Abstract

We focus on the construction of confidence intervals for the ratios of medians of two independent, log-normal distributions based on the normal approximation (NA) approach, the method of variance estimate recovery (MOVER), and the generalized confidence interval (GCI) approach. We also compare the performance of the three confidence intervals in terms of the coverage probabilities, and average lengths, using Monte Carlo simulations. The results show that the GCI confidence interval is generally preferred in terms of coverage probabilities; however, the average length for the GCI is always wider than for other approaches. The NA and MOVER approaches could be recommended on the basis of the specific values of ${\mu }_i,{\sigma }_i^2$ and/or sample sizes. The confidence intervals are illustrated using real data examples.

摘要

我们专注于基于正态近似 (NA) 方法、方差估计恢复方法 (MOVER) 和广义置信区间 (GCI) 方法为两个独立的对数正态分布的中位数比率构建置信区间. 我们还使用蒙特卡罗模拟比较了三个置信区间在覆盖概率和平均长度方面的性能。结果表明，在覆盖概率方面，GCI置信区间通常是首选；然而，GCI 的平均长度总是比其他方法宽。可以根据具体值推荐 NA 和 MOVER 方法${\mu }_{\mathrm{一世}},{\sigma }_{\mathrm{一世}}^2$和/或样本量。置信区间使用真实数据示例进行说明。