Computing the distribution and expected value of the concomitant rank-order statistics

This work gives a new representation of the distribution and expected value of the concomitant rank of order statistics. An advantage of this representation is its ability to extend without any complexity to the multivariate case. Moreover. it gives a new direct approach to compute an approximate formula for the distribution and expected value of the concomitant rank of order statistics. Finally, an upper bound is derived for the confidence level of the tolerance region of the original bivariate (resp., multivariate) d.f., from which the sample is drawn.