Some new measures of dependence for random variables based on Spearman's ρ and Kendall's τ

In this paper, we extend the traditional Spearman's ρ and Kendall's τ which are widely used to measure the dependence between continuous random variables to the generalised ones that can measure the dependence between discrete or even more general random variables. Furthermore, applying these two generalised correlation coefficients to the trinomial distribution, we study how they vary with the parameter, and point out they are more reasonable than Pearson's correlation coefficient in some ways. Based on Spearman's ρ and Kendall's τ, two new measures are proposed with their respective asymptotic distributions. Finally, we run a Monte Carlo experiment and give the example analysis to investigate the performance of our dependence measures.