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The Full Tails Gamma Distribution Applied To Model Extreme Values

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  • del Castillo, Joan
  • Daoudi, Jalila
  • Serra, Isabel

Abstract

In this paper, we introduce the simplest exponential dispersion model containing the Pareto and exponential distributions. In this way, we obtain distributions with support (0, ∞) that in a long interval are equivalent to the Pareto distribution; however, for very high values, decrease like the exponential. This model is useful for solving relevant problems that arise in the practical use of extreme value theory. The results are applied to two real examples, the first of these on the analysis of aggregate loss distributions associated to the quantitative modelling of operational risk. The second example shows that the new model improves adjustments to the destructive power of hurricanes, which are among the major causes of insurance losses worldwide.

Suggested Citation

  • del Castillo, Joan & Daoudi, Jalila & Serra, Isabel, 2017. "The Full Tails Gamma Distribution Applied To Model Extreme Values," ASTIN Bulletin, Cambridge University Press, vol. 47(3), pages 895-917, September.
    • Handle: RePEc:cup:astinb:v:47:y:2017:i:03:p:895-917_00
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    Cited by:

    1. Elio Roca-Flores & Gerardo G. Naumis, 2021. "Assessing statistical hurricane risks: nonlinear regression and time-window analysis of North Atlantic annual accumulated cyclonic energy rank profile," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(3), pages 2455-2465, September.
    2. Li, Zhengxiao & Wang, Fei & Zhao, Zhengtang, 2024. "A new class of composite GBII regression models with varying threshold for modeling heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 45-66.

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