Finite mixture of skewed sub-Gaussian stable distributions

TL;DR

This paper introduces a finite mixture model based on skewed sub-Gaussian stable distributions, offering a robust alternative for clustering data with heavy tails, and demonstrates its effectiveness through simulations and real data applications.

Contribution

It presents a novel finite mixture model with skewed sub-Gaussian stable distributions and an EM algorithm for parameter estimation, extending existing models like normal and skewed normal mixtures.

Findings

Model effectively captures heavy-tailed data.

Outperforms traditional models in clustering robustness.

Demonstrated success on simulated and real datasets.

Abstract

We propose the finite mixture of skewed sub-Gaussian stable distributions. The maximum likelihood estimator for the parameters of proposed finite mixture model is computed through the expectation-maximization algorithm. The proposed model contains the finite mixture of normal and skewed normal distributions. Since the tails of proposed model is heavier than even the Student's t distribution, it can be used as a powerful model for robust model-based clustering. Performance of the proposed model is demonstrated by clustering simulation data and two sets of real data.