  In the present paper, we first discuss the Kendall rank correlation
coefficient. In continuous case, we define the Kendall rank correlation
coefficient in terms of the concomitants of order statistics, find the expected
value of the Kendall rank correlation coefficient and show that the later is
free of n. We also prove that in continuous case the Kendall correlation
coefficient converges in probability to its expected value. We then propose to
consider the expected value of the Kendall rank correlation coefficient as a
new theoretical correlation coefficient which can be an alternative to the
classical Pearson product-moment correlation coefficient. At the end of this
work we analyze illustrative examples.
