Kernel Method for Estimating Matusita Overlapping Coefficient Using Numerical Approximations

Abstract

In this paper, a nonparametric kernel method is introduced to estimate the well-known overlapping coefficient, Matusita \(\rho (X,Y)\), between two random variables \(X\) and \(Y\). Due to the complexity of finding the formula expression of this coefficient when using the kernel estimators, we suggest to use the numerical integration method to approximate its integral as a first step. Then the kernel estimators were combined with the new approximation to formulate the proposed estimators. Two numerical integration rules known as trapezoidal and Simpson rules were used to approximate the interesting integral. The proposed technique produces two new estimators for \(\rho (X,Y)\). The resulting estimators are studied and compared with existing estimator developed by Eidous and Al-Talafheh (Commun Stat Simul Comput 51(9):5139–5156, 2022. https://doi.org/10.1080/03610918.2020.1757711) via Monte-Carlo simulation technique. The simulation results demonstrated the usefulness and effectiveness of the new technique for estimating \(\rho (X,Y)\).