The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (nI < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.

中文翻译：

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泰国降雨量共同变异系数的置信区间

对数正态分布通常用于分析环境数据，例如日降雨量。降雨在泰国很受关注，因为高度多变的气候会导致周期性的缺水和缺水。通常估计该地区降雨量的平均值、标准偏差或变异系数。气候水分指数是植物需水量与降水量之比。气候水分指数应使用变异系数而不是标准差来比较平均值相差很大的地区。变异系数越大表示分散程度越大，而变异系数越小表示风险越低。公共变异系数，是基于k个区域的加权变异系数，表示日均降雨量。所以，共同变异系数用于描述k个区域的总体水问题。在本文中，我们提出了四种基于基准广义置信区间 (FGCI)、方差估计恢复方法 (MOVER)、计算和贝叶斯方法的对数正态分布公共变异系数的置信区间估计新方法. Monte Carlo 模拟用于评估覆盖概率和置信区间的平均长度。在覆盖概率方面，结果表明 FGCI 方法为大多数情况提供了最佳置信区间估计值，除非样本情况等于 6 个总体 (k = 6) 并且样本量很小 (nI < 50)， MOVER 置信区间估计是最好的。