For climate studies in agriculture, rainfall records often involve data which contain zeros and highly non-zero skewness. This is mostly used in models for prediction or that use the mean for approximation. Rainfall dispersion is also important in evaluations as it can vary enormously, and it is a natural phenomenon which can lead to drought or flood. Herein, the goal of this paper is to propose a variational approximation computed with interval estimator based on Bayesian approach for delta-lognormal variance consisting of the highest posterior density interval based on vague prior (HPD-V) and the method of variance estimates recovery (MOVER). By way of comparison, the performances of these intervals were evaluated in terms of coverage probability and relative average length via a Monte Carlo simulation. The numerical results show that HPD-V was much more likely to outperform the other methods in many situations even large variance, although MOVER became the recommended method when both of variance and the probability of having zero were small. Our methods were then be utilized to analyze the variability in Nan province’s daily rainfall dataset in a comparison with the other methods.

中文翻译：

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贝叶斯置信区间的三角对数正态分布方差及其在降雨弥散中的应用

对于农业气候研究，降雨记录通常涉及包含零和高度非零偏度的数据。这主要用于预测模型或使用均值进行近似的模型。降雨散布在评估中也很重要，因为它变化很大，并且是自然现象，可能导致干旱或洪水。在此，本文的目的是针对基于对数正态方差的三角对数方差提出基于贝叶斯方法的，基于贝叶斯方法的区间估计器计算的变分逼近（HPD-V）和方差估计恢复方法（移动）。作为比较，通过蒙特卡洛模拟就覆盖概率和相对平均长度评估了这些间隔的性能。数值结果表明，即使在方差很大的情况下，即使方差较大，MOVER仍是推荐的方法，即使在方差较大的情况下，HPD-V也更有可能胜过其他方法。然后将我们的方法与其他方法进行比较，以分析南省日降水量数据集的变异性。