General Distribution Theory of the Concomitants of Order Statistics

Abstract

Let (Xi, Yi) (i = 1, 2, ⋯, n) be n independent rv's from some bivariate distribution. If Xr:n denotes the rth ordered X-variate, then the Y-variate Y[ r:n] paired with Xr:n is termed the concomitant of the rth order statistics. The exact and asymptotic distribution theory of Y[ r:n] and of its rank are studied. The results obtained are applied to a prediction problem in a Round Robin tournament.