Nadarajah, Saralees
(2006)
*The exponentiated Gumbel distribution with climate application.*
Environmetrics, 17 (1).
pp. 13-23.
ISSN 1180-4009

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## Abstract

The Gumbel distribution is perhaps the most widely applied statistical distribution for climate modeling. In this article we introduce a distribution that generalizes the standard Gumbel distribution in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated Gumbel distribution. We provide a comprehensive treatment of the mathematical properties of this new distribution and illustrate its use for modeling rainfall data from Orlando, Florida. Among the mathematical properties, we derive the analytical shapes of the corresponding probability density function and the hazard rate function, calculate expressions for the nth moment and the asymptotic distribution of the extreme order statistics, and investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. Copyright © 2005 John Wiley & Sons, Ltd.

Item Type: | Article |
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Uncontrolled Keywords: | climate modeling • exponentiated Gumbel distribution • GEV distribution • Gumbel distribution |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 33 Special functions (properties of functions as functions) MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 29 Mar 2007 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/741 |

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