Robust mixture modelling using sub-Gaussian stable distribution
This work addresses robust statistical modelling for data with outliers, but it is incremental as it builds on existing sub-Gaussian stable distribution methods.
The authors tackled robust mixture modelling by introducing an expectation maximization algorithm for mixtures of sub-Gaussian stable distributions, showing improved robustness and performance in comparative studies on simulated and real data.
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 $α$-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 $α$-stable distributions for modelling, simulated, synthetic, and real data.