On dispersive ordering between order statistics in one-sample and two-sample problems

Let Xi:n denote the ith-order statistic of a random sample of size n from a continuous distribution with distribution function F. It is shown that if F is a decreasing failure rate (DFR) distribution, then Xi:n is less dispersed than Xj:m for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j. Let Yj:m denote the jth-order statistic of a random sample of size m from a continuous distribution G. We prove that if F is less dispersed than G and either F or G is DFR, then Xi:n is less dispersed than Yj:m for i[less-than-or-equals, slant]j and n-i[greater-or-equal, slanted]m-j.