  Copula models have been widely used to model the dependence between
continuous random variables, but modeling count data via copulas has recently
become popular in the statistics literature. Spearman's rho is an appropriate
and effective tool to measure the degree of dependence between two random
variables. In this paper, we derived the population version of Spearman's rho
correlation via copulas when both random variables are discrete. The
closed-form expressions of the Spearman correlation are obtained for some
copulas of simple structure such as Archimedean copulas with different marginal
distributions. We derive the upper bound and the lower bound of the Spearman's
rho for Bernoulli random variables. Then, the proposed Spearman's rho
correlations are compared with their corresponding Kendall's tau values. We
characterize the functional relationship between these two measures of
dependence in some special cases. An extensive simulation study is conducted to
demonstrate the validity of our theoretical results. Finally, we propose a
bivariate copula regression model to analyze the count data of a \emph{cervical
cancer} dataset.
