The centred parameterization and related quantities of the skew-tt distribution

The skew-tt family, in its univariate and multivariate versions, is a parametric family of probability distributions which is currently under intense investigation because of several appealing properties. The present paper addresses the question of the choice of its parameterization, and more generally of the selection of quantities of interest associated to this distribution.

► The skew-tt distribution represents a flexible family of multivariate densities.
► The problem of its parameterization more suitable for statistical work is examined.
► A natural proposal is the centred parameterization similarly to the skew-normal case.
► For low degrees of freedom, moments fail to exist, and a suitable variant is introduced.
► The asymptotic variance matrix of the proposed summary quantities is obtained.