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On Modelling Insurance Data by Using a Generalized Lognormal Distribution || Sobre la modelización de datos de seguros usando una distribución lognormal generalizada

Author

Listed:
  • García, Victoriano J.

    (Departamento de Estadística e Investigación Operativa, Universidad de Cádiz (España))

  • Gómez-Déniz, Emilio

    (Departamento de Métodos Cuantitativos e Instituto TiDES, Universidad de Las Palmas de Gran Canaria (España))

  • Vázquez-Polo, Francisco J.

    (Departamento de Métodos Cuantitativos e Instituto TiDES, Universidad de Las Palmas de Gran Canaria (España))

Abstract

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occurs in practical situations. The distribution proposed is derived from the lognormal distribution, by using the Marshall and Olkin procedure. Some basic properties of this new distribution are obtained and we present situations where this new distribution correctly reflects the sample behaviour for the right tail probability. An application of the model to dental insurance data is presented and analysed in depth. We conclude that the generalized lognormal distribution proposed is a distribution that should be taken into account among other possible distributions for insurance data in which the properties of a heavy-tailed distribution are present. || Presentamos una nueva distribución lognormal con colas pesadas que se adapta bien a muchas situaciones prácticas en el campo de los seguros. Utilizamos el procedimiento de Marshall y Olkin para generar tal distribución y estudiamos sus propiedades básicas. Se presenta una aplicación de la misma para datos de seguros dentales que es analizada en profundidad, concluyendo que tal distribución deberá formar parte del catálogo de distribuciones a tener cuenta para la modernización de datos en seguros cuando hay presencia de colas pesadas.

Suggested Citation

  • García, Victoriano J. & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2014. "On Modelling Insurance Data by Using a Generalized Lognormal Distribution || Sobre la modelización de datos de seguros usando una distribución lognormal generalizada," 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. 18(1), pages 146-162, December.
    • Handle: RePEc:pab:rmcpee:v:18:y:2014:i:1:p:146-162
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    References listed on IDEAS

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    3. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
    4. K. Jose & Shanoja Naik & Miroslav Ristić, 2010. "Marshall–Olkin q-Weibull distribution and max–min processes," Statistical Papers, Springer, vol. 51(4), pages 837-851, December.
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    More about this item

    Keywords

    heavy-tailed; insurance; lognormal distribution; loss distribution; seguros; distribución lognormal; función de pérdidas; colas pesadas;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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