Pescim, Rodrigo R.; Cordeiro, Gauss M.; Demétrio, Clarice G. B.; Ortega, Edwin M. M.; Nadarajah, Saralees The new class of Kummer beta generalized distributions. (English) Zbl 1296.62036 SORT 36, No. 2, 153-180 (2012). Summary: K. W. Ng and S. Kotz [Kummer-gamma and Kummer-beta univariate and multivariate distributions. Res. Rep., Dept. Stat., Univ. Hong Kong (1995)] introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set. Cited in 12 Documents MSC: 62E15 Exact distribution theory in statistics Keywords:generalized distribution; Kummer beta distribution; likelihood ratio test; moment; order statistic; Weibull distribution PDFBibTeX XMLCite \textit{R. R. Pescim} et al., SORT 36, No. 2, 153--180 (2012; Zbl 1296.62036) Full Text: Link