中文摘要：

为检验未知总体的中位数,提出基于非均等排序集抽样的符号检验.通过比较符号检验的Pitman效率,表明非均等排序集抽样效率高于排序集抽样和简单随机抽样.考虑到非均等排序集样本独立但不同分布,提出与秩次有关的加权符号检验,具体给出使检验效率达到最大的权数,并证明出最优权数具有适应任意分布性.Pitman相对效率的计算结果表明,非均等排序集抽样下最优加权符号检验优于排序集抽样下最优加权符号检验.最后,对阔叶松树的一组真实数据进行了实际应用.

英文摘要：

To test the median of an infinite population, a sign test based on ranked set sampling with unequal samples was proposed. According to compare the Pitman efficiencies of sign tests, the ranked set sampling with unequal samples is more efficient than ranked set sampling and the simple random sampling. Considering observations of ranked set sample with unequal samples are independent but not identically distributed, weighted sign tests in which weights associate with the judgment rank were presented, the weight that maximizes the test efficiency was identified and shown to be distribution-free. The computational results of Pitman relative efficiencies showed that the optimal weighted sign test under ranked set sampling with unequal samples is superior to the optimal weighted sign test under ranked set sampling. Finally, a practical application for a real data set related to a pine hardwood forest is made.