Bayesian computation for the common coefficient of variation of delta-lognormal distributions with application to common rainfall dispersion in Thailand

Abstract

Rainfall fluctuation makes precipitation and flood prediction difficult. The coefficient of variation can be used to measure rainfall dispersion to produce information for predicting future rainfall, thereby mitigating future disasters. Rainfall data usually consist of positive and true zero values that correspond to a delta-lognormal distribution. Therefore, the coefficient of variation of delta-lognormal distribution is appropriate to measure the rainfall dispersion more than lognormal distribution. In particular, the measurement of the dispersion of precipitation from several areas can be determined by measuring the common coefficient of variation in the rainfall from those areas together. Herein, we compose confidence intervals for the common coefficient of variation of delta-lognormal distributions by employing the fiducial generalized confidence interval, equal-tailed Bayesian credible intervals incorporating the independent Jeffreys or uniform priors, and the method of variance estimates recovery. A combination of the coverage probabilities and expected lengths of the proposed methods obtained via a Monte Carlo simulation study were used to compare their performances. The results show that the equal-tailed Bayesian based on the independent Jeffreys prior was suitable. In addition, it can be used the equal-tailed Bayesian based on the uniform prior as an alternative. The efficacies of the proposed confidence intervals are demonstrated via applying them to analyze daily rainfall datasets from Nan, Thailand.

Spatiotemporal Pattern, Evolutionary Trend, and Driving Forces Analysis of Ecological Quality in the Irtysh River Basin (2000–2020)

“…The coefficient of variation (CV) is the ratio of the standard deviation to the mean, which is a measure of the variability relative to the mean. It is free of units of measurement and is often used to measure the dispersion of data and to compare them with each other [74][75][76]. In this paper, it is used to reflect the degree of dispersion of the ARSEI and to assess the inter-annual time series stability of the ARSEI.…”

Bayesian Estimation for the Difference between Coefficients of Quartile Variation of Delta-Lognormal Distributions: An Application to Rainfall in Thailand

“…Several researchers have investigated rainfall dispersion in Thailand, such as Kumphon et al [3], Szyniszewska and Waylen [4], and Thodsan et al [5]. Additionally, studies on statistical inference for rainfall distribution in Thailand have been reported by Maneerat et al [6], Khooriphan et al [7], Yosboonruang et al [8,9], and Thangjai et al [10]. Previous research on statistical inference has primarily focused on measuring rainfall dispersion using variance and coefficient of variation.…”

“…The lognormal distribution plays a significant role in climate change studies due to its ability to model skewed data, analyze extreme events, quantify uncertainty, and facilitate econometric analyses. According to the rainfall data, several researchers have reported that the data follow a lognormal distribution with zero values, also known as a deltalognormal distribution [8,9,[25][26][27][28]. The delta-lognormal distribution consists of positive values following a lognormal distribution and actual zero values following a binomial distribution.…”

Confidence Intervals for Mean and Difference between Means of Delta-Lognormal Distributions Based on Left-Censored Data

“…Moreover, several researchers have proposed confidence intervals for various functions of the DLN distribution, such as the mean, coefficient of variation, and percentile. For instance, Maneerat et al [14], Maneerat et al [15], Yosboonruang et al [16], and Thangjai et al [17] have all explored this topic.…”