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