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

We establish an identity for $$Ef\left( \varvec{Y}\right) - Ef\left( \varvec{X}\right) $$ , when $$\varvec{X}$$ and $$\varvec{Y}$$ both have matrix variate skew-normal distributions the function f satisfies some weak conditions. The characteristic of skew normal distribution is then derived. make use it to derive necessary sufficient conditions comparison under six different orders, such as usual stochastic order, convex increasing upper orthant directionally order supermodular order.