We show that Spearman's rho is a measure of average positive (and negative) quadrant dependence, and that Kendall's tau is a measure of average total positivity (and reverse regularity) of order two.

We study a method, which we call a copula (or quasi-copula) diagonal splice, for creating new functions by joining portions of two copulas (or quasi-copulas) with a common diagonal section. The diagonal splice of two quasi-copulas is always a quasi-copula, and we find a necessary and sufficient...

We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H1 and H2, i.e., the distribution function of the random variable H1(X,Y) given that the joint distribution function of the random variables X and Y is H2. We study the case when H1 and...

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]...