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...

If X and Y are continuous random variables with joint distribution function H, then the Kendall distribution function of (X,Y) is the distribution function of the random variable H(X,Y). Kendall distribution functions arise in the study of stochastic orderings of random vectors. In this paper we...

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 study a wide class of bivariate copulas depending on two univariate functions which generalizes many known families of copulas. We measure the dependence of any copula of this class in different ways, exhibit several properties concerning symmetry, dependence concepts, and concordance...

We investigate some properties of the partially ordered sets of multivariate copulas and quasi-copulas. Whereas the set of bivariate quasi-copulas is a complete lattice, which is order-isomorphic to the Dedekind-MacNeille completion of the set of bivariate copulas, we show that this is not the...

Using the technique of finding bounds on sets of copulas with particular properties, we compare the distribution of an n-dimensional (n≥3) vector of continuous pairwise independent random variables to the distribution of a similar vector of mutually independent random variables. We examine the...

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.

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]...

This paper studies the problem of finding best-possible upper bounds on the Value-at-Risk for a function of two random variables when the marginal distributions are known and additional nonparametric information on the dependence structure, such as the value of a measure of association, is...