Parameter Estimation for a Mixture of Two Univariate Gaussian Distributions: A Comparative Analysis of The Proposed and Maximum Likelihood Methods

Two approaches to parameter estimation for a mixture of two univariate Gaussian distributions are numerically compared. The proposed method (PM) is based on decomposing a continuous function into its odd and even components and estimating them as polynomials, the other is the usual maximum likelihood (ML) method via the expected maximisation (EM) algorithm. An overlapped mixture of two univariate Gaussian distributions is simulated. The PM and ML are used to re-estimate the known mixture model parameters and the measure of performance is the absolute percentage error. The PM produces comparable results to those of to the ML approach. Given that the PM produces good estimates, and knowing that the ML always converges given good initial guess values (IGVs), it is thus recommended that the PM be used symbiotically with the ML to provide IGVs for the EM algorithm.