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Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model

Author

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  • Agustin Hernandez Bastida
  • Emilio Gomez Deniz
  • Jose Maria Perez Sanchez

Abstract

The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma. This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.

Suggested Citation

  • Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
  • Handle: RePEc:taf:japsta:v:36:y:2009:i:8:p:853-869
    DOI: 10.1080/02664760802510059
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    Citations

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    Cited by:

    1. Hernández-Bastida, Agustin & Fernández-Sánchez, Mª Pilar & Gómez-Déniz, Emilio, 2011. "A Desirable Aspect in the Variance Premium in a Collective Risk Model/Un aspecto deseable de la Prima Varianza en el Modelo Colectivo de Riesgo," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 29, pages 395(18.)-39, Abril.
    2. Gómez Déniz, Emilio & Calderín Ojeda, Enrique, 2013. "The Compound DGL/Erlang Distribution in the Collective Risk Model || La distribución compuesta DGL/Erlang en el modelo de riesgo colectivo," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 16(1), pages 121-142, December.
    3. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    4. Hernández-Bastida, A. & Fernández-Sánchez, M.P. & Gómez-Déniz, E., 2009. "The net Bayes premium with dependence between the risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 247-254, October.

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