MOMENTS OF A RANK VECTOR WITH APPLICATIONS TO SELECTION AND RANKING

Abstract

Let k populations π_i be given with a continuous cumulative distribution function F_i(x), i=1, 2, …, k. Also let X₁, X₂, …, X_k be a set of mutually independent observations from respective populations π₁. π₂, …, π_k. A rank vector R=(R₁, R₂, …, R_k) is defined for these observations as follows: R_i=s if X_i is the s-th smallest of the variables X₁, X₂, …, X_k. The purpose of this paper is to give the mean, variance and covariance of rank vector R under the population model stated above. Applications to the slippage configuration of distributions and the normal distribution are also given.