Sampling multivariate count variables with prespecified Pearson correlation using marginal regular vine copulas

The problem of sampling multivariate count variables has practical significance. Ref.1proposed an algorithm for sampling multivariate count random variables based on C-vine copulas, by which the parameters
ρi,j|D
of edge
ei,j|D
of the C-vine structure are estimated by optimizing the difference between the sample partial correlation
σ︿i,j|D
and the partial correlation
σi,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
σ︿ij
and the targeted correlation
σij
for pairs of variables. Three simulation studies illustrate that the new sampling method generates more accurate results than the C-vine sampling method in Ref.1and the Naive sampling method in Ref.3. The sampling algorithm routines are implemented in Python as package countvar in PyPi.