A short review of multivariate t-distribution

This paper reviews most important properties of a location-scale multivariate
t-distribution. A conditional representation of the distribution is exploited to
outline moments, characteristic function, marginal and conditional distributions,
distribution of linear combinations and quadratic forms. Stochastic representation
is also used to determine the covariance matrix of the distribution. It also
makes an attempt to justify an uncorrelated t– model and overviews distribution
of the sum of products matrix and correlation matrix. Estimation strategies for
parameters of the model is briefly discussed. Finally the recent trend of linear
regression with the uncorrelated t– model is discussed.