Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand.
PLoS One. 2022 Mar 23;17(3):e0265875. doi: 10.1371/journal.pone.0265875. eCollection 2022.
Rainfall fluctuation is directly affected by the Earth's climate change. It can be described using the coefficient of variation (CV). Similarly, the ratio of CVs can be used to compare the rainfall variation between two regions. The ratio of CVs has been widely used in statistical inference in a number of applications. Meanwhile, the confidence interval constructed with this statistic is also of interest. In this paper, confidence intervals for the ratio of two independent CVs of lognormal distributions with excess zeros using the fiducial generalized confidence interval (FGCI), Bayesian methods based on the left-invariant Jeffreys, Jeffreys rule, and uniform priors, and the Wald and Fieller log-likelihood methods are proposed. The results of a simulation study reveal that the highest posterior density (HPD) Bayesian using the Jeffreys rule prior method performed the best in terms of the coverage probability and the average length for almost all cases of small sample size and a large sample size together with a large variance and a small proportion of non-zero values. The performance of the statistic is demonstrated on two rainfall datasets from the central and southern regions in Thailand.
降雨波动直接受到地球气候变化的影响。可以使用变异系数 (CV) 来描述。同样，可以使用 CV 比值来比较两个地区的降雨变化。该比值已在许多应用的统计推断中得到广泛应用。同时，使用该统计量构造的置信区间也很有意义。本文提出了使用基准广义置信区间 (FGCI)、基于左不变杰弗里斯的贝叶斯方法、杰弗里斯规则和均匀先验、以及 Wald 和 Fieller 对数似然方法对具有超额零的对数正态分布的两个独立 CV 的比值的置信区间。模拟研究的结果表明，在小样本量和大样本量以及大方差和小非零值比例的几乎所有情况下，使用杰弗里斯规则先验方法的最高后验密度 (HPD) 贝叶斯方法在覆盖概率和平均长度方面表现最好。该统计量在来自泰国中部和南部地区的两个降雨数据集上的性能得到了证明。
