Distribution of concomitants of order statistics and their order statistics

For a random sample of size n from an absolutely continuous random vector ( X , Y ) , let Y i : n be i th Y -order statistic and Y [ j : n ] be the Y -concomitant of X j : n . We determine the joint pdf of Y i : n and Y [ j : n ] for all i , j = 1 to n , and establish some symmetry properties of the joint distribution for symmetric populations. We discuss the uses of the joint distribution in the computation of moments and probabilities of various ranks for Y [ j : n ] . We also show how our results can be used to determine the expected cost of mismatch in broken bivariate samples and approximate the first two moments of the ratios of linear functions of Y i : n and Y [ j : n ] . For the bivariate normal case, we compute the expectations of the product of Y i : n and Y [ i : n ] for n = 2 to 8 for selected values of the correlation coefficient and illustrate their uses.