On the exact region determined by Spearman’s footrule and Gini’s gamma

A concordance measure is often a better way to model dependence than Pearson’s correlation coefficient since it is invariant with respect to monotone increasing transformations of the random variables. In this paper, we focus on the relationships between Gini’s gamma and Spearman’s footrule. We establish the exact region determined by them. We also present copulas where the bounds of the region are attained. We introduce the concordance similarity measure and compute it for all pairs of (weak) concordance measures for which the exact regions determined by them are known.