In the present paper, we discuss the Pearson \(\rho \) , Spearman \(\rho _S\) , Kendall \(\tau \) correlation coefficients and their statistical analogues \(\rho _n, \rho _{n,S}\) and \(\tau _n\) . We propose a new correlation coefficient r and its statistical analogue \(r_n\) . 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 \(\rho _n\) can be very different from the behavior of the rank correlation coefficients \(\rho _{n,S}, \tau _n\) and \(r_n\) , 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.
