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The Compound DGL/Erlang Distribution in the Collective Risk Model || La distribución compuesta DGL/Erlang en el modelo de riesgo colectivo

Author

Listed:
  • Gómez Déniz, Emilio

    (Departamento de Métodos Cuantitativos en Economía y Gestión. Universidad de Las Palmas de Gran Canaria (Spain))

  • Calderín Ojeda, Enrique

    (Centre for Actuarial Studies, Department of Economics. The University of Melbourne (Australia))

Abstract

In this paper the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribution, is considered. After providing some new results of this discrete model, analytical expressions for the aggregate claim size distribution in general insurance in the case that the discrete generalized Lindley distribution is assumed as the primary distribution while claim size, the secondary distribution, is modeled using an Erlang(r) distribution (r = 1; 2). Comparisons with the compound Poisson and compound negative binomial are developed to explain the viability of the new compound model in two examples in automobile insurance. || En este artículo se analiza el modelo de riesgo colectivo asumiendo que la cantidad individual reclamada sigue una función de densidad Erlang y el número de reclamaciones es una variable aleatoria cuya función masa de probabilidad es la generalizada discreta Lindley. En la primera parte de este trabajo se presentan nuevas propiedades de esta distribución discreta; seguidamente, se calculan expresiones analíticas para la cantidad total reclamada en seguros generales cuando la distribución primaria es la generalizada discreta Lindley, asumiendo la densidad Erlang(r) (r = 1; 2) como distribución secundaria. En la ilustración numérica, el nuevo modelo expuesto en este artículo se compara con los modelos compuestos Poisson y Binomial Negativa en dos ejemplos, en el contexto de seguros de automóviles, para mostrar su efectividad.

Suggested Citation

  • 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.
  • Handle: RePEc:pab:rmcpee:v:16:y:2013:i:1:p:121-142
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    References listed on IDEAS

    as
    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. E. Gómez-Déniz, 2010. "Another generalization of the geometric distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 399-415, August.
    3. 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.
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    More about this item

    Keywords

    automobile insurance; collective risk model; Lindley distribution; seguro de automóviles; modelo de riesgo colectivo; distribución Lindley;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • M20 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - General

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