The beta Fréchet distribution. (English) Zbl 1074.62008

Nadarajah, Saralees; Gupta, Arjun K.

Far East J. Theor. Stat. 14, No. 1, 15-24 (2004).

Summary: Motivated by recent work of N. Eugene et al. [Commun. Stat., Theory Methods 31, No. 4, 497–512 (2002; Zbl 1009.62516)] and A. K. Gupta and S. Nadarajah [ibid. 33, No. 1, 1–13 (2004; Zbl 1210.60018)], 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 \(n\) 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.

MSC:

62E10	Characterization and structure theory of statistical distributions
62E20	Asymptotic distribution theory in statistics
62G32	Statistics of extreme values; tail inference
62N05	Reliability and life testing

Keywords:

hazard rate function