Evaluating methods for addressing skewness in clustering: a focus on generalized hyperbolic mixture models

Publication Date

8-13-2025

Document Type

Article

Publication Title

Journal of Statistical Computation and Simulation

Volume

95

Issue

12

DOI

10.1080/00949655.2025.2502535

First Page

2643

Last Page

2658

Abstract

In model-based clustering, the population is assumed to be a combination of sub-populations. Typically, each sub-population is modeled by a mixture model component, distributed according to a known probability distribution. Each component is considered a cluster. Two primary approaches have been used in the literature when clusters are skewed: (1) transforming the data within each cluster and applying a mixture of symmetric distributions to the transformed data, and (2) directly modeling each cluster using a skewed distribution. Among skewed distributions, the generalized hyperbolic distribution is notably flexible and includes many other known distributions as special or limiting cases. This paper achieves two goals. First, it extends the flexibility of transformation-based methods as outlined in approach (1) by employing a flexible symmetric generalized hyperbolic distribution to model each transformed cluster. This innovation results in the introduction of two new models, each derived from distinct within-cluster data transformations. Second, the paper benchmarks the approaches listed in (1) and (2) for handling skewness using both simulated and real data. The findings highlight the necessity of both approaches in varying contexts.

Funding Number

2209974

Funding Sponsor

National Science Foundation

Keywords

benchmarking, finite mixture models, Generalized hyperbolic distribution, manly transformation, power transformation

Department

Mathematics and Statistics

Link to Full Text

Share

COinS