Bayesian confidence intervals for the difference between variances of delta‐lognormal distributions

Abstract

This article has earned an open data badge "Reproducible Research" for making publicly available the code necessary to reproduce the reported results. The results reported in this article could fully be reproduced.

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

“…2 together with the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) indicate that the daily rainfall data from the three areas follow delta-lognormal distributions. Furthermore, many researchers have reported that rainfall data follow a delta-lognormal distribution ( Fukuchi, 1988 ; Shimizu, 1993 ; Yue, 2000 ; Kong et al, 2012 ; Maneerat, Niwitpong & Niwitpong, 2019a , 2020a , 2020b ; Yosboonruang, Niwitpong & Niwitpong, 2019b , 2020 ; Yosboonruang & Niwitpong, 2020 ).…”

“…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.…”

Bayesian interval estimations for the mean of delta-three parameter lognormal distribution with application to heavy rainfall data

“…Recently, Maneerat et al [ 17 ] revealed that the highest posterior density (HPD) interval-based beta prior was the best-performing method for estimating a single mean and the difference between two delta-lognormal means. After that the HPD-based normal gamma prior was developed in the comparison of the estimated rainfall dispersion between northern and northeastern regions in Thailand proposed by Maneerat et al [ 18 ], while the HPD-based probability matching prior was recommended to construct the CIs for the difference between two delta-lognormal variances [ 19 ]. Unfortunately, the CI for the mean of a delta-three parameter lognormal distribution, especially when the highly skewed non-zero values are present with the zero observations, has not yet been established.…”

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

“…Thailand often endures flooding due to thunderstorms, which can take lives and damage property, especially on farms due to Thailand being an agricultural country. Thailand is divided into five regions according to its & Niwitpong (2019a); Yosboonruang, Niwitpong & Niwitpong (2019b); Yosboonruang, Niwitpong & Niwitpong (2020); Yosboonruang & Niwitpong (2020), and Maneerat, Niwitpong & Niwitpong (2020a); Maneerat, Niwitpong & Niwitpong (2020b).…”