On Concordance Measures for Discrete Data and Dependence Properties of Poisson Model

We study Kendall's tau and Spearman's rho concordance measures for discretevariables. We mainly provide their best bounds using positive dependence properties. Thesebounds are difficult to write down explicitly in general. Here, we give the explicit formula of thebest bounds in a particular Fréchet space in order to understand the behavior of the ranges ofthese measures. Also, based on the empirical copula which is viewed as a discrete distribution, wepropose a new estimator of the copula function. Finally, we give useful dependence properties ofthe bivariate Poisson distribution and show the relationship between parameters of the Poissondistribution and both tau and rho