Families of copulas closed under the construction of generalized linear means

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: IWQW Discussion Papers ; No. 04/2011

Classification and Topics

• Classification: Wirtschaft ; International Migration ; Wage Level and Structure; Wage Differentials ; Geographic Labor Mobility; Immigrant Workers
• Subject: copula ; generalized linear means ; Spearman's ρ ; tail dependence

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Klein, Ingo ; Christa, Florian
• Event: Veröffentlichung
• (who): Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW)
• (where): Nürnberg
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/44400
• Last update: 10.03.2025, 11:42 AM CET