Concordance and Gini's measure of association

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