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A new extension of the FGM copula for negative association

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  • Kahadawala Cooray

Abstract

In this paper we introduced a single parameter, absolutely continuous and radially symmetric bivariate extension of the Farlie-Gumbel-Morgenstern (FGM) family of copulas. Specifically, this extension measures the higher negative dependencies than most FGM extensions available in literature. Closed-form formulas for distribution, quantile, density, conditional distribution, regression, Spearman's rho, Kendall's tau, and Gini's gamma are obtained. In addition, a formula for random variate generations is presented in closed-form to facilitate simulation studies. We conduct both paired and multiple comparisons with Frank, Gaussian, and Plackett copulas to investigate the performance based on Vuong's test. Furthermore, the new copula is compared with Frank, Gaussian, and Plackett copulas using both Kolmogorov-Smirnov and Cramér-von Mises type test statistics. Finally, a bivariate dataset is analyzed to compare and illustrate the flexibility of the new copula for negative dependence.

Suggested Citation

  • Kahadawala Cooray, 2019. "A new extension of the FGM copula for negative association," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1902-1919, April.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:8:p:1902-1919
    DOI: 10.1080/03610926.2018.1440312
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    Cited by:

    1. 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.
    2. Farid El Ktaibi & Rachid Bentoumi & Mhamed Mesfioui, 2024. "On the Ratio-Type Family of Copulas," Mathematics, MDPI, vol. 12(11), pages 1-17, June.
    3. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.
    4. Fadal A.A. Aldhufairi & Jungsywan H. Sepanski, 2020. "New families of bivariate copulas via unit weibull distortion," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.

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