A proposal for modeling and simulating correlated discrete Weibull variables

Abstract

Researchers in applied sciences are often concerned with multivariate random vari9ables. In particular, multivariate discrete data often arise in many fields (statistical10 quality control, biostatistics, failure and reliability analysis, etc.) and modeling such11 data is a relevant task, as well as simulating correlated discrete data satisfying some spe12cific constraints. Here we consider the discrete Weibull distribution as an alternative to13 the popular Poisson random variable and propose a procedure for simulating correlated14 discrete Weibull random variables, with marginal distributions and correlation matrix as15signed by the user. The procedure indeed relies upon the Gaussian copula model and an16 iterative algorithm for recovering the proper correlation matrix for the copula ensuring17 the desired correlation matrix on the discrete margins. A simulation study is presented,18 which empirically assesses the performance of the procedure in terms of accuracy and19 computational burden, also in relation to the necessary (but temporary) truncation of20 the support of the discrete Weibull random variable. Inferential issues for the proposed21 model are also discussed and are eventually applied to a dataset taken from the literature,22 which shows that the proposed multivariate model can satisfactorily fit real-life correlated23 counts even better than the most popular or recent existing ones.