The minimum information copula (Bedford et al. 2016; Daneshkhah et al. 2016) provides a parametric class of copula which can be determined to any required degree of precision based on the observed data or elicited judgments. The only technical assumptions should be made are that the copula density under study is continuous and non-zero. One of the main challenges of the minimum information copula is that a uniform discretization gird is used for approximating each copula density. In this paper, we enhance the approximation accuracy of the minimum information copula using several other discretization algorithms including Chebyshev and Halton methods. We illustrate that the Chebyshev method enables us to select more points in the tail or boundaries of the density which are more desired in investigating the applications in Finance, extreme environmental events, etc. The next drawback of the minimum information copula is determining the Lagrange coefficients which are derived by solving a non-linear optimization problem. The current method (Nelder-Mead simplex method) to tackle this optimization problem is quite challenging for the complex scenarios. In this paper, we propose using an alternative method which requires local knowledge of the gradient of the bivariate densities. We exhibit this method is computationally more appealing and simply can be implemented by the FMINCON function in MATLAB. We finally show the approximation enhancement of the minimum information copula using the proposed changes using some real-world illustration example.
