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.