Numerical Integral Approximation to Estimate Matusita Overlapping Coefficient for Normal Distributions

Abstract

The overlapping coefficients are defined as the measures of similarity and agreement between two or more distributions. Estimation of the well-known overlapping coefficient; Matusita ρ under normal distributions is the main aim of this paper. Given that we have two independent random samples each following a normal distribution, a new method is proposed to estimate ρ without using any assumptions about the equality of the location or scale parameters. Three numerical integration methods are suggested and used to achieve our main objective. The maximum likelihood estimation method is used to estimate the interesting parameters. The properties of the resulting estimators are investigated and compared with some corresponding estimators that have been developed in the literature by using the simulation method. The simulation results show the effectiveness of the proposed technique over the existing ones for almost all considered cases in this study.