Multivariate skewing mechanisms: A unified perspective based on the transformation approach

In recent years, models for (possibly multivariate) skewed distributions have become more and more popular. In the univariate case, Ferreira and Steel (2006) [Ferreira, J.T.A.S., Steel, M.F.J., 2006. A constructive representation of univariate skewed distributions. J. Amer. Statist. Assoc. 101, 823–829] introduced general skewing mechanisms in order to compare existing skewing methods in a common framework and to ease construction of new such methods according to the needs in given situations. In this paper, we make use of the classical transformation approach to define alternative skewing mechanisms for the same purpose. While keeping all the nice features of Ferreira and Steel’s skewing mechanisms (flexibility, surjectivity, the possibility of retaining prespecified characteristics of the original symmetric distribution, etc.), our skewing mechanisms, unlike theirs, can easily be extended to the multivariate case. We describe our skewing schemes, investigate their main properties, and illustrate their effects on standard (multi)normal distributions by means of a few examples. Finally, we briefly discuss their relevance in the context of optimal symmetry testing.