Testing the equality of two coefficients of variation: a new Bayesian approach

The use of testing procedures for comparing two coefficients of variation (CVs) of independent populations is not extensively explored in the Bayesian context. We propose to address this issue through a test based on a measure of evidence, the Bayesian Discrepancy Measure, recently introduced in the literature. Computing the Bayesian Discrepancy Measure is straightforward when the CVs depend on a single parameter of the distribution. In contrast, it becomes more difficult when this simplification does not occur since more parameters are involved, requiring often the use of MCMC methods. We derive the Bayesian Discrepancy Measure and the related test by considering a variety of distribution assumptions with multiparametric CVs and apply them to real datasets. As far as we know, some of the examined problems have not yet been covered in the literature.