Inducing a Target Association between Ordinal Variables by Using a Parametric Copula Family

The need for building and generating statistically dependent random variables arises in various fields of study where simulation has proven to be a useful tool. In this work, we present an approach for constructing ordinal variables with arbitrarily assigned marginal distributions and value of association or correlation, expressed in terms of either Goodman and Kruskal's gamma or Pearson's linear correlation. The approach first constructs a class of bivariate copula-based distributions matching the assigned margins, and then, within this class, identifies the distribution matching the assigned association or correlation, by calibrating the copula parameter. A numerical example and a possible application are illustrated.