A new extension of the FGM copula for negative association

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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.

Original languageEnglish
Pages (from-to)1902-1919
Number of pages18
JournalCommunications in Statistics - Theory and Methods
Issue number8
StatePublished - Apr 18 2019


  • Coverage probabilities
  • Kendall's distribution function
  • goodness-of-fit
  • maximum likelihood estimation
  • measures of association
  • p-value


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