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The unwalked path between quasi-copulas and copulas: stepping stones in higher dimensions. (English) Zbl 1401.62078

Summary: We show that as the dimensionality increases, more and more interesting classes of operations can be identified between the class of \(n\)-quasi-copulas and the class of \(n\)-copulas. One such class is the class of supermodular \(n\)-quasi-copulas. We observe that some properties of 2-copulas that cannot be generalized to higher-dimensional copulas, hold true for supermodular \(n\)-quasi-copulas. Additionally, we show that trying to generalize a volume-based characterization of bivariate copulas to higher dimensions, results in a restrictive class of \(n\)-quasi-copulas.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
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