An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normal Distribution with Applications to Associated Stochastic Orderings
Tong Pu , Narayanaswamy Balakrishnan , Chuancun Yin
Communications in Mathematics and Statistics ›› 2023, Vol. 11 ›› Issue (3) : 629 -647.
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 and the function f satisfies some weak conditions. The characteristic function of matrix variate skew normal distribution is then derived. We then make use of it to derive some necessary and sufficient conditions for the comparison of matrix variate skew-normal distributions under six different orders, such as usual stochastic order, convex order, increasing convex order, upper orthant order, directionally convex order and supermodular order.
Characteristic function / Integral order / Matrix variate skew-normal distributions / Stochastic comparisons
/
| 〈 |
|
〉 |