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...

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...