# A Matrix Variate Skew-t Distribution

## TL;DR

This paper introduces a matrix variate skew-t distribution derived from a mean-variance matrix normal mixture, along with an EM algorithm for parameter estimation, addressing a gap in modeling three-way data.

## Contribution

It proposes the first matrix variate skew-t distribution and an associated estimation algorithm, expanding skewness modeling in three-way data analysis.

## Key findings

- Demonstrates the distribution's applicability through simulations
- Provides an EM algorithm for efficient parameter estimation
- Addresses the lack of skew-t models in matrix variate settings

## Abstract

Although there is ample work in the literature dealing with skewness in the multivariate setting, there is a relative paucity of work in the matrix variate paradigm. Such work is, for example, useful for modelling three-way data. A matrix variate skew-t distribution is derived based on a mean-variance matrix normal mixture. An expectation-conditional maximization algorithm is developed for parameter estimation. Simulated data are used for illustration.