Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-25T07:40:37.274Z Has data issue: false hasContentIssue false
  • English
  • Français

On A Model for the Claim Number Process*

Published online by Cambridge University Press:  29 August 2014

Matti Ruohonen
Matti Ruohonen*
Affiliation:
The Sampo Group, Turku, Finland
*
The Sampo Group, P.O. Box 216, SF-20101 Turku, Finland.
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 model for the claim number process is considered. The claim number process is assumed to be a weighted Poisson process with a three-parameter gamma distribution as the structure function. Fitting of this model to several data encountered in the literature is considered, and the model is compared with the two-parameter gamma model giving the negative binomial distribution. Some credibility theory formulae are also presented.

Keywords

Claim number processweighted Poissonthree-parameter gamma distribution
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 18 , Issue 1 , April 1988 , pp. 57 - 68
Copyright
Copyright © International Actuarial Association 1988

Footnotes

*

This paper was presented to the ASTIN Colloquium at Scheveningen, the Netherlands, September 1987.

References

Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag, Berlin.Google Scholar
Dei aporte, P. (1960) Un problème de tarification de l'assurance accidents d'automobiles examiné par la statistique mathématique. Transactions of the International Actuarial Congress, Subject Bl.Google Scholar
Dei aporte, P. (1962) Sur l'efficacité des critères de tarification de l'assurance contre les accidents d'automobiles. ASTIN Bulletin 2 (1), 84–95.CrossRefGoogle Scholar
Gossieux, A. and Lemaire, J. (1981) Methodes d'ajustement de distribution de sinistres. Bulletin of the Association of Swiss Actuaries 81, 87–95.Google Scholar
Johnson, N. I. and Kotz, S. (1969) Discrete Distributions. Houghton Mifflin, Boston.Google Scholar
Kupper, J. (1962) Wahrscheinlichkeitstheoretische Modelle in der Schadenversicherung. Bl. Deuts. Gesell. Versich. Math. Band V. Heft 4, 451–503.Google Scholar
Lemaire, J. (1979) How to define a bonus–malus system with an exponential utility function. ASTIN Bulletin 10 (3), 274–282.CrossRefGoogle Scholar
Muff, M. (1972) The influence of the franchise on the number of claims in motor insurance. ASTIN Bulletin 6 (3), 191–194.CrossRefGoogle Scholar
Pesonen, E. (1962) A numerical method of finding a suitable bonus scale. ASTIN Bulletin 2(1), 102–108.CrossRefGoogle Scholar
Rao, C. R. (1973) Linear Statistical Inference and its Applications. Wiley, New York.CrossRefGoogle Scholar
Rao, S. S. (1978) Optimization Theory and Applications. Wiley Eastern, New Delhi.Google Scholar
Ruohonen, M. (1983) Fitting a convolution of Poisson and negative binomial distributions on data. Rep. Inst. Appl. Math. Univ. Turku No. 118.Google Scholar
Seal, H. L. (1969) Stochastic Theory of a Risk Business. Wiley, New York.Google Scholar
Self, S. G. and Liang, K.-Y. (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association 82 (398), 605–610.CrossRefGoogle Scholar
Snyder, D. L. (1975) Random Point Processes. Wiley, New York.Google Scholar
Thyrion, P. (1960) Contribution à l'étude du bonus pour non sinistre en assurence automobile. ASTIN Bulletin 1 (3), 142–162.CrossRefGoogle Scholar
Tröbliger, A. (1961) Mathematische Untersuchungen zur Beitragsrückgewähr in der Kraftfahrversicherung. Bl. Deuts. Gesell. Versich. Math. 5, 327–348.Google Scholar
Willmot, G. (1988) Sundt and Jewell's family of discrete distributions. ASTIN Bulletin 18 (1), 17–29.CrossRefGoogle Scholar