In this paper, we advance new families of bivariate copulas constructed by distributional distortions of existing bivariate copulas. The distortions under consideration are based on the unit gamma distribution of two forms. When the initial copula is Archimedean, the induced copula is also Archimedean under the admissible parameter space. Properties such as Kendall’s tau coefficient, tail dependence coefficients and tail orders for the new families of copulas are derived. An empirical application to economic indicator data is presented.
Abstract: The association between bivariate binary responses has been studied using Pearson’s correlation coefficient, odds ratio, and tetrachoric correlation coefficient. This paper introduces a copula to model the association. Numerical comparisons between the proposed method and the existing methods are presented. Results show that these methods are comparative. However, the copula method has a clearer interpretation and is easier to extend to bivariate responses with three or more ordinal categories. In addition, a goodness-of-fit test for the selection of a model is performed. Applications of the method on two real data sets are also presented.