On Correlation Coefficients

Abstract: 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.