Comparison of the multivariate skew-normal random vectors based on the integral stochastic ordering

Abstract

In this paper, we derive the conditions to compare multivariate skew-normal random vectors X and Y. Then, we present an identity for where the function f fulfills some weak regularity conditions. For comparison purposes, we use six important cases of the integral stochastic orders: the usual order, the convex order, the increasing convex order, the upper orthant order, the directionally convex order, and the supermodular order.