On Distributions of Generalized Order Statistics from Kumaraswamy Distribution in Closed Forms

Abstract

The Kumaraswamy distribution which introduced by Poondi Kumaraswamy (1980) is similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function. With its two non-negative shape parameters p and q, it was originally conceived to model hydrological phenomena,(See for example Mitnik, 2008). In this paper, we study some distributions of generalized order statistics on Kumaraswamy distribution. We have derived the joint probability density functions for generalized order statistics from Kumaraswamy distribution in closed-forms. In addition, the pdf of the conditional distribution for generalized order statistics from Kumaraswamy distribution is obtained. Furthermore, some special cases have been discussed.