Digital Object Identifier (DOI)
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.
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Citation / Publisher Attribution
Mathematical Problems in Engineering, v. 2004, art. 529485
Scholar Commons Citation
Nadarajah, Saralees and Kotz, Samuel, "The Beta Gumbel Distribution" (2004). Mathematics and Statistics Faculty Publications. 35.