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Families of copulas closed under the construction of generalized linear means

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  • Klein, Ingo
  • Christa, Florian

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.

Suggested Citation

  • Klein, Ingo & Christa, Florian, 2011. "Families of copulas closed under the construction of generalized linear means," FAU Discussion Papers in Economics 04/2011, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    • Handle: RePEc:zbw:iwqwdp:042011
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    References listed on IDEAS

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    1. Matthias Fischer & Ingo Klein, 2007. "Constructing Generalized FGM Copulas by Means of Certain Univariate Distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 243-260, February.
    2. Klein, Ingo & Fischer, Matthias J. & Pleier, Thomas, 2011. "Weighted power mean copulas: Theory and application," FAU Discussion Papers in Economics 01/2011, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
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    Cited by:

    1. Schnitzlein, Daniel D., 2012. "How important is cultural background for the level of intergenerational mobility?," Economics Letters, Elsevier, vol. 114(3), pages 335-337.

    More about this item

    Keywords

    copula; generalized linear means; Spearman's ρ; tail dependence;

    JEL classification:

    • F22 - International Economics - - International Factor Movements and International Business - - - International Migration
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J61 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Geographic Labor Mobility; Immigrant Workers

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