Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution

Understand

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities.

• The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution.
• The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work.
• The final part of the paper specializes further to a form of multivariate skew $t$ density.