Bounds on Spearman’s rho when at least one random variable is discrete

Spearman’s rho is one of the most popular dependence measures used in practice to describe association between two random variables. However, case at least variable being discrete, correlations are often bounded and restricted a sub-interval $$[-1,1]$$ . Hence, small positive values may actually support strong when getting close its highest attainable value. Similarly, slight negative can mean dependence. In this paper, we derive best-possible upper lower bounds for discrete. We illustrate obtained some situations practical relevance.