Sampling Count Variables with Specified Pearson Correlation: A Comparison Between a Naive and a C-Vine Sampling Approach

Erhardt and Czado11 suggest an approximative method for sampling high-dimensional count random variables with a specified Pearson correlation. They utilize Gaussian copulae for the construction of multivariate discrete distributions. A major task is to determine the appropriate copula parameters for the achievement of a specified target correlation. Erhardt and Czado11 develop an optimization routine to determine these copula parameters sequentially. Thereby, they use pair-copula decompositions of n-dimensional distributions, i.e., a decomposition consisting only of bivariate copula with one parameter each. C-vines, a graphical tool to organize such pair-copula decompositions, are used to select a possible decomposition. In the paper mentioned, the approach was compared to the NORTA method for discrete margins described in Ref. 2. Here, we will compare it to a widely used naive sampling approach for an even larger variety of marginal distributions such as the Poisson, generalized Poisson, negative binomial and zero-inflated generalized Poisson distributions.