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Copulas, stable tail dependence functions, and multivariate monotonicity

Copulas, stable tail dependence functions, and multivariate monotonicity AbstractFor functions of several variables there exist many notions of monotonicity, three of them being characteristic for resp. distribution, survival and co-survival functions. In each case the “degree” of monotonicity is just the basic one of a whole scale.Copulas are special distribution functions, and stable tail dependence functions are special co-survival functions. It will turn out that for both classes the basic degree of monotonicity is the only one possible, apart from the (trivial) independence functions. As a consequence a “nesting” of such functions depends on particular circumstances. For nested Archimedean copulas the rather restrictive conditions known so far are considerably weakened. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

Copulas, stable tail dependence functions, and multivariate monotonicity

Dependence Modeling , Volume 7 (1): 12 – Jan 1, 2019

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Publisher
de Gruyter
Copyright
© 2019 Paul Ressel, published by De Gruyter
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2019-0013
Publisher site
See Article on Publisher Site

Abstract

AbstractFor functions of several variables there exist many notions of monotonicity, three of them being characteristic for resp. distribution, survival and co-survival functions. In each case the “degree” of monotonicity is just the basic one of a whole scale.Copulas are special distribution functions, and stable tail dependence functions are special co-survival functions. It will turn out that for both classes the basic degree of monotonicity is the only one possible, apart from the (trivial) independence functions. As a consequence a “nesting” of such functions depends on particular circumstances. For nested Archimedean copulas the rather restrictive conditions known so far are considerably weakened.

Journal

Dependence Modelingde Gruyter

Published: Jan 1, 2019

References