Sampling Count Variables with specified Pearson Correlation - a Comparison between a naive and a C-vine Sampling Approach

Erhardt and Czado (2008) suggest an approximative method for sampling highdimensional 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 Czado (2008) 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 Avramidis, Channouf, and L’Ecuyer (2008). 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 distribution.