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Homogeneous distributions — and a spectral representation of classical mean values and stable tail dependence functions

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Ressel, Paul:
Homogeneous distributions — and a spectral representation of classical mean values and stable tail dependence functions.
In: Journal of multivariate analysis. 117 (2013). - S. 246-256.
ISSN 0047-259x ; 1095-7243

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Kurzfassung/Abstract

Homogeneous distributions on Rd+ and on Rd+ r {∞d} are shown to be Bauer simplices when normalized. This is used to provide spectral representations for the classical power mean values Mt(x) which turn out to be unique mixtures of the functions x −→ mini≤d(aixi) for t ≤ 1 (with some gaps depending on the dimension d), resp. x −→ maxi≤d(aixi) for t ≥ 1 (without gaps), where ai ≥ 0.
There exists a very close connection with so-called stable tail dependence functions of multivariate extreme value distributions. Their characterization by Hofmann (2009) [7] is improved by showing that it is not necessary to assume the triangle inequality — which instead can be deduced.

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Publikationsform:Artikel
Schlagwörter:Homogeneous distribution ; Classical mean value ; Fully d-increasing ; Co-survival function ; Stable tail dependence function ; Spectral representation
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Stochastik (bis 2016)
Peer-Review-Journal:Ja
Verlag:Elsevier
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Ja
KU.edoc-ID:13875
Eingestellt am: 17. Dez 2013 07:57
Letzte Änderung: 10. Jun 2016 11:10
URL zu dieser Anzeige: https://edoc.ku.de/id/eprint/13875/
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