Abstract
In this paper, we study the Pitman measure of closeness of order statistics of two independent samples from the same distribution to population quantiles. We then derive various exact expressions of the probability closeness of order statistics from the X and Y samples. Some distribution-free results for the median of the sampling distribution are obtained. Exact and explicit expressions are presented for Uniform(-1, 1) and exponential distributions. Numerical results for illustrative purposes are also provided.