Far East Journal of Theoretical Statistics
Volume 14, Issue 1, Pages 15 - 24
(September 2004)
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THE BETA FRÉCHET DISTRIBUTION
Saralees Nadarajah (U. S. A.) and Arjun K. Gupta (U. S. A.)
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Abstract: Motivated by the recent work of Eugene et al. [Comm. Stat. Theo. Meth. 31 (2002), 497-512] and Gupta and Nadarajah [Comm. Stat. Theo. Meth. 33 (2004), 1-13], we introduce the beta Fréchet 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. |
Keywords and phrases: beta distribution, Fréchet distribution. |
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