THE FULL TAILS GAMMA DISTRIBUTION APPLIED to MODEL EXTREME VALUES

Joan Del Castillo, Jalila Daoudi, Isabel Serra

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

Copyright © Astin Bulletin 2017. 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.
Original languageEnglish
Pages (from-to)895-917
JournalASTIN Bulletin
Volume47
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • Pareto distribution
  • Risk models
  • exponential models
  • heavy tailed distributions
  • power-law distribution
  • type III distribution

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