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Title:Unter verallgemeinerter Mittelwertbildung abgeschlossene Familien von Copulas PDF Logo
Authors:Klein, Ingo
Issue Date:2010
Series/Report no.:Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 86/2010
Abstract (Translated):We will identify sufficient and partly necessary conditions for a family of copulas to be closed under the construction of generalized linear mean values. These families of copulas generalize results well-known from the literature for the Farlie-Gumbel-Morgenstern (FGM), the Ali-Mikhai-Haq (AMH) and the Barnett-Gumbel (BG) families of copulas closed under weighted linear, harmonic and geometric mean. For these generalizations we calculate the range of Spearman's ρ depending on the choice of weights α, the copulas generating function φ and the exponent γ determining what kind of mean value will be considered. It seems that FGM and AMH generating function φ(υ) = 1 - υ maximizes the range of Spearman's ρ. Furthermore, it will be shown that the considered families of copulas closed under the construction of generalized linear means have no tail dependence in the sense of Ledford & Tawn.
Subjects:copula
generalized linear means
Spearman's ρ
tail dependence
Document Type:Working Paper
Appears in Collections:Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg

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