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On A Model for the Claim Number Process

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  • Ruohonen, Matti

Abstract

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.

Suggested Citation

  • Ruohonen, Matti, 1988. "On A Model for the Claim Number Process," ASTIN Bulletin, Cambridge University Press, vol. 18(1), pages 57-68, April.
    • Handle: RePEc:cup:astinb:v:18:y:1988:i:01:p:57-68_00
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    Cited by:

    1. Finner, H. & Kern, P. & Scheer, M., 2015. "On some compound distributions with Borel summands," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 234-244.
    2. A.Hernández-Bastida & J. M. Pérez–Sánchez & E. Gómez-Deniz, 2007. "Bayesian Analysis Of The Compound Collective Model: The Net Premium Principle With Exponential Poisson And Gamma–Gamma Distributions," FEG Working Paper Series 07/03, Faculty of Economics and Business (University of Granada).
    3. Martin Bøgsted & Susan Pitts, 2010. "Decompounding random sums: a nonparametric approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 855-872, October.
    4. Fang, Yue, 2008. "Semi-parametric specification tests for mixing distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2829-2839, January.

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