New results on stochastic comparison of order statistics from heterogeneous Weibull populations

Let X1,…,Xn be independent random variables with Xi∼W(α,λi),i=1,…,n. Let Y1,…,Yn be a random sample of size n from a Weibull distribution with common parameters α,λ. Let λmin denote the minimum of λi,i=1,…,n. If λ≥(∏i=1nλiα)1nλminα−1, where α>1, it is shown that the largest order statistics Xn:n is greater than the largest order statistics Yn:n according to the dispersive ordering.