On Distribution of Order Statistics from Kumaraswamy Distribution

Abstract

Abstract. In the present paper we derive the distribution of single order statistics, jointdistribution of two order statistics and the distribution of product and quotient of two or-der statistics when the independent random variables are from continuous Kumaraswamydistribution. In particular the distribution of product and quotient of extreme order statis-tics and consecutive order statistics have also been obtained. The method used is basedon Mellin transform and its inverse. 1. IntroductionIf the random variables X 1 ,X 2 ,···X n are arranged in ascending order of mag-nitudes and then written as X (1) ≤ X (2) ≤ ··· ≤ X (n) Then X (i) is called the i t h order statistics i = 1,··· ,n. The unordered randomvariables X i are usually statistically independent and identically distributed butthe ordered random variables X (i) ,i = 1,2,··· ,n are necessarily dependent. Thedistribution of product and quotient of random variables finds an important placein the literature and much work is done when the random variables are independent.However Subramaniam [9] has derived the distribution of the product and quotientof order statistics from a uniform distribution and negative exponential distributionrespectively. Further Trudel and Malik [6] have derived the distribution of productand ratio of order statistics from Pareto, power and Weibull distributions.Order statistics play an important supporting role in the multiple comparisonsand multiple decision procedures such as the distribution of extreme order statisticsX