  In the present paper, we discuss the Pearson, Spearman, Kendall correlation
coefficients and their statistical analogues. We propose a new correlation
coefficient r and its statistical analogue. The coefficient r is based on
Kendal's and Spearman's correlation coefficients. A new extension of the
Pearson correlation coefficient is also discussed. We conduct simulation
experiments and study the behavior of the above correlation coefficients. We
observe that the behavior of Pearson's sample correlation coefficient can be
very different from the behavior of the rank correlation coefficients, which,
in turn, behave in a similar way. The question arises: which correlation
coefficient better measures the dependence rate? We try to answer this question
in the final conclusion.
