Some New Inequalities for the Range Distribution, with Application to the Determination of Optimum Significance Levels of Multiple Range Tests
本文证明了极差分布函数的一个一般不等式，保证了特定临界值集的单调性，并讨论了与其他不等式的关系，对多重极差检验的可容许性和最优性概念有重要意义。
Abstract A problem arising in multiple range tests is the monotonicity of the defining critical values, which ws first treated by Lehmann and Shaffer (1977). This article proves a general inequality for the distribution function of the range, which guarantees the monotonicity of a special set of critical values. It also discusses the relation to some other inequalities. The importance of these inequalities is pointed out in considering some concepts of admissibility and optimality of multiple range tests.