On Inference of Overlapping Coefficients in Two Inverse Lomax Populations

TL;DR

This paper explores methods to estimate the similarity between two inverse Lomax distributions using measures like Matusita's, Weitzman's, and Kullback-Leibler based overlap, comparing point and Bayesian estimators through simulations and real data.

Contribution

It introduces estimation techniques for overlap measures between inverse Lomax populations, including Bayesian methods, and evaluates their performance via simulation and real data.

Findings

Bayesian estimators show lower bias in simulations.

Point estimators have higher mean square error.

Overlap measures effectively quantify distribution similarity.

Abstract

Overlapping coefficient is a direct measure of similarity between two distributions which is recently becoming very useful. This paper investigates estimation for some well-known measures of overlap, namely Matusita's measure $\rho$, Weitzman's measure $\Delta$ and $\Lambda$ based on Kullback-Leibler. Two estimation methods considered in this study are point estimation and Bayesian approach. Two Inverse Lomax populations with different shape parameters are considered. The bias and mean square error properties of the estimators are studied through a simulation study and a real data example.