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

arXiv: https://arxiv.org/abs/1707.02247 · HTML: https://mlsanity.com/paper/1707.02247/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2017.

## Built on by (most cited first, 2 of 2)

- [Signal Recovery Using a Spiked Mixture Model](https://mlsanity.com/paper/2501.01840/) (2025)
- [Parsimonious Mixtures of Skewed Bilinear Factor Analyzers](https://mlsanity.com/paper/2607.14297/) (2026)

## Abstract (arXiv)

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.