On likelihood-ratio ordering of order statistics

Abstract

Let X1,..., Xn be independent random variables such that X1 < lr X2 < lr ... < lr Xn, where < lr denotes likelihood-ratio ordering. It is shown that, under mild assumptions, the corresponding order statistics X1 ≤ ... ≤ X(n) are similarly ordered, i.e., X(1) < lr X(2) < lr ... < lr X(n). © 1994.