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

Homogeneous distributions on R+d and on R¯+d∖︀{∞¯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.

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Year of publication:	2013
Authors:	Ressel, Paul
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 117.2013, C, p. 246-256
Publisher:	Elsevier
Subject:	Homogeneous distribution \| Classical mean value \| Fully d-increasing \| Co-survival function \| Stable tail dependence function \| Spectral representation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011041967