Yosboonruang Noppadon, Niwitpong Sa-Aat, Niwitpong Suparat
Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand.
PeerJ. 2019 Jul 22;7:e7344. doi: 10.7717/peerj.7344. eCollection 2019.
Since rainfall data series often contain zero values and thus follow a delta-lognormal distribution, the coefficient of variation is often used to illustrate the dispersion of rainfall in a number of areas and so is an important tool in statistical inference for a rainfall data series. Therefore, the aim in this paper is to establish new confidence intervals for a single coefficient of variation for delta-lognormal distributions using Bayesian methods based on the independent Jeffreys', the Jeffreys' Rule, and the uniform priors compared with the fiducial generalized confidence interval. The Bayesian methods are constructed with either equitailed confidence intervals or the highest posterior density interval. The performance of the proposed confidence intervals was evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian equitailed confidence interval based on the independent Jeffreys' prior outperformed the other methods. Rainfall data recorded in national parks in July 2015 and in precipitation stations in August 2018 in Nan province, Thailand are used to illustrate the efficacy of the proposed methods using a real-life dataset.
由于降雨数据系列通常包含零值，因此服从delta对数正态分布，变异系数常被用来描述多个地区降雨的离散程度，是降雨数据系列统计推断中的一个重要工具。因此，本文的目的是基于独立杰弗里斯先验、杰弗里斯规则和均匀先验，使用贝叶斯方法为delta对数正态分布的单个变异系数建立新的置信区间，并与 fiducial广义置信区间进行比较。贝叶斯方法采用等尾置信区间或最高后验密度区间构建。通过蒙特卡罗模拟，利用覆盖概率和期望长度对所提出的置信区间的性能进行了评估。结果表明，基于独立杰弗里斯先验的贝叶斯等尾置信区间优于其他方法。利用泰国楠府2015年7月国家公园记录的降雨数据和2018年8月降水站的降雨数据，通过实际数据集说明了所提方法的有效性。
