Concordance and Gini's measure of association

We study the relationship between concordance and the population version γ of Gini's rank correlation coefficient. For a pair {X, Y) of continuous random variables, we show that γ is a function of probabilities of concordance and discordance between (X, Y) and pairs with the same margins but whose joint distributions are the Fréchet upper and lower bounds. We also show that γ depends only on the diagonal and secondary diagonal sections of the copula of (X, Y) and present corresponding results for the sample statistic.