STOCHASTIC ORDERING OF A CLASS OF SYMMETRIC DISTRIBUTIONS

In this article, we investigate the sufficient and/or necessary conditions in order to stochastically compare the order statistics and their spacing vectors of two random vectors X and Y with special symmetric distributions. The conditions are imposed on the sample ranges Xn:n–X1:n and Yn:n–Y1:n or on (X1:n, Xn:n–X1:n) and (Y1:n, Yn:n–Y1:n). In particular, we consider the multivariate usual stochastic order, the convex order, the increasing convex order, and the directionally convex order. Several examples are also given to illustrate the power of the main results.