  The unified skew-t (SUT) is a flexible parametric multivariate distribution
that accounts for skewness and heavy tails in the data. A few of its properties
can be found scattered in the literature or in a parameterization that does not
follow the original one for unified skew-normal (SUN) distributions, yet a
systematic study is lacking. In this work, explicit properties of the
multivariate SUT distribution are presented, such as its stochastic
representations, moments, SUN-scale mixture representation, linear
transformation, additivity, marginal distribution, canonical form, quadratic
form, conditional distribution, change of latent dimensions, Mardia measures of
multivariate skewness and kurtosis, and non-identifiability issue. These
results are given in a parametrization that reduces to the original SUN
distribution as a sub-model, hence facilitating the use of the SUT for
applications. Several models based on the SUT distribution are provided for
illustration.
