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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

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.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:246-256
    DOI: 10.1016/j.jmva.2013.02.013
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    References listed on IDEAS

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    1. Ressel, Paul, 2011. "Monotonicity properties of multivariate distribution and survival functions -- With an application to Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 393-404, March.
    2. Genest, Christian & Rivest, Louis-Paul, 1989. "A characterization of gumbel's family of extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 207-211, August.
    3. Ressel, Paul, 2012. "Functions operating on multivariate distribution and survival functions—With applications to classical mean-values and to copulas," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 55-67.
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