Bayesian confidence intervals for means and variances of lognormal and bivariate lognormal distributions

2012 ◽  
Vol 142 (6) ◽  
pp. 1294-1309 ◽  
Author(s):  
J. Harvey ◽  
A.J. van der Merwe
Keyword(s):  
Confidence Intervals ◽  
Lognormal Distributions ◽  
Bivariate Lognormal

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

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9662
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Rainfall Data ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
The Difference ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

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.

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

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11651
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Credible Interval ◽  
Rainfall Series ◽  
Good Tool ◽  
Simultaneous Confidence Intervals ◽  
Lognormal Distributions ◽  
Bayesian Credible Interval ◽  
Coefficients Of Variation ◽  
Pairwise Differences ◽  
Fiducial Generalized Confidence Interval

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.

scholarly journals Simultaneous confidence intervals for all pairwise comparisons of the means of delta-lognormal distributions with application to rainfall data

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0253935
Author(s):  
Patcharee Maneerat ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Rainy Season ◽  
Direct Action ◽  
Parametric Bootstrap ◽  
Rainfall Data ◽  
Pairwise Comparisons ◽  
Simultaneous Confidence Intervals ◽  
Lognormal Distributions ◽  
Natural Rainfall ◽  
Fiducial Generalized Confidence Interval

Natural disasters such as flooding and landslides are important unexpected events during the rainy season in Thailand, and how to direct action to avoid their impacts is the motivation behind this study. The differences between the means of natural rainfall datasets in different areas can be estimated using simultaneous confidence intervals (SCIs) for pairwise comparisons of the means of delta-lognormal distributions. Our proposed methods are based on a parametric bootstrap (PB), a fiducial generalized confidence interval (FGCI), the method of variance estimates recovery (MOVER), and Bayesian credible intervals based on mixed (BCI-M) and uniform (BCI-U) priors. Their coverage probabilities, lower and upper error probabilities, and relative average lengths were used to evaluate and compare their SCI performances through Monte Carlo simulation. The results show that BCI-U and PB work well in different situations, even with large differences in variances σ j 2. All of the methods were applied to estimate pairwise differences between the means of natural rainfall data from five areas in Thailand during the rainy season to determine their abilities to predict occurrences of flooding and landslides.

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