Comparison of Correlation Coefficients

In the present paper, we discuss the Pearson $$\rho $$ ρ , Spearman $$\rho _S$$ ρ S , Kendall $$\tau $$ τ correlation coefficients and their statistical analogues $$\rho _n, \rho _{n,S}$$ ρ n , ρ n , S and $$\tau _n$$ τ n . We propose a new correlation coefficient r and its statistical analogue $$r_n$$ r n . The coefficient r is based on Kendal’s and Spearman’s correlation coefficients. In the situation when the second moments do not exist, we also offer a new extension of the Pearson correlation coefficient. We conduct simulation experiments and study the behavior of the above correlation coefficients. By these experiments, we show that the behavior of $$\rho _n$$ ρ n can be very different from the behavior of the rank correlation coefficients $$\rho _{n,S}, \tau _n$$ ρ n , S , τ n and $$r_n$$ r n , which, in turn, behave in a similar way in each discussed example. The question arises: which correlation coefficient best measures the dependence rate? We try to answer this question in our work.