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

摘要

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