Open AccessThe beta Gumbel distribution
Author(s) -
Saralees Nadarajah,
Samuel Kotz
Publication year - 2004
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/s1024123x04403068
Subject(s) - gumbel distribution , kurtosis , beta distribution , mathematics , generalization , generalized beta distribution , weibull distribution , skewness , random variable , distribution (mathematics) , statistics , distribution fitting , probability distribution , extreme value theory , mathematical analysis
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
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