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The full-tails gamma distribution applied to model extreme values

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  • Joan del castillo
  • Jalila Daoudi
  • Isabel Serra

Abstract

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory. The results are useful to certain phenomena that are fitted by the Pareto distribution but, at the same time, they present a deviation from this law for very large values. Two examples of data analysis with the new model are provided. The first one is on the influence of climate variability on the occurrence of tropical cyclones. The second one on the analysis of aggregate loss distributions associated to operational risk management.

Suggested Citation

  • Joan del castillo & Jalila Daoudi & Isabel Serra, 2012. "The full-tails gamma distribution applied to model extreme values," Papers 1211.0130, arXiv.org.
    • Handle: RePEc:arx:papers:1211.0130
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    References listed on IDEAS

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    1. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    2. Degen, Matthias & Embrechts, Paul & Lambrigger, Dominik D., 2007. "The Quantitative Modeling of Operational Risk: Between G-and-H and EVT," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 265-291, November.
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    Cited by:

    1. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.

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