  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.
