Inequalities for expected extreme order statistics

We obtain one-sided bounds for differences of expected extreme order statistics, when the involved random vectors have (integrable) independent components, and the marginal distributions satisfy a suitable condition. The general results are applied to random samples whose parent distributions are binomial, Poisson, and negative binomial distributions having the same mean. We also derive a method to give lower (upper) bounds for expected maxima (minima) of integrable independent random variables.