Functions operating on multivariate distribution and survival functions—With applications to classical mean-values and to copulas |
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Authors: | Paul Ressel |
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Institution: | Katholische Universität Eichstätt-Ingolstadt, Ostenstraße 28, 85072 Eichstätt, Germany |
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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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Keywords: | 60E05 62H05 26A48 |
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