The problems of finding confidence limits for the difference between two gamma means and the difference between two upper percentiles based on samples with multiple detection limits are considered. Simple methods for constructing confidence intervals and upper tolerance limits are developed based on cube root transformation and fiducial inferences. The performances of the proposed methods are evaluated by Monte Carlo simulations and are compared with parametric bootstrap and the method of variance estimates recovery. Computational results indicate that the proposed methods provide more satisfactory results even for small samples with high proportion of nondetects. The approaches are illustrated with some practical datasets.

考虑了基于具有多个检测限的样本寻找两个伽马平均值之间的差异和两个上百分位数之间的差异的置信限问题。基于立方根变换和基准推论，开发了构建置信区间和公差上限的简单方法。所提出方法的性能通过蒙特卡洛模拟进行评估，并与参数自举法和方差估计恢复方法进行了比较。计算结果表明，即使对于具有高比例未检测到的小样本，所提出的方法也能提供更令人满意的结果。这些方法用一些实际的数据集来说明。