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