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

Paul Ressel

Journal of Multivariate Analysis, 2013, vol. 117, issue C, 246-256

Abstract: 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.

Keywords: Homogeneous distribution; Classical mean value; Fully d-increasing; Co-survival function; Stable tail dependence function; Spectral representation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (29)

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DOI: 10.1016/j.jmva.2013.02.013

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