On the relationships between copulas of order statistics and marginal distributions

In this paper we study the relationships between copulas of order statistics from heterogeneous samples and the marginal distributions of the parent random variables. Specifically, we study the copula of the order statistics obtained from a general random vector X = (X-1, X-2, ..., X-n). We show that the copula of the order statistics from X only depends on the copula of X and on the marginal distributions of X-1, X-2, ..., X-n through an exchangeable copula and the average of the marginal distribution functions. We study in detail some relevant cases. (C) 2009 Elsevier B.V. All rights reserved.