Krishnamoorthy K, Mathew Thomas, Xu Zhao
a Department of Mathematics , University of Louisiana at Lafayette , Lafayette , Louisiana.
J Occup Environ Hyg. 2014;11(8):538-46. doi: 10.1080/15459624.2014.881487.
The problem of comparing the means of two lognormal distributions based on samples with multiple detection limits is considered. Tests and confidence intervals for the ratio of the two means, based on pivotal quantities involving the maximum likelihood estimators, are proposed. The merits of the proposed approaches are evaluated by Monte Carlo simulation. Simulation study indicates that the procedures are satisfactory in terms of coverage probabilities of confidence intervals, and powers of tests. The proposed approach can also be applied to find confidence intervals for the difference between the means of the two lognormal distributions. Illustrative examples with a real data set and with a simulated data set are given.
考虑基于具有多个检测限的样本比较两个对数正态分布均值的问题。提出了基于涉及最大似然估计量的枢轴量的两个均值之比的检验和置信区间。通过蒙特卡罗模拟评估了所提出方法的优点。模拟研究表明，这些程序在置信区间的覆盖概率和检验功效方面是令人满意的。所提出的方法还可用于找到两个对数正态分布均值之差的置信区间。给出了真实数据集和模拟数据集的示例。
