Bounds on Distributions Arising in Order Restricted Inferences with Restricted Weights
研究了在简单线性序和简单树序中，当权重单调时，对水平概率的等权重近似和模式近似所做的改进，得到了带限制权重的卡方杠平方和E杠平方分布的严格上下界，并应用于多项总体间随机排序的检验。
SUMMARY Level probabilities, which are central to the theory of testing order restricted hypotheses, are intractable in some applications. Thus, approximations for them and the associated distributions are of considerable importance. The level probabilities depend on weights which in some situations are monotonic. For the simple linear and simple tree orderings, we study the improvements in the equal-weights and pattern approximations which arise when the weights are monotonic. In this study, sharp upper and lower bounds for the related chi-bar-squared and E-bar-squared distributions are obtained for restricted weights. An application of these results in testing for a stochastic ordering between multinomial populations is discussed.