# Overlap Coefficients Based on Kullback-Leibler Divergence: Exponential Populations Case

## TL;DR

This paper introduces a new overlap coefficient based on Kullback-Leibler divergence for exponential populations, compares it with existing measures, and discusses statistical inference methods including confidence intervals and estimator properties.

## Contribution

A novel overlap measure $ ext{ extLambda}$ based on Kullback-Leibler divergence is proposed for exponential populations, along with inference techniques and property analyses.

## Key findings

- The new measure $ ext{ extLambda}$ is invariant and effective.
- Confidence intervals for overlap measures are constructed using Taylor series.
- Simulation studies evaluate bias and mean square error of estimators.

## Abstract

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita's measure $\rho$, Morisita's measure $\lambda$ and Weitzman's measure $\Delta$. A new overlap measure $\Lambda$ 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.