Gaussian Mixtures with common Variance

Abstract

The interest in Gaussian mixtures has grown significantly in recent years, primarily owing to their adaptability and widespread applications across various fields of knowledge. A specific category within these mixtures is Gaussian mixtures with common variance, wherein the assumption is made that the variances of all subpopulations are equal. This study delves Gaussian location mixtures family, exploring their applications, characterizations, and the challenges associated with estimation. Following this, we introduce an approximation to the beta distribution. When addressing scenarios involving two subpopulations, a novel test for equality of variances is proposed, employing the beta distribution approximation. This paper presents a new test for variance equality which is a novelty in the Gaussian mixture context. Practical applications for the proposed test are provided and discussed.