  Representations of measures of concordance in terms of Pearson' s correlation
coefficient are studied. All transforms of random variables are characterized
such that the correlation coefficient of the transformed random variables is a
measure of concordance. Next, Gini' s gamma is generalized and it is shown that
the resulting generalized Gini' s gamma can be represented as a mixture of
measures of concordance that are Pearson' s correlation coefficients of
transformed random variables. As an application of this correlation mixture
representation of generalized Gini' s gamma, lower and upper bounds of the
compatible set of generalized Gini' s gamma, which is the collection of all
possible square matrices whose entries are pairwise bivariate generalized Gini'
s gammas, are derived.
