Copula models have been widely used to model the dependence between continuous random variables, but modelling 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 derive the population version of Spearman's rho via copulas when both random variables are discrete. The closed-form expressions of the Spearman correlation are obtained for some copulas with different marginal distributions. We derive the upper and lower bounds of Spearman's rho for Bernoulli marginals. The proposed Spearman's rho correlations are compared with their corresponding Kendall's tau values and their functional relationships are characterized 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 analyse the count data of a cervical cancer dataset.

Copula模型已被广泛用于对连续随机变量之间的相关性进行建模，但是最近在统计文献中流行了通过copulas对计数数据进行建模。Spearman的rho是测量两个随机变量之间的依存度的合适而有效的工具。在本文中，当两个随机变量都是离散的时，我们通过copula推导了Spearman的rho的种群版本。对于一些具有不同边际分布的系动词，获得了Spearman相关性的闭式表达式。我们得出伯努利边际的Spearman的rho的上限和下限。将拟议的Spearman的rho相关性与其对应的Kendall的tau值进行比较，并在某些特殊情况下对它们的功能关系进行了表征。进行了广泛的模拟研究，以证明我们理论结果的有效性。最后，我们提出了一个二元copula回归模型来分析a的计数数据。宫颈癌数据集。