On the joint distribution of the random variables ‘number of inversions’ and ‘number of outstanding variables’ in a randomly arranged sequence

The bivariate probability distribution of the random variables number of inversions] and number of outstanding variables] in a sequence of n i.i.d. random variables is derived. As an application, the null covariance between the test statistics proposed by Mann and Brunk, respectively, for the ‘trend in location’ problem is obtained. It is shown that these test statistics are asymptotically uncorrelated under the null hypothesis.