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Copulas, stable tail dependence functions, and multivariate monotonicity

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  • Ressel Paul

    (Kath. Universität Eichstätt-Ingolstadt)

Abstract

For 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.

Suggested Citation

  • Ressel Paul, 2019. "Copulas, stable tail dependence functions, and multivariate monotonicity," Dependence Modeling, De Gruyter, vol. 7(1), pages 247-258, January.
    • Handle: RePEc:vrs:demode:v:7:y:2019:i:1:p:247-258:n:13
    DOI: 10.1515/demo-2019-0013
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    References listed on IDEAS

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    1. Mai, Jan-Frederik & Scherer, Matthias, 2012. "H-extendible copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 151-160.
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    5. Hering, Christian & Hofert, Marius & Mai, Jan-Frederik & Scherer, Matthias, 2010. "Constructing hierarchical Archimedean copulas with Lévy subordinators," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1428-1433, July.
    6. Ressel, Paul, 2013. "Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 246-256.
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