Confidence Intervals for the Mean of Delta-Lognormal Distribution

Self Cite

The delta-lognormal distribution is a combination of binomial and lognormal distributions, and so rainfall series that include zero and positive values conform to this distribution. The coefficient of variation is a good tool for measuring the dispersion of rainfall. Statistical estimation can be used not only to illustrate the dispersion of rainfall but also to describe the differences between rainfall dispersions from several areas simultaneously. Therefore, the purpose of this study is to construct simultaneous confidence intervals for all pairwise differences between the coefficients of variation of delta-lognormal distributions using three methods: fiducial generalized confidence interval, Bayesian, and the method of variance estimates recovery. Their performances were gauged by measuring their coverage probabilities together with their expected lengths via Monte Carlo simulation. The results indicate that the Bayesian credible interval using the Jeffreys’ rule prior outperformed the others in virtually all cases. Rainfall series from five regions in Thailand were used to demonstrate the efficacies of the proposed methods.

Section: The Bayesian Methodsmentioning

confidence: 99%

Simultaneous confidence intervals for all pairwise differences between the coefficients of variation of rainfall series in Thailand

Yosboonruang

Niwitpong

2021

Self Cite

“…The fact that daily rainfall data can usually be fitted to a delta-lognormal distribution after collecting data over a sufficiently long period has drawn interest from several researchers to present statistical inference for its parameters. Several researchers have suggested confidence intervals for the mean and functions of the mean of delta-lognormal distributions, such as the traditional method, the normal algorithm, the exponential algorithm ( Kvanli, Shen & Deng, 1998 ), bootstrapping, the likelihood ratio, the signed log-likelihood ratio ( Zhou & Tu, 2000 ; Tian, 2005 ; Tian & Wu, 2006 ), GCI ( Tian, 2005 ; Chen & Zhou, 2006 ; Li, Zhou & Tian, 2013 ; Wu & Hsieh, 2014 ; Hasan & Krishnamoorthy, 2018 ; Maneerat, Niwitpong & Niwitpong, 2018 , 2019b ), MOVER ( Maneerat, Niwitpong & Niwitpong, 2018 , 2019a , 2019b ), Aitchison’s estimator, a modified Cox’s method, a modified Land’s method, the profile likelihood interval ( Fletcher, 2008 ; Wu & Hsieh, 2014 ), FGCI ( Li, Zhou & Tian, 2013 ; Hasan & Krishnamoorthy, 2018 ; Maneerat, Niwitpong & Niwitpong, 2019a ), as well as Bayesian approaches ( Maneerat, Niwitpong & Niwitpong, 2019a ). Moreover, confidence interval estimations for the variance ( Maneerat, Niwitpong & Niwitpong, 2020a , 2020b ), CV ( Yosboonruang, Niwitpong & Niwitpong, 2018 , 2019a , 2019b ), and functions of the CV ( Yosboonruang & Niwitpong, 2020 ; Yosboonruang & Niwitpong, 2020 ) of delta-lognormal distributions have been suggested, including GCI, the modified Fletcher’s method, FGCI, MOVER, the Bayesian approach, and bootstrapping.…”

Section: Introductionmentioning

confidence: 99%

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

Yosboonruang¹,

Niwitpong²,

Niwitpong³

2022

Self Cite

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.

“…Maneerat, Niwitpong & Niwitpong (2018) constructed confidence intervals for the mean using GCI, the method of variance estimate recovery (MOVER) based on the variance stabilizing transformation (VST), Wilson's score, and Jeffrey's method; GCI and the three MOVER methods had similar performances except for cases where the probability had values close to zero and the coefficient of variation was large. Moreover, they compared GCI and MOVER based on a weighted beta distribution and VST to construct confidence intervals for the mean and recommended MOVER based on VST (Maneerat, Niwitpong & Niwitpong, 2019b). In addition, Maneerat, Niwitpong & Niwitpong (2019a) suggested Bayesian methods to construct the highest posterior density (HPD) intervals for a single mean and the difference between two means.…”

Section: Introductionmentioning

confidence: 99%

“…The government can use this information for advanced planning to prevent problems caused by excessive rainfall. Many researchers have found that rainfall data series follow a bivariate lognormal distribution (a delta-lognormal distribution) ( Fukuchi, 1988 ; Shimizu, 1993 ; Kong et al, 2012 ; Maneerat, Niwitpong & Niwitpong, 2019a , 2019b ; Yosboonruang, Niwitpong & Niwitpong, 2019b ; Yue, 2000 ).…”

Section: Introductionmentioning

confidence: 99%

The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

Yosboonruang¹,

Niwitpong²,

Niwitpong³

2020

Self Cite

The coefficient of variation is often used to illustrate the variability of precipitation. Moreover, the difference of two independent coefficients of variation can describe the dissimilarity of rainfall from two areas or times. Several researches reported that the rainfall data has a delta-lognormal distribution. To estimate the dynamics of precipitation, confidence interval construction is another method of effectively statistical inference for the rainfall data. In this study, we propose confidence intervals for the difference of two independent coefficients of variation for two delta-lognormal distributions using the concept that include the fiducial generalized confidence interval, the Bayesian methods, and the standard bootstrap. The performance of the proposed methods was gauged in terms of the coverage probabilities and the expected lengths via Monte Carlo simulations. Simulation studies shown that the highest posterior density Bayesian using the Jeffreys’ Rule prior outperformed other methods in virtually cases except for the cases of large variance, for which the standard bootstrap was the best. The rainfall series from Songkhla, Thailand are used to illustrate the proposed confidence intervals.