非均等排序集抽样下位置参数的Mann-Whitney检验

Mann-Whitney Test of Location Parameters under Ranked Set Sampling with Unequal Samples

针对两总体位置参数的检验问题,提出了基于非均等排序集抽样方法的Mann-Whitney检验统计量,证明了当原假设成立时其分布具有对称性且不依赖于总体分布,证明了新统计量的渐近正态性,计算出其数学期望和渐近方差,并确定出检验拒绝域。模拟检验功效的比较结果表明:新检验优于基于简单随机样本和均等排序集样本的相应检验。

For the test problem of the location parameters of two populations,the Mann-Whitney test statistic using ranked set sampling with unequal samples was proposed.Under null hypothesis the new test statistic was shown to be symmetric distribution and not depend on the population distribution.The new test statistic was shown to have asymptotic normality,and its mathematical expectation and asymptotic variance were calculated.Test critical value of the new statistic was determined.The results of simulated test efficacy showed that the new test was better than the Mann-Whitney tests based on simple random samples and ranked set samples with equal samples.