The space of D-norms revisited
The theory of D -norms is an offspring of multivariate extreme value theory. We present recent results on D -norms, which are completely determined by a certain random vector called generator. In the first part it is shown that the space of D -norms is a complete separable metric space, if equipped...
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Veröffentlicht in: | Extremes (Boston) 2015-03, Vol.18 (1), p.85-97 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | The theory of
D
-norms is an offspring of multivariate extreme value theory. We present recent results on
D
-norms, which are completely determined by a certain random vector called generator. In the first part it is shown that the space of
D
-norms is a complete separable metric space, if equipped with the Wasserstein-metric in a suitable way. Secondly, multiplying a generator with a doubly stochastic matrix yields another generator. An iteration of this multiplication provides a sequence of
D
-norms and we compute its limit. Finally, we consider a parametric family of
D
-norms, where we assume that the generator follows a symmetric Dirichlet distribution. This family covers the whole range between complete dependence and independence. |
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ISSN: | 1386-1999 1572-915X |
DOI: | 10.1007/s10687-014-0204-y |