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Functions operating on multivariate distribution and survival functions—With applications to classical mean-values and to copulas

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  • Ressel, Paul

Abstract

Functions operating on multivariate distribution and survival functions are characterized, based on a theorem of Morillas, for which a new proof is presented. These results are applied to determine those classical mean values on [0,1]n which are distribution functions of probability measures on [0,1]n. As it turns out, the arithmetic mean plays a universal rôle for the characterization of distribution as well as survival functions. Another consequence is a far reaching generalization of Kimberling’s theorem, tightly connected to Archimedean copulas.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:55-67
    DOI: 10.1016/j.jmva.2011.08.007
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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. Ressel, Paul, 2011. "A revision of Kimberling's results -- With an application to max-infinite divisibility of some Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 207-211, February.
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    Cited by:

    1. Ressel Paul, 2018. "A multivariate version of Williamson’s theorem, ℓ-symmetric survival functions, and generalized Archimedean copulas," Dependence Modeling, De Gruyter, vol. 6(1), pages 356-368, December.
    2. Ressel Paul, 2023. "Functions operating on several multivariate distribution functions," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-11, January.
    3. Ressel Paul, 2022. "Stable tail dependence functions – some basic properties," Dependence Modeling, De Gruyter, vol. 10(1), pages 225-235, January.
    4. 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.
    5. Mercadier Cécile & Ressel Paul, 2021. "Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application," Dependence Modeling, De Gruyter, vol. 9(1), pages 179-198, January.
    6. Ressel Paul, 2019. "Copulas, stable tail dependence functions, and multivariate monotonicity," Dependence Modeling, De Gruyter, vol. 7(1), pages 247-258, January.

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