Comment on "On Nomenclature, and the Relative Merits of Two Formulations of Skew Distributions" by A. Azzalini, R. Browne, M. Genton, and P. McNicholas

TL;DR

This paper clarifies the distinctions between two skew distribution models, discusses improved results for the unrestricted model, and highlights the flexibility of the CFUST class for data modeling.

Contribution

It corrects a nomenclature misunderstanding and emphasizes the advantages of the CFUST class over restricted and unrestricted models.

Findings

Improved results for the unrestricted skew t-distribution.

The CFUST class includes both models as special cases.

Users can choose the most appropriate model based on data.

Abstract

We comment on the recent paper by Azzalini et al. (2015) on two different distributions proposed in the literature for the modelling of data that have asymmetric and possibly long-tailed clusters. They are referred to as the restricted and unrestricted skew normal and skew t-distributions by Lee and McLachlan (2013a). We clarify an apparent misunderstanding in Azzalini et al.(2015) of this nomenclature to distinguish between these two models. Also, we note that McLachlan and Lee (2014) have obtained improved results for the unrestricted model over those reported in Azzalini et al. (2015) for the two datasets that were analysed by them to form the basis of their claimson the relative superiority of the restricted and unrestricted models. On this matter of the relative superiority of these two models, Lee and McLachlan (2014b, 2016) have shown how a distribution belonging to the broader class, the canonical fundamental skew t (CFUST) class, can be fitted with little additional computational effort than for the unrestricted distribution. The CFUST class includes the restricted and unrestricted distributions as special cases. Thus the user now has the option of letting the data decide as to which model is appropriate for their particular dataset.