Characterizing and generating bivariate empirical rank distributions satisfying certain positive dependence concepts

This article introduces an approach for characterizing the classes of empirical distributions that satisfy certain positive dependence notions. Mathematically, this can be expressed as studying certain subsets of the class SN of permutations of 1, ., N, where each subset corresponds to some positive dependence notions. Explicit techniques for it-eratively characterizing subsets of SN that satisfy certain positive dependence concepts are obtained and various counting formulas are given. Based on these techniques, graph-theoretic methods are used to introduce new and more efficient algorithms for constructively generating and enumerating the elements of various of these subsets of SN. For example, the class of positively quadrant dependent permutations in SN is characterized in this fashion.