The new class of Kummer beta generalized distributions

Abstract

Ng and Kotz (1995) introduced a distribution that provides g reater 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 sev eral other well-known distributions. Some special models are discussed. The ordinary moments of a ny distribution in the new family can be expressed as linear functions of probability weighte d moments of the baseline distribution. We examine the asymptotic distributions of the extreme valu es. We derive the density function of the order statistics, mean absolute deviations and entro pies. We use maximum likelihood estimation to fit the distributions in the new class and illus trate its potentiality with an application to a real data set