Estimation of Matusita Overlapping Coefficient p for Pair Normal Distributions

Abstract

The Matusita overlapping coefficient ρ is defined as agreement or similarity between two or more distributions. The parametric normal distribution is one of the most important statistical distributions. Under the assumption that the data at hand follow two independent normal distributions, this paper suggests a new technique to estimate the Matusita coefficient ρ. In contrast to the studies in the literature, the suggested technique requires no assumptions on the location and scale parameters of the normal distributions. The finite properties of the resulting estimators are investigated and compared with the nonparametric kernel estimators and with some existing estimators via simulation techniques. The results show that the performance of the proposed estimators is better than the kernel estimators for all considered cases.

Key words and phrases. Matusita Overlapping Coefficient; Maximum Likelihood Method; Parametric Method; Normal Distribution; Relative Bias and Relative Mean Square Error.

2000 Mathematics Subject Classification. 40H05, 46A45