Parametric Families of Multivariate Distributions with Given Margins

Parametric families of continuous bivariate distributions with given margins that include independence and perfect positive dependence are compared on the basis on some important properties. Since many such families exist, the comparisons are helpful for deciding on suitable models for multivariate data. The study of the properties has motivation from applications in extreme value inference. One property considered for bivariate families is whether they extend to multivariate families, and extensions are given when possible. Several new bivariate and multivariate families are included and some open research problems in the area of multivariate families are mentioned.