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Evaluating Compound Generalized Poisson Distributions Recursively

Author

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  • Goovaerts, M. J.
  • Kaas, R.

Abstract

In this paper we give a recursive scheme, involving Panjer's recursion, to compute the distribution of a compound sum of integer claims, when the number of summands follows a Generalized Poisson distribution. Also, an elegant derivation is given for some basic properties of this counting distribution.

Suggested Citation

  • Goovaerts, M. J. & Kaas, R., 1991. "Evaluating Compound Generalized Poisson Distributions Recursively," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 193-198, November.
    • Handle: RePEc:cup:astinb:v:21:y:1991:i:02:p:193-198_00
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    Citations

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    Cited by:

    1. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    2. 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.
    3. Barbosa, Valmir C & Donangelo, Raul & Souza, Sergio R, 2003. "Directed cycles and related structures in random graphs: I—Static properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 381-397.
    4. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
    5. A. Sharif & S. Csörgö & S. Takenaka & D. Dacunha-Castelle & H. Basler, 1996. "Book-reviews," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 91-100, December.
    6. Martel-Escobar, M. & Hernández-Bastida, A. & Vázquez-Polo, F.J., 2012. "On the independence between risk profiles in the compound collective risk actuarial model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1419-1431.
    7. 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.
    8. 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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