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Componentwise concave copulas and their asymmetry. (English) Zbl 1191.62095
Summary: The class of componentwise concave copulas is considered, with particular emphasis on their closure under some constructions of copulas (e.g., ordinal sums) and their relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the \(L^\infty\)-measure of non-exchangeability for copulas belonging to this class.

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
60E05 Probability distributions: general theory
60G09 Exchangeability for stochastic processes
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