Hidden Truncation Hyperbolic Distributions, Finite Mixtures Thereof, and Their Application for Clustering

TL;DR

This paper introduces the hidden truncation hyperbolic (HTH) distribution and its finite mixtures, providing new theoretical insights and demonstrating their effectiveness for clustering tasks.

Contribution

The paper develops the HTH distribution, proves the identifiability of its finite mixtures, and explores their application in clustering with theoretical and practical illustrations.

Findings

The HTH distribution has a valid density and hierarchical representation.

Finite mixtures of HTH are identifiable.

Applications demonstrate improved clustering performance.

Abstract

A hidden truncation hyperbolic (HTH) distribution is introduced and finite mixtures thereof are applied for clustering. A stochastic representation of the HTH distribution is given and a density is derived. A hierarchical representation is described, which aids in parameter estimation. Finite mixtures of HTH distributions are presented and their identifiability is proved. The convexity of the HTH distribution is discussed, which is important in clustering applications, and some theoretical results in this direction are presented. The relationship between the HTH distribution and other skewed distributions in the literature is discussed. Illustrations are provided --- both of the HTH distribution and application of finite mixtures thereof for clustering.