A Mixture of Generalized Hyperbolic Distributions

TL;DR

This paper proposes a mixture model based on generalized hyperbolic distributions as a flexible alternative to Gaussian and t-distribution mixtures, with demonstrated effectiveness in clustering and data modeling.

Contribution

It introduces a novel mixture of generalized hyperbolic distributions, detailing parameter estimation and showcasing improved clustering performance over traditional models.

Findings

Successfully recovers parameters for Gaussian and skew-t data

Demonstrates superior clustering on simulated and real datasets

Provides a comprehensive framework for model-based clustering

Abstract

We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are predominant. The mathematical development of our mixture of generalized hyperbolic distributions model relies on its relationship with the generalized inverse Gaussian distribution. The latter is reviewed before our mixture models are presented along with details of the aforesaid reliance. Parameter estimation is outlined within the expectation-maximization framework before the clustering performance of our mixture models is illustrated via applications on simulated and real data. In particular, the ability of our models to recover parameters for data from underlying Gaussian and skew-t distributions is demonstrated. Finally, the role of Generalized hyperbolic mixtures within the wider model-based clustering, classification, and density estimation literature is discussed.