Enhancing parameter estimation in finite mixture of generalized normal distributions

TL;DR

This paper presents an improved expectation conditional maximization algorithm with adaptive step size for better parameter estimation in finite mixtures of generalized normal distributions, addressing numerical issues and enhancing fit quality.

Contribution

Introduces a novel EM-based algorithm with adaptive Newton-Raphson updates and modified stopping criteria for MGND parameter estimation.

Findings

Algorithm effectively overcomes numerical and degeneracy issues.

Superior goodness-of-fit compared to normal and Student-t mixtures.

Performs well with high shape parameters, overlaps, and small samples.

Abstract

Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex, presenting the risk of numerical and degeneracy issues. This study introduced an expectation conditional maximization algorithm that includes an adaptive step size function within Newton-Raphson updates of the shape parameter and a modified criterion for stopping the EM iterations. Through extensive simulations, the effectiveness of the proposed algorithm in overcoming the limitations of existing approaches, especially in scenarios with high shape parameter values, high parameters overalp and low sample sizes, is shown. A detailed comparative analysis with a mixture of normals and Student-t distributions revealed that the MGND model exhibited superior goodness-of-fit performance when used to fit the density of the returns of 50 stocks belonging to the Euro Stoxx index.