A proposal for modeling and simulating correlated discrete Weibull variables

Researchers in applied sciences are often concerned with multivariate random variables. In particular, multivariate discrete data often arise in many fields (statistical quality control, biostatistics, failure and reliability analysis, etc.) and modeling such data is a relevant task, as well as simulating correlated discrete data satisfying some specific constraints. Here we consider the discrete Weibull distribution as an alternative to the popular Poisson random variable and propose a procedure for simulating correlated discrete Weibull random variables, with marginal distributions and correlation matrix assigned by the user. The procedure indeed relies upon the Gaussian copula model and an iterative algorithm for recovering the proper correlation matrix for the copula ensuring the desired correlation matrix on the discrete margins. A simulation study is presented, which empirically assesses the performance of the procedure in terms of accuracy and computational burden, also in relation to the necessary (but temporary) truncation of the support of the discrete Weibull random variable. Inferential issues for the proposed model are also discussed and are eventually applied to a dataset taken from the literature, which shows that the proposed multivariate model can satisfactorily fit real-life correlated counts even better than the most popular or recent existing ones.