On Inference of Weitzman Overlapping Coefficient in Two Weibull Distributions

TL;DR

This paper investigates the estimation of the Weitzman overlapping coefficient between two Weibull distributions, emphasizing its importance and analyzing estimator bias and error through simulation.

Contribution

It introduces a method to estimate the Weitzman coefficient for Weibull distributions without parameter restrictions and evaluates its performance.

Findings

Estimator shows low bias in simulations

Relative mean square error is acceptable

Highlights importance of accurate overlap measurement

Abstract

Studying overlapping coefficients has recently become of great benefit, especially after its use in goodness-of-fit tests. These coefficients are defined as the amount of similarity between two statistical distributions. This research examines the estimation of one of these overlapping coefficients, which is the Weitzman coefficient {\Delta}, assuming two Weibull distributions and without using any restrictions on the parameters of these distributions. We studied the relative bias and relative mean square error of the resulting estimator by implementing a simulation study. The results show the importance of the resulting estimator.