In this paper, we provide a new family of trivariate proper quasi-copulas. As an application, we show that W3 - the best-possible lower bound for the set of trivariate quasi-copulas (and copulas) - is the limit member of this family, showing how the mass of W3 is distributed on the plane x+y+z=2 of [0,1]3 in an easy manner, and providing the generalization of this result to n dimensions.
In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.
In this paper we study some properties of the distribution function of the random variable C(X,Y) when the copula of the random pair (X,Y) is M (respectively, W) - the copula for which each of X and Y is almost surely an increasing (respectively, decreasing) function of the other -, and C is any copula. We also study the distribution functions of M(X,Y) and W(X,Y) given that the joint distribution function of the random variables X and Y is any copula.
We study a wide class of copulas which generalizes well-known families of copulas, such as the semilinear copulas. We also study corresponding results for the case of quasi-copulas.
We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.