Abstract
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.
Highlights
The effects of global climate change caused by many factors, both natural and man-made, are continuous
The goal of this study is to propose new confidence intervals using Bayesian methods and comparing them with fiducial generalized confidence interval (FGCI) proposed by Yosboonruang, Niwitpong & Niwitpong (2019) for a single coefficient of variation of a delta-lognormal distribution
To evaluate the performance of the proposed methods, their coverage probabilities and expected lengths were estimated via Monte Carlo simulation using the R statistical programming language (Venables & Smith, 2009)
Summary
The effects of global climate change caused by many factors, both natural and man-made (such as fuel burning, burning forests, deforestation, and oil drilling), are continuous. In the north of Thailand, a lot of deforestation has caused flooding because there are insufficient trees to absorb water due to heavy rain. Many organizations, both governmental and from the private sector, are interested in finding ways to mitigate the damage from such events, and a study on measuring the dispersion of rainfall in areas with the potential risk of flooding has become necessary.
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