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\(L^{\infty }\)-measure of non-exchangeability for bivariate extreme value and Archimax copulas. (English) Zbl 1191.62094
Summary: In the class of bivariate extreme value copulas, an upper bound is calculated for the measure of non-exchangeability \(\mu _{\infty }\) based on the \(L^{\infty }\)-norm distance between a copula \(C\) and its transpose \(C^t(x,y)=C(y,x)\). Copulas that are maximally non-exchangeable with respect to \(\mu _{\infty }\) are also determined. Moreover, similar upper bounds are given, respectively, for the class of all EV copulas having a fixed upper tail dependence coefficient and for the larger class of Archimax copulas.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
60G09 Exchangeability for stochastic processes
Software:
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