A proposal for modeling and simulating correlated discrete Weibull variables

Document Type: Article

Author

Department of Economics, Management and Quantitative Methods, 4 Universit`a degli Studi di Milano, via Conservatorio 7, 20122 Milan, Italy

Abstract

Researchers in applied sciences are often concerned with multivariate random vari9
ables. In particular, multivariate discrete data often arise in many fields (statistical
10 quality control, biostatistics, failure and reliability analysis, etc.) and modeling such
11 data is a relevant task, as well as simulating correlated discrete data satisfying some spe12
cific constraints. Here we consider the discrete Weibull distribution as an alternative to
13 the popular Poisson random variable and propose a procedure for simulating correlated
14 discrete Weibull random variables, with marginal distributions and correlation matrix as15
signed by the user. The procedure indeed relies upon the Gaussian copula model and an
16 iterative algorithm for recovering the proper correlation matrix for the copula ensuring
17 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 and
19 computational burden, also in relation to the necessary (but temporary) truncation of
20 the support of the discrete Weibull random variable. Inferential issues for the proposed
21 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 correlated
23 counts even better than the most popular or recent existing ones.

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