The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Frechet-Hoeffding inequality: If H denotes the joint distribution function of random variables X and Y whose margins are F and G, respectively, then...

The copula for a bivariate distribution functionH(x, y) with marginal distribution functionsF(x) andG(y) is the functionCdefined byH(x, y)=C(F(x), G(y)).Cis called Archimedean ifC(u, v)=[phi]-1([phi](u)+[phi](v)), where[phi]is a convex decreasing continuous function on (0, 1]...