Unter verallgemeinerter Mittelwertbildung abgeschlossene Familien von Copulas

Ingo Klein

No 86/2010, Discussion Papers from Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics

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 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.

Keywords: copula; generalized linear means; Spearman's ρ; tail dependence (search for similar items in EconPapers)
Date: 2010
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:faucse:862010

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