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

Abstract

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.

Estimation of common percentile of rainfall datasets in Thailand using delta-lognormal distributions

“… Maneerat, Niwitpong & Niwitpong (2020) constructed Bayesian credible intervals for the difference between variances of delta-lognormal distributions. Yosboonruang, Niwitpong & Niwitpong (2020) proposed Bayesian credible intervals for measuring the difference between rainfall dispersions datasets for regions in Thailand. Thangjai, Niwitpong & Niwitpong (2020c) estimated Bayesian credible intervals for the means of normal distributions with unknown coefficients of variation.…”

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 ).…”

“…For statistical inference, several methods for constructing confidence intervals for the CV and functions of the CV have been suggested ( e.g . Pang et al, 2005 ; Hayter, 2015 ; Nam & Kwon, 2017 ; Yosboonruang, Niwitpong & Niwitpong, 2018 , 2019a , 2019b , 2020 ; Yosboonruang & Niwitpong, 2020 ). However, since using the common CV of delta-lognormal distributions for statistical inference has not previously been reported, this has become our research interest as it is useful for measuring the dispersion in several independent data series, especially rainfall data.…”

Confidence intervals for the difference between the coefficients of variation of Weibull distributions for analyzing wind speed dispersion

“…Sangnawakij, Niwitpong & Niwitpong (2015) presented confidence intervals for the ratio of coefficients of variation of gamma distributions. Yosboonruang, Niwitpong & Niwitpong (2020) proposed confidence intervals for the difference between the coefficients of variation of delta-lognormal distributions. La-ongkaew, Niwitpong & Niwitpong (2009) constructed confidence interval for single coefficient of variation of Weibull distribution.…”