In statistics, the concept of a concomitant, also called the induced order statistic, arises when one sorts the members of a random sample according to corresponding values of another random sample.
Let (X<sub>i</sub>, Y<sub>i</sub>), i = 1, . . ., n be a random sample from a bivariate distribution. If the sample is ordered by the X<sub>i</sub>, then the Y-variate associated with X<sub>r:n</sub> will be denoted by Y<sub>[r:n]</sub> and termed the concomitant of the r<sup>th</sup> order statistic.
Suppose the parent bivariate distribution having the cumulative distribution function F(x,y) and its probability density function f(x,y), then the probability density function of r<sup>th</sup> concomitant for is
If all are assumed to be i.i.d., then for , the joint density for is given by
That is, in general, the joint concomitants of order statistics is dependent, but are conditionally independent given for all k where . The conditional distribution of the joint concomitants can be derived from the above result by comparing the formula in marginal distribution and hence