An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normalDistribution with Applications to Associated Stochastic Orderings

TL;DR

This paper derives an identity and characteristic function for matrix variate skew-normal distributions, enabling comparison under various stochastic orders, with potential applications in multivariate statistical analysis.

Contribution

It introduces a new identity and characteristic function for matrix variate skew-normal distributions, facilitating stochastic ordering comparisons.

Findings

Derived an identity for expectations involving matrix variate skew-normal distributions.

Established the characteristic function for these distributions.

Provided necessary and sufficient conditions for distribution comparisons under six stochastic orders.

Abstract

We establish an identity for E f (Y) -E f (X), when X and Y both have matrix variateskew-normal distributions and the function f fulfills some weak conditions. Thecharacteristic function of matrix variate skew normal distribution is then derived. Finally,we make use of it to derive some necessary and sucient conditions for the comparisonof matrix variate skew-normal distributions under six di erent orders, such as usualstochastic order, convex order, increasing convex order, upper orthant order,directionally convex order and supermodular order.