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Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. (Archimedean copulas and families of bivariate laws with given marginals). (French) Zbl 0605.62049
A distribution function H on [0,1]$$\times [0,1]$$ with uniform marginals is called ”Archimedean” if it is of the form $$H(x,y)=\phi^{-1}(\phi (x)+\phi (y))$$ for some continuous, strictly decreasing and convex function $$\phi$$ : [0,1]$$\to [0,\infty]$$. The authors discuss some examples for parametric families of Archimedean distribution functions, where the parameter is related to the dependence properties of the distributions. They, furthermore, characterize the property that a limit H of a sequence of Archimedean df’s again is Archimedean.
Reviewer: L.Rüschendorf

##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 26A48 Monotonic functions, generalizations
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##### References:
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