Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T12:21:43.681Z Has data issue: false hasContentIssue false
  • English
  • Français

Sundt and Jewell's Family of Discrete Distributions

Published online by Cambridge University Press:  29 August 2014

Gordon Willmot
Gordon Willmot*
Affiliation:
University of Waterloo
*
University of Waterloo, Faculty of Mathematics, Department of Statistics and Actuarial Science, Waterloo, Ontario N2L 3G1, 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.

A class of claim frequency distributions discussed by Sundt and Jewell (1981) is completely enumerated. Computational techniques for the associated compound total claims distribution in the presence of policy modifications are then derived.

Keywords

Panjer's recursiondeductiblesmaximumsextended truncated negative binomial
Type
Prize-Winning Papers of the ASTIN Competition 1987
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 1 , April 1988 , pp. 17 - 29
Copyright
Copyright © International Actuarial Association 1988

References

Anscombe, F. (1950) Sampling theory of the negative binomial and logarithmic series distributions. Biomelrika 37, 358–382.CrossRefGoogle ScholarPubMed
Embrechts, P., Maejima, M., and Teugels, J. (1985) Asymptotic behaviour of compound distributions. ASTIN Bulletin 15, 45–48.CrossRefGoogle Scholar
Engen, S. (1974) On species frequency models. Biomelrika 61, 263–270.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1 (3rd edn). Wiley, New York.Google Scholar
Gossiaux, A. and Lemaire, J. (1981) Methodes d'ajustement de distributions de Sinistres. Bulletin of the Association of Swiss Actuaries 81, 87–95.Google Scholar
Jewell, W. and Sundt, B. (1981) Improved approximations for the distribution of a heterogeneous risk portfolio. Bulletin of the Association of Swiss Actuaries 81, 221–240.Google Scholar
Karlin, S. and Taylor, H. (1981) A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
Marsden, J. (1974) Elementary Classical Analysis. W. H. Freeman, San Fransisco.Google Scholar
Panjer, H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
Panjer, H. and Willmot, G. (1984) Computational techniques in reinsurance models. Transactions of the 22nd International Congress of Actuaries, Sydney, 4, 111–120.Google Scholar
Ströter, B. (1985) The numerical evaluation of the aggregate claim density function via integral equations. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 17, 1–14.Google Scholar
Sundt, B. and Jewell, W. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 27–39.CrossRefGoogle Scholar
Wani, J. and Lo, H. (1983) A characterization of invariant power series abundance distributions. Canadian Journal of Statistics 11, 317–323.CrossRefGoogle Scholar
Wani, J. and Lo, H. (1986) Selecting a power-series distribution for goodness of fit. Canadian Journal of Statistics 14, 347–353.CrossRefGoogle Scholar
Willmot, G. (1986) Mixed compound Poisson distributions. ASTIN Bulletin 16S, S59–S79.CrossRefGoogle Scholar
Willmot, G. and Panjer, H. (1987) Difference equation approaches in evaluation of compound distributions. Insurance: Mathematics and Economics 6, 43–56.Google Scholar