On a problem by Schweizer and Sklar (Q2907897)
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scientific article; zbMATH DE number 6076228
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a problem by Schweizer and Sklar |
scientific article; zbMATH DE number 6076228 |
Statements
4 September 2012
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copulas
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distributions with given marginals
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Fréchet--Hoeffding bounds
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partial mutual independence
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On a problem by Schweizer and Sklar (English)
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A representation of the class of all copulas is given where all \(m\)-dimensional marginals are independent. The condition essentially says that the conditional distributions of the copula given any \(m-1\) coordinates have uniform marginals. In general this condition is not easy to check, however several examples can be given. A related characterization result, formulated for copulas with densities w.r.t. the n-dimensional Lebesgue-measure, was given by the reviewer in Ann. Inst. Stat. Math. 37, 225--233 (1985; Zbl 0573.62045).NEWLINENEWLINE See also the book of \textit{B. Schweizer} and \textit{A. Sklar}, Probabilistic metric spaces. NY etc.: (1983; Zbl 0546.60010).
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