93.Google Scholar
Johnson, N. L., Kotz, S. and Kemp, A.W. (1992) Univariate Discrete Distributions. (2. ed.) John Wiley & Sons, New York.Google Scholar
Milidiu, R. (1985) The Computation of Compound Distributions With Two-Sided Severities. Ph.D. dissertation. Department of Industrial Engineering and Operation Research, University of California, Berkeley, CA.Google Scholar
Milne-Thompson, L. M. (1968) The Calculus of Finite Differences. Macmillan, London.Google Scholar
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
Panjer, H.H. and Wang, S. (1993) On the stability of recursive formulas. ASTIN Bulletin 23, 227–258.CrossRefGoogle Scholar
Panjer, H.H. and Willmot, G.E. (1992) Insurance Risk Models. Society of Actuaries, Schaumburg, IL.Google Scholar
Ruohonen, M. (1988) A model for the claim number process. ASTIN Bulletin 18, 57–68.CrossRefGoogle Scholar
Schröter, K.J. (1990) On a family of counting distributions and recursions for related compound distributions. Scandinavian Actuarial Journal, 161–175.CrossRefGoogle Scholar
Sundt, B. and Jewell, W. S. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 27–39.CrossRefGoogle Scholar
Sundt, B. (1992) On some extensions of Panjer's class of counting distributions. ASTIN Bulletin 22, 61–80.CrossRefGoogle Scholar
Wang, S. and Panjer, H.H. (1993) Critical starting points for stable evaluation of mixed Poisson probabilities. Insurance: Mathematics and Economics 13, 287–297.Google Scholar
Willmot, G. E. (1987) The Poisson-Inverse-Gaussian as an alternative to the Negative Binomial. Scandinavian Actuarial Journal, 113–127.CrossRefGoogle Scholar
Willmot, G.E. (1988) Sund and Jewell's family of discrete distributions. ASTIN Bulletin 18, 17–29.CrossRefGoogle Scholar
Willmot, G. E. (1989) Limiting tail behaviour of some discrete compound distributions. Insurance: Mathematics and Economics 8, 175–185.Google Scholar
Willmot, G. E. (1993) On the recursive evaluatoin of mixed Poisson probabilities and related quantities. Scandinavian Actuarial Journal 2, 114–133.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
Willmot, G.E. and Sundt, B. (1989) On evaluation of the Delaporte distribution and related distribution. Scandinavian Actuarial Journal, 101–113.CrossRefGoogle Scholar
Wimp, J. (1984) Computation With Recurrence Relations. Pitman Advanced Publishing Program, London, 1984. Applicable Mathematics Series.Google Scholar