Comparison of two coefficients of variation: a new Bayesian approach

TL;DR

This paper introduces a Bayesian approach to compare the equality of coefficients of variation from two independent populations, addressing computational challenges with multi-parameter distributions and applying the method to real data.

Contribution

It develops a new Bayesian Discrepancy Measure for coefficients of variation involving multiple parameters, expanding the methodology beyond single-parameter cases.

Findings

The Bayesian measure effectively compares coefficients of variation across distributions.

Application to real data demonstrates practical utility.

Some problems addressed are novel in the literature.

Abstract

The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of variation from two independent populations. In order to do this we rely on the Bayesian Discrepancy Measure recently introduced in the literature. Computing this Bayesian measure of evidence is straightforward when the coefficient of variation is a function of a single parameter of the distribution. In contrast, it becomes difficult when it is a function of more parameters, often requiring the use of MCMC methods. We calculate the Bayesian Discrepancy Measure by considering a variety of distributions whose coefficients of variation depend on more than one parameter. We consider also applications to real data. As far as we know, some of the examined problems have not yet been covered in the literature.