A Simpson Based Estimation Approach for the Overlapping Coefficient of k>=2 Normal Distributions

TL;DR

This paper introduces a novel Simpson's rule-based estimation method for calculating the overlapping coefficient among multiple normal distributions, addressing analytical and computational challenges in extending the measure beyond two populations.

Contribution

It proposes a flexible, consistent estimation framework for the overlapping coefficient of multiple normal distributions using Simpson's rule and maximum likelihood estimators.

Findings

Estimator performs well across various overlap scenarios

Advantages in low overlap situations

Method is computationally efficient and applicable to any number of populations

Abstract

The overlapping coefficient is a fundamental measure of similarity between probability distributions. While the case of two distributions has been extensively studied, extending this measure to multiple populations presents both analytical and computational challenges. In this paper, we propose a general estimation framework for the overlapping coefficient of k>=2 normal distributions. The method employs Simpsons numerical integration rule combined with plug-in maximum likelihood estimators of the normal parameters. The resulting estimator is shown to be consistent under standard regularity conditions. A Monte Carlo simulation study is conducted across various overlap scenarios and sample sizes. The results demonstrate that the proposed Simpson based estimator performs competitively for all overlap levels, with notable advantages in low overlap situations. This methodology offers a flexible and computationally efficient approach applicable to an arbitrary number of normal populations.