# A Mixture of Generalized Hyperbolic Distributions

arXiv: https://arxiv.org/abs/1305.1036 · HTML: https://mlsanity.com/paper/1305.1036/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2013.

## Built on by (most cited first, 18 of 18)

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- [Generalized Fast Multichannel Nonnegative Matrix Factorization Based on Gaussian Scale Mixtures for Blind Source Separation](https://mlsanity.com/paper/2205.05330/) (2022)
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- [FiMReSt: Finite Mixture of Multivariate Regulated Skew-t Kernels -- A Flexible Probabilistic Model for Multi-Clustered Data with Asymmetrically-Scattered Non-Gaussian Kernels](https://mlsanity.com/paper/2305.09071/) (2023)
- [Finite Mixtures of Multivariate Poisson-Log Normal Factor Analyzers for Clustering Count Data](https://mlsanity.com/paper/2311.07762/) (2023)
- [FastManly: An EM-Gradient Algorithm for Manly Mixture Models](https://mlsanity.com/paper/2410.00848/) (2024)
- [Signal Recovery Using a Spiked Mixture Model](https://mlsanity.com/paper/2501.01840/) (2025)
- [Kernel-Based Anomaly Detection Using Generalized Hyperbolic Processes](https://mlsanity.com/paper/2501.15265/) (2025)
- [Cluster weighted models with multivariate skewed distributions for functional data](https://mlsanity.com/paper/2504.12683/) (2025)
- [Crowdsourcing Without People: Modelling Clustering Algorithms as Experts](https://mlsanity.com/paper/2509.25395/) (2025)
- [Parsimonious Mixtures of Skewed Bilinear Factor Analyzers](https://mlsanity.com/paper/2607.14297/) (2026)
- [Deep Skew-t Mixture Models](https://mlsanity.com/paper/2609.00773/) (2026)

## Abstract (arXiv)

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.