  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.
