Overlap coefficients based on Kullback-Leibler divergence: Exponential populations case

Hamza Dhaker,Malick Mbodj,Papa Ngom

doi:10.14419/ijamr.v6i4.8493

Abstract

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure ∆. A new overlap measure Λ based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefficients also are presented. Taylor series approximation are used to construct confidence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

Highlights

The similarity between two densities can be considered as the commonality shared by both populations
Mulekar and Mishra [14] simulated the sampling distribution of estimators of the overlap measures when the two densities correspond to the normal case with equal means and obtained the approximate expressions for the bias and variance of their estimators
Smith [20] derived approximate formulas using the delta method for estimating the mean and variance of the discrete version of one such measure known as Weitzman's measure D(Weitzman [21])

Summary

Introduction

The similarity between two densities can be considered as the commonality shared by both populations. Mishra et al [12] gave the small and large sample properties of the sampling distributions for a function of this overlap measure estimator, under the assumption of homogeneity of variances for the case of two normal distributions. Mulekar and Mishra [14] simulated the sampling distribution of estimators of the overlap measures when the two densities correspond to the normal case with equal means and obtained the approximate expressions for the bias and variance of their estimators. Smith [20] derived approximate formulas using the delta method for estimating the mean and variance of the discrete version of one such measure known as Weitzman's measure D(Weitzman [21]) ( known as the overlap coefcient).

Overlap Coefcients

Bias and Variance of Estimates

Condence Interval Eestimation of Overlap

Simulation Study

Conclusion