Multivariate properties of random vectors of order statistics

The purpose of this paper is to extend some known results about stochastic comparisons of univariate order statistics to the case of random vectors of order statistics. These multivariate stochastic comparisons are given under conditions of stochastic orders, like the hazard rate order, likelihood ratio order and dispersive order, of the parent distributions. We obtain also some other results about multivariate classification of random vectors of order statistics, in particular, we give conditions on the parent distribution to classify the random vector of order statistics in the MIFR or MPF2 classes. Applications to stochastic comparisons of some transformations of order statistics are also given. (C) 2002 Elsevier Science B.V. All rights reserved.