# Robust mixture modelling using sub-Gaussian stable distribution

## TL;DR

This paper introduces an EM algorithm for mixture models based on sub-Gaussian stable distributions, demonstrating robustness and effectiveness in modeling heavy-tailed data across various datasets.

## Contribution

It presents a novel EM algorithm for parameter estimation in mixtures of sub-Gaussian stable distributions, a computationally tractable subclass of stable distributions.

## Key findings

- The proposed model shows robustness in heavy-tailed data scenarios.
- It outperforms some existing mixture models in simulations and real data.
- The approach is effective for synthetic, simulated, and real datasets.

## Abstract

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that estimates parameters of a mixture of sub-Gaussian stable distributions. A comparative study, in the presence of some well-known mixture models, is performed to show the robustness and performance of the mixture of sub-Gaussian $\alpha$-stable distributions for modelling, simulated, synthetic, and real data.