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On the Compound Generalized Poisson Distributions

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  • Ambagaspitiya, R.S.
  • Balakrishnan, N.

Abstract

Goovaerts and Kaas (1991) present a recursive scheme, involving Panjer's recursion, to compute the compound generalized Poisson distribution (CGPD). In the present paper, we study the CGPD in detail. First, we express the generating functions in terms of Lambert's W function. An integral equation is derived for the pdf of CGPD, when the claim severities are absolutely continuous, from the basic principles. Also we derive the asymptotic formula for CGPD when the distribution of claim severity satisfies certain conditions. Then we present a recursive formula somewhat different and easier to implement than the recursive scheme of Goovaerts and Kaas (1991), when the distribution of claim severity follows an arithmetic distribution, which can be used to evaluate the CGPD. We illustrate the usage of this formula with a numerical example.

Suggested Citation

  • Ambagaspitiya, R.S. & Balakrishnan, N., 1994. "On the Compound Generalized Poisson Distributions," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 255-263, November.
    • Handle: RePEc:cup:astinb:v:24:y:1994:i:02:p:255-263_00
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    Cited by:

    1. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    2. Shang-Yin Yang & Chou-Wen Wang & Hong-Chih Huang, 2016. "The Valuation of Lifetime Health Insurance Policies with Limited Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 777-800, September.
    3. Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
    4. Vicente G. Cancho & Elizbeth C. Bedia & Gauss M. Cordeiro & Fábio Prataviera & Edwin M. M. Ortega & Ana P. J. E. Santo, 2023. "A survival regression with cure fraction applied to cervical cancer," Computational Statistics, Springer, vol. 38(1), pages 403-418, March.
    5. Vera Hofer & Johannes Leitner, 2012. "A bivariate Sarmanov regression model for count data with generalised Poisson marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2599-2617, August.
    6. Ambagaspitiya, Rohana S., 1998. "Compound bivariate Lagrangian Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 21-31, October.

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