Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2004 / Article

Open Access

Volume 2004 |Article ID 529485 | https://doi.org/10.1155/S1024123X04403068

Saralees Nadarajah, Samuel Kotz, "The beta Gumbel distribution", Mathematical Problems in Engineering, vol. 2004, Article ID 529485, 10 pages, 2004. https://doi.org/10.1155/S1024123X04403068

The beta Gumbel distribution

Received22 Mar 2004
Revised16 Jun 2004

Abstract

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. In this paper, we introduce a generalization—referred to as the beta Gumbel distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. We calculate expressions for the nth moment and the asymptotic distribution of the extreme order statistics. We investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. We hope that this generalization will attract wider applicability in engineering.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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