Estimating a multivariate model with discrete Weibull margins

Recently, a proposal for simulating correlated discrete Weibull variables has been suggested, based on the Gaussian copula. Although the procedure is straightforward and allows the user to directly assign the desired pairwise correlations between the discrete margins (or simply assign the correlation matrix of the Gaussian copula), on the other hand the estimation process is more tricky. In this work, we describe and assess, with a special focus on the bivariate case, three techniques for the estimation of the model parameters; an application to real data is provided as well.