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Title:Families of copulas closed under the construction of generalized linear means PDF Logo
Authors:Klein, Ingo
Christa, Florian
Issue Date:2011
Series/Report no.:IWQW discussion paper series 04/2011
Abstract: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 generation 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
JEL:F22
J31
J61
Document Type:Working Paper
Appears in Collections:IWQW Discussion Paper Series, FAU Erlangen-Nürnberg

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