Maximizing the Probability That Adjacent Order Statistics of Samples from Several Populations Form Overlapping Intervals

1. Summary. Let samples of size n be drawn from each of k univariate continuous cumulative distribution functions on the same real line, and consider the intersection of the k intervals between the rth and (r + l)st order statistics in the several samples. Then, to maximize the probability that that intersection be nonempty the distributions should be identical. Furthermore, for each sample, consider two intervals-that between the rth and (r + 1)st and that between the sth and (s + l)st order statistics-then to maximize the probability that both the intersection of the "r" intervals and the intersection of the "s" intervals be nonempty, the distributions again should be identical and the value of the maximum probability is