Simulation of correlated discrete Weibull variables: a proposal and an implementation in the R environment

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 analysis, etc). 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 shows the performance of the procedure.