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THE FULL TAILS GAMMA DISTRIBUTION APPLIED TO MODEL EXTREME VALUES

Published online by Cambridge University Press:  19 June 2017

Joan del Castillo ,
Jalila Daoudi  and
Isabel Serra
Joan del Castillo*
Affiliation:
Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Spain
Jalila Daoudi
Affiliation:
Universitat Pompeu Fabra, Barcelona, Spain, jalila.daoudi@upf.edu
Isabel Serra
Affiliation:
Centre de Recerca Matemàtica, Barcelona, Spain, E-Mail: iserra@crm.cat
*
E-Mail: castillo@mat.uab.cat
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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.

Keywords

Risk modelsexponential modelsheavy tailed distributionsPareto distributionpower-law distributiontype III distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 895 - 917
Copyright
Copyright © Astin Bulletin 2017 

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