Comment on "Hidden truncation hyperbolic distributions, finite mixtures thereof and their application for clustering" Murray, Browne, and \McNicholas

TL;DR

This paper provides a critical commentary on the work of Murray, Browne, and McNicholas regarding hidden truncation hyperbolic distributions, clarifying misconceptions and discussing their properties in the context of mixture models.

Contribution

It clarifies and corrects previous claims about the relationship between CFUST and HTH distributions, and discusses other aspects needing clarification.

Findings

Corrected the claim that CFUST is a special case of HTH

Clarified properties of HTH distributions in mixture models

Identified areas needing further clarification in the original work

Abstract

We comment on the paper of Murray, Browne, and McNicholas (2017), who proposed mixtures of skew distributions, which they termed hidden truncation hyperbolic (HTH). They recently made a clarification (Murray, Browne, McNicholas, 2019) concerning their claim that the so-called CFUST distribution is a special case of the HTH distribution. There are also some other matters in the original version of the paper that were in need of clarification as discussed here.