On the sums of probability functions of order statistics

Abstract

When a random vector is independent and identically distributed, we have expressed the sums of the marginal probability functions of the order statistics of the random vector in terms of the common marginal probability functions of the random vector. We have also derived the relationships between the sums of the joint probability functions of two order statistics of the random vector and the common marginal probability functions of the random vector. (C) 2012 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.