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A Loglinear Lagrangian Poisson Model

Published online by Cambridge University Press:  29 August 2014

Peter ter Berg
Peter ter Berg*
Affiliation:
SFB Verzekeringen, Amsterdam, Netherlands
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Abstract

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Maximum likelihood estimation is derived for the Lagrangian Poisson distribution for a simple and a loglinear model and illustrated with real data.

Keywords

LoglinearLagrangian PoissonMaximum likelihoodNewton-Raphson
Type
Short Contribution
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 123 - 129
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

Bailey, R. A. and Simon, L.J. (1960) Two studies in automobile insurance ratemaking. ASTIN Bulletin 1, 192–217.CrossRefGoogle Scholar
Bichsel, F. (1964) Erfahrungs-Tarifierung in der Motorfahrzeughaftpflicht-Versicherung. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker 64, 119–129.Google Scholar
Consul, P.C. (1989) Generalized Poisson Distributions. Marcel Dekker, New York.Google Scholar
Consul, P.C. and Shenton, L. R. (1972) Use of Lagrange expansion for generating discrete generalized probability distributions. SIAM Journal of Applied Mathematics 23, 239–248.CrossRefGoogle Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Chapman & Hal, London.Google Scholar
Goovaerts, M. and Kaas, R. (1991) Evaluating compound generalized Poisson distributions recursively. ASTIN Bulletin 21, 193–198.CrossRefGoogle Scholar
McMillan, B. and Riordan, J. (1957) A moving single server problem. Annals of Mathematical Statistics 28, 471–478.CrossRefGoogle Scholar
ter Berg, P. (1980) On the loglinear Poisson and Gamma model. ASTIN Bulletin 11, 35–40.CrossRefGoogle Scholar