Concomitants of multivariate order statistics from multivariate elliptical distributions

In this article, we consider a (k + 1)n-dimensional elliptically contoured random vector (X-1(T), X-2(T), ..., X-k(T), Z(T))(T) = (X-11, ..., X-1n, ..., X-k1, ..., X-kn, Z(1), ..., Z(n))(T) and derive the distribution of concomitant of multivariate order statistics arising from X-1, X-2, ..., X-k. Specially, we derive a mixture representation for concomitant of bivariate order statistics. The joint distribution of the concomitant of bivariate order statistics is also obtained. Finally, the usefulness of our result is illustrated by a real-life data.