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A new class of bivariate copulas: dependence measures and properties

Author

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  • 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

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    1. 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.
    2. 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.
    3. 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.
    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.
    5. 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, revised 2011.
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    Cited by:

    1. Jie Huang & Haiming Zhou & Nader Ebrahimi, 2022. "Bayesian Bivariate Cure Rate Models Using Copula Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(3), pages 1-9, May.
    2. Šeliga Adam & Kauers Manuel & Saminger-Platz Susanne & Mesiar Radko & Kolesárová Anna & Klement Erich Peter, 2021. "Polynomial bivariate copulas of degree five: characterization and some particular inequalities," Dependence Modeling, De Gruyter, vol. 9(1), pages 13-42, January.
    3. Shyamal Ghosh & Prajamitra Bhuyan & Maxim Finkelstein, 2022. "On a bivariate copula for modeling negative dependence: application to New York air quality data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1329-1353, December.

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