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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 n th 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.
Nadarajah et al. (Thu,) studied this question.