# Three Skewed Matrix Variate Distributions

## TL;DR

This paper introduces three new matrix variate skew distributions, extending the normal distribution to better model three-way data with skewness and flexibility, including parameter estimation and simulation.

## Contribution

It presents three novel matrix variate skew distributions, their properties, and methods for parameter estimation, filling a gap in the modeling of skewed three-way data.

## Key findings

- Derived moment generating functions for the distributions.
- Presented maximum likelihood estimation methods.
- Illustrated with simulated data.

## Abstract

Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix variate distributions that incorporate skewness, as well as other flexible properties such as concentration, are discussed. Equivalences to multivariate analogues are presented, and moment generating functions are derived. Maximum likelihood parameter estimation is discussed, and simulated data is used for illustration.