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A new class of bivariate copulas: dependence measures and properties


  • Hakim Bekrizadeh

    () (Payam-e-Noor University)

  • Babak Jamshidi

    () (Shahid Chamran University)


Abstract In this paper, we propose a new class of bivariate Farlie–Gumbel–Morgenstern (FGM) copula. This class includes some known extensions of FGM copulas. Some general formulas for well-known association measures of this class are obtained, and various properties of the proposed model are studied. The tail dependence range of the new class is 0 to 1, and its correlation range is more efficient. We apply some sub-families of the proposed new class to model a dataset of medical science to show the superiority of our approach in comparison with the presented generalized FGM family in the literature. We also present a method to simulate from our generalized FGM copula, and validate our method and its accuracy using the simulation results to recover the same dependency structure of the original data.

Suggested Citation

  • Hakim Bekrizadeh & Babak Jamshidi, 2017. "A new class of bivariate copulas: dependence measures and properties," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 31-50, April.
  • Handle: RePEc:spr:metron:v:75:y:2017:i:1:d:10.1007_s40300-017-0107-1
    DOI: 10.1007/s40300-017-0107-1

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    References listed on IDEAS

    1. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
    2. Cécile Amblard & Stéphane Girard, 2009. "A new extension of bivariate FGM copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 1-17, June.
    3. Lai, C. D. & Xie, M., 2000. "A new family of positive quadrant dependent bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 359-364, February.
    4. Cuadras, Carles M., 2015. "Contributions to the diagonal expansion of a bivariate copula with continuous extensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 28-44.
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