Constrained mixtures of generalized normal distributions

TL;DR

This paper introduces a family of constrained mixture models of generalized normal distributions, improving parameter estimation accuracy and interpretability, especially for overlapping components and complex data.

Contribution

It proposes a novel constrained mixture model framework with an ECM algorithm, enhancing interpretability and efficiency over existing models.

Findings

Constrained models outperform unconstrained mixtures in parameter estimation.

They effectively capture distribution characteristics like kurtosis.

On real data, they outperform normal and Student's t mixture models.

Abstract

This work introduces a family of univariate constrained mixtures of generalized normal distributions (CMGND) where the location, scale, and shape parameters can be constrained to be equal across any subset of mixture components. An expectation conditional maximisation (ECM) algorithm with Newton-Raphson updates is used to estimate the model parameters under the constraints. Simulation studies demonstrate that imposing correct constraints leads to more accurate parameter estimation compared to unconstrained mixtures, especially when components substantially overlap. Constrained models also exhibit competitive performance in capturing key characteristics of the marginal distribution, such as kurtosis. On a real dataset of daily stock index returns, CMGND models outperform constrained mixtures of normals and Student's t distributions based on the BIC criterion, highlighting their flexibility in modelling nonnormal features. The proposed constrained approach enhances interpretability and can improve parametric efficiency without compromising distributional flexibility for complex data.