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A framework for positive dependence. (English) Zbl 0701.62061
The authors define the abstract concept of a positive dependence ordering (PDO) on the set of bivariate distributions. The class of all distributions which are larger w.r.t. a PDO than the product measure then satisfies some properties which are called positive dependence properties (PDP). The authors ask whether one can generate the class of associated distributions by a PDO. Monotone functions w.r.t. PDO’s are called measures of positive dependence (MPD). Some examples are discussed.
Reviewer: L.Rüschendorf

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E15 Inequalities; stochastic orderings