Sampling multivariate count variables with prespecified Pearson correlation using marginal regular vine copulas. (English) Zbl 1474.62026

Summary: The problem of sampling multivariate count variables has practical significance. Some previous researchers had proposed an algorithm for sampling multivariate count random variables based on C-vine copulas, by which the parameters \({\rho_{i, j|D}}\) of edge \({e_{i, j|D}}\) of the C-vine structure are estimated by optimizing the difference between the sample partial correlation \({\hat{\sigma}_{i, j|D}}\) and the partial correlation \({\sigma_{i, j|D}}\) calculated from the prespecified correlation matrix by the Pearson recurrence formula, where \(D\) is a conditioning node set. We introduce the concept of marginal regular vine copula, which leads to directly optimizing the difference between the sample correlation \({\hat{\sigma}_{ij}}\) and the targeted correlation \({\sigma_{ij}}\) for pairs of variables. Three simulation studies illustrate that the new sampling method generates more accurate results than the C-vine sampling method and the Naive sampling method. The sampling algorithm routines are implemented in Python as package countvar in PyPi.


62D05 Sampling theory, sample surveys
62H05 Characterization and structure theory for multivariate probability distributions; copulas


PyPI; countvar; Python
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