Parametric bootstrap simultaneous confidence intervals for differences of means from several two-parameter exponential distributions

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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Confidence intervals for coefficients of variation in two-parameter exponential distributions

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918.2016.1208236 ◽

2016 ◽

Vol 46 (8) ◽

pp. 6618-6630 ◽

Cited By ~ 10

Author(s):

Patarawan Sangnawakij ◽

Sa-aat Niwitpong

Keyword(s):

Confidence Intervals ◽

Exponential Distributions ◽

Coefficients Of Variation ◽

Two Parameter

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Multiple comparisons of precipitation variations in different areas using simultaneous confidence intervals for all possible ratios of variances of several zero-inflated lognormal models

PeerJ ◽

10.7717/peerj.12659 ◽

2021 ◽

Vol 9 ◽

pp. e12659

Author(s):

Patcharee Maneerat ◽

Sa-Aat Niwitpong

Keyword(s):

Confidence Intervals ◽

Large Population ◽

Parametric Bootstrap ◽

Multiple Comparisons ◽

Precipitation Data ◽

Injury Death ◽

Simultaneous Confidence Intervals ◽

Southern Thailand ◽

Precipitation Variation ◽

Weather Stations

Flash flooding and landslides regularly cause injury, death, and homelessness in Thailand. An advancedwarning system is necessary for predicting natural disasters, and analyzing the variability of daily precipitation might be usable in this regard. Moreover, analyzing the differences in precipitation data among multiple weather stations could be used to predict variations in meteorological conditions throughout the country. Since precipitation data in Thailand follow a zero-inflated lognormal (ZILN) distribution, multiple comparisons of precipitation variation in different areas can be addressed by using simultaneous confidence intervals (SCIs) for all possible pairwise ratios of variances of several ZILN models. Herein, we formulate SCIs using Bayesian, generalized pivotal quantity (GPQ), and parametric bootstrap (PB) approaches. The results of a simulation study provide insight into the performances of the SCIs. Those based on PB and the Bayesian approach via probability matching with the beta prior performed well in situations with a large amount of zero-inflated data with a large variance. Besides, the Bayesian based on the reference-beta prior and GPQ SCIs can be considered as alternative approaches for small-to-large and medium-to-large sample sizes from large population, respectively. These approaches were applied to estimate the precipitation variability among weather stations in lower southern Thailand to illustrate their efficacies.

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