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

Patcharee Maneerat,Sa-Aat Niwitpong,Suparat Niwitpong,Mohammad Asghari Jafarabadi

doi:10.1371/journal.pone.0253935

Abstract

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 [Formula: see text]. 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.

Highlights

Thailand, which is located above the Equator in the tropical zone, is in the center of Southeast Asia and shares borders with Laos, Myanmar, Cambodia, and Malaysia
We propose five methods for constructing simultaneous confidence intervals (SCIs): the parametric bootstrap (PB), the 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
For sample case k = 3 (Table 1 and Fig 1), the numerical evaluations show that BCI-U provided the correct coverage probabilities (CPs) with the shortest interval for small-to-large differences in s2j and δi and equal sample sizes

Summary

Introduction

Thailand, which is located above the Equator in the tropical zone, is in the center of Southeast Asia and shares borders with Laos (north and east), Myanmar (north and west), Cambodia (east), and Malaysia (south). From climatological and meteorological perspectives, Thailand is divided into northern, northeastern, central, eastern, and southern (east and west coast) areas. Past natural disasters in Thailand have involved flooding, drought, tropical storms, earthquakes, landslides, and forest fires. When considering natural rainfall in the rainy season (mid-May to mid-October), heavy storms can cause flooding and landslides. Basins, caves, and waterfalls are especially susceptible to dangerous flash flooding during the rainy season.

Objectives

Methods

Results

Discussion

Conclusion