  In this paper, we present an algorithm for the fitting of a location-scale
variant of the canonical fundamental skew t (CFUST) distribution, a superclass
of the restricted and unrestricted skew t-distributions. In recent years, a few
versions of the multivariate skew $t$ (MST) model have been put forward,
together with various EM-type algorithms for parameter estimation. These
formulations adopted either a restricted or unrestricted characterization for
their MST densities.
  In this paper, we examine a natural generalization of these developments,
employing the CFUST distribution as the parametric family for the component
distributions, and point out that the restricted and unrestricted
characterizations can be unified under this general formulation. We show that
an exact implementation of the EM algorithm can be achieved for the CFUST
distribution and mixtures of this distribution, and present some new analytical
results for a conditional expectation involved in the E-step.
