Thangjai Warisa, Niwitpong Sa-Aat, Niwitpong Suparat
Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok, Thailand.
Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangok, Bangkok, Thailand.
PeerJ. 2020 Sep 21;8:e10004. doi: 10.7717/peerj.10004. eCollection 2020.
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 areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of 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 ( = 6) and the sample sizes were small ( < 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.
对数正态分布常用于分析环境数据，如日降雨量。泰国对降雨情况十分关注，因为气候多变会导致周期性的水资源压力和短缺。通常会估算该地区降雨的均值、标准差或变异系数。气候湿度指数是植物需水量与降水量的比值。在比较均值差异较大的地区时，气候湿度指数应使用变异系数而非标准差。变异系数越大表明离散程度越高，而变异系数越低则表明风险越低。常用变异系数是基于各区域的加权变异系数，它呈现了日平均降雨量。因此，常用变异系数用于描述各区域的整体水问题。在本文中，我们基于 fiducial 广义置信区间（FGCI）、方差估计恢复法（MOVER）、计算方法和贝叶斯方法，提出了四种新颖的方法来估计对数正态分布的常用变异系数的置信区间。使用蒙特卡罗模拟来评估置信区间的覆盖概率和平均长度。在覆盖概率方面，结果表明，除了样本案例等于六个总体（(n = 6)）且样本量较小（(n < 50)）的情况外，FGCI 方法在大多数情况下提供了最佳的置信区间估计，在这种情况下，MOVER 置信区间估计是最好的。通过使用来自泰国各地区的实际日降雨数据集进行示例，说明了所提出方法的有效性。
