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Due to slash/burn agricultural activity and frequent forest fires, P M 2.5 has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating P M 2.5 concentrations discretely by area, for which the inverse Gaussian distribution is suitable, can provide valuable information. Herein, we provide derivations of the simultaneous confidence interval for the ratios of the coefficients of variation of multiple inverse Gaussian distributions using the generalized confidence interval, the Bayesian interval based on the Jeffreys' rule prior, the fiducial interval, and the method of variance estimates recovery. The efficacies of these methods were compared by considering the coverage probability and average length obtained from simulation results of daily P M 2.5 datasets. The findings indicate that in most instances, the fiducial method with the highest posterior density demonstrated a superior performance. However, in certain scenarios, the Bayesian approach using the Jeffreys' rule prior for the highest posterior density yielded favorable results. [ABSTRACT FROM AUTHOR]

The Weibull distribution is a continuous probability distribution that finds wide application in various fields for analyzing real-world data. Specifically, wind speed data often adhere to the Weibull distribution. In our study, our aim is to compare the mean wind speed datasets from different areas in Thailand. To achieve this, we proposed simultaneous confidence intervals for all pairwise differences between the means of Weibull distributions. The generalized confidence interval (GCI), method of variance estimates recovery (MOVER), and a Bayesian approach, utilizing both gamma and uniform prior distributions, are proposed to construct simultaneous confidence intervals. Through simulations, we find that the Bayesian highest posterior density (HPD) interval using a gamma prior distribution demonstrates satisfactory performance, while the GCI proves to be a viable alternative. Finally, we applied these proposed approaches to real wind speed data in northeastern and southern Thailand to illustrate their effectiveness and practicality. [ABSTRACT FROM AUTHOR]

A new three-parameter discrete distribution called the zero-inflated cosine geometric (ZICG) distribution is proposed for the first time herein. It can be used to analyze over-dispersed count data with excess zeros. The basic statistical properties of the new distribution, such as the moment generating function, mean, and variance are presented. Furthermore, confidence intervals are constructed by using the Wald, Bayesian, and highest posterior density (HPD) methods to estimate the true confidence intervals for the parameters of the ZICG distribution. Their efficacies were investigated by using both simulation and real-world data comprising the number of daily COVID-19 positive cases at the Olympic Games in Tokyo 2020. The results show that the HPD interval performed better than the other methods in terms of coverage probability and average length in most cases studied. [ABSTRACT FROM AUTHOR]

The log-normal distribution (skewed distribution or asymmetry distribution) is used to describe random variables comprising positive real values. It is well known that the logarithm values of these are normally distributed (symmetry distribution). Positively right-skewed data applicable to the log-normal distribution are frequently observed in the fields of environmental studies, biology, and medicine. The number of zero observations follows a binomial distribution. However, problems can arise in the analysis of data containing zero observations along with log-normally distributed data, for which the delta-lognormal distribution is often referred to for using the analysis of the data. In statistics, the percentile provides the relative standing of a numerical data point when compared to all of the others in a distribution with reference to the observations at or below it. In this study, estimates for the confidence interval for the ratio of the percentiles of two delta-lognormal distributions are constructed using fiducial generalized confidence interval approaches based on the fiducial quantity and the optimal generalized fiducial quantity, the Bayesian approach, and the parametric bootstrap method. As assessed by Monte Carlo simulations using the RStudio programming in terms of the coverage probability and the average length, the Bayesian approach performed quite well by providing adequate coverage probabilities along with the shortest average lengths in all of the scenarios tested. Daily rainfall data contain both zero and positive values. The daily rainfall data can usually be fitted to the delta-lognormal distribution. Their application to rainfall data is also provided to illustrate their efficacies with real data. The efficacy of the approach is used to compare two rainfall dispersion populations. [ABSTRACT FROM AUTHOR]

In this study, we propose estimates for the confidence interval for the common mean of several zero-inflated gamma (ZIG) distributions based on the fiducial generalized confidence interval (GCI) and Bayesian and highest posterior density (HPD) methods based on the Jeffreys rule or uniform prior. Their performances in terms of their coverage probabilities and expected lengths are compared via a Monte Carlo simulation study. For almost all of the scenarios considered, the simulation results show that the fiducial GCI performed better than the Bayesian and HPD methods. Daily rainfall data from Chiang Mai Province, Thailand that contains several zero entries and follows a ZIG distribution is used to test the efficacies of the methods in real-world situations. [ABSTRACT FROM AUTHOR]

The Weibull distribution, one of the most significant distributions with applications in numerous fields, is associated with numerous distributions such as generalized gamma distribution, exponential distribution, and Rayleigh distribution, which are asymmetric. Nevertheless, it shares a close relationship with a normal distribution where a process of transformation allows them to become symmetric. The Weibull distribution is commonly used to study the failure of components and phenomena. It has been applied to a variety of scenarios, including failure time, claims amount, unemployment duration, survival time, and especially wind speed data. A suitable area for installing a wind turbine requires a wind speed that is both sufficiently high and consistent, and so comparing the variation in wind speed in two areas is eminently desirable. In this paper, methods to estimate the confidence interval for the ratio of the coefficients of variation of two Weibull distributions are proposed and applied to compare the variation in wind speed in two areas. The methods are the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER), and Bayesian methods based on the gamma and uniform priors. The Bayesian methods comprise the equal-tailed confidence interval and the highest posterior density (HPD) interval. The effectiveness of the methods was evaluated in terms of their coverage probabilities and expected lengths and also empirically applied to wind speed datasets from two different areas in Thailand. The results indicate that the HPD interval based on the uniform prior outperformed the others in most of the scenarios tested and so it is suggested for estimating the confidence interval for the ratio of the coefficients of variation of two Weibull distributions. [ABSTRACT FROM AUTHOR]

Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, which combines the binomial and gamma distributions. Precipitation in various areas of a country can be estimated by using simultaneous confidence intervals (CIs) for the ratios of the means of multiple zero-inflated gamma populations. Herein, we propose six simultaneous CIs constructed using the fiducial generalized CI method, Bayesian and highest posterior density (HPD) interval methods based on the Jeffreys'rule or uniform prior, and method of variance estimates recovery (MOVER). The performances of the proposed simultaneous CI methods were evaluated using a Monte Carlo simulation in terms of the coverage probabilities and expected lengths. The results from a comparative simulation study show that the HPD interval based on the Jeffreys'rule prior performed the best in most cases, while in some situations, the fiducial generalized CI performed well. All of the methods were applied to estimate the simultaneous CIs for the ratios of the means of natural rainfall data from six regions in Thailand. [ABSTRACT FROM AUTHOR]

Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two delta-gamma distributions by using the fiducial quantity method, Bayesian credible intervals based on the Jeffreys, uniform, or normal-gamma-beta priors, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or normal-gamma-beta priors. The performances of the proposed confidence interval methods were evaluated in terms of their coverage probabilities and average lengths via Monte Carlo simulation. Our findings show that the HPD intervals based on Jeffreys prior and the normal-gamma-beta prior are both suitable for datasets with a small and large probability of containing zeros, respectively. Rainfall data from Phrae province, Thailand, are used to illustrate the practicability of the proposed methods with real data. [ABSTRACT FROM AUTHOR]

In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μ m (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Count data containing both excess zeros and ones occur in many fields, and the zero-and-one inflated distribution is suitable for analyzing them. Herein, we construct confidence intervals (CIs) for the parameters of the zero-and-one inflated cosine geometric (ZOICG) distribution constructed by using five methods: a Wald CI based on the maximum likelihood estimate, equal-tailed Bayesian CIs based on the uniform or Jeffreys prior, and the highest posterior density intervals based on the uniform or Jeffreys prior. Their efficiencies were compared in terms of their coverage probabilities and average lengths via a simulation study. The results show that the highest posterior density intervals based on the uniform prior performed the best in most cases. The number of new daily COVID-19-related deaths in Luxembourg in 2020 involving data with a high proportion of zeros and ones were analyzed. It was found that the ZOICG model was appropriate for this scenario. [ABSTRACT FROM AUTHOR]

The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand. [ABSTRACT FROM AUTHOR]

The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is required. Rainfall dispersion is important and interesting, the confidence intervals for the variance of a gamma distribution with excess zeros help to examine rainfall intensity, which may be high or low risk. Herein, we propose confidence intervals for the variance of a gamma distribution with excess zeros by using fiducial quantities and parametric bootstrapping, as well as Bayesian credible intervals and highest posterior density intervals based on the Jeffreys', uniform, or normal-gamma-beta prior. The performances of the proposed confidence interval were evaluated by establishing their coverage probabilities and average lengths via Monte Carlo simulations. The fiducial quantity confidence interval performed the best for a small probability of the sample containing zero observations (°) whereas the Bayesian credible interval based on the normal-gamma-beta prior performed the best for large°. Rainfall data from the Kiew Lom Dam in Lampang province, Thailand, are used to illustrate the efficacies of the proposed methods in practice. [ABSTRACT FROM AUTHOR]

Herein, we present confidence intervals for the variance and difference of variances of Birnbaum-Saunders distributions constructed by using the bootstrap confidence interval (BCI), the generalized confidence interval (GCI), the Bayesian confidence interval (BayCI), and the highest posterior density interval (HPD). The performances of the proposed confidence intervals were investigated in terms of their coverage probabilities and average lengths by running a Monte Carlo simulation. The simulation results reveal that HPD performed the best, even for small sample sizes and/or different values of the shape parameter. To illustrate the efficacy of the proposed confidence intervals, we applied them to datasets of the PM 2.5 concentration in Chiang Mai, Thailand. [ABSTRACT FROM AUTHOR]

Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets. [ABSTRACT FROM AUTHOR]

Signal-to-noise ratio (SNR) is a reciprocal of coefficient of variation. The SNR is a measure of mean relative to the variability. Confidence procedures for common SNR of two-parameter exponential distributions were developed using generalized confidence interval (GCI) approach, large sample (LS) approach, adjusted method of variance estimates recovery (Adjusted MOVER) approach, and bootstrap approaches based on standard bootstrap (SB) and parametric bootstrap (PB). The performances of all approaches are measured by coverage probability and average length. Simulation studies show that all approaches have the coverage probabilities below the nominal confidence level of 0.95 when the common SNR is negative value. However, the coverage probabilities of all approaches are greater than the nominal confidence level of 0.95 when the common SNR is positive value. Moreover, the LS and AM approaches are the conservative confidence intervals. In addition, the GCI and PB approaches provide the confidence intervals with coverage probabilities close to the nominal confidence level of 0.95 when the sample sizes are large and the common SNR is positive value. The GCI and PB approaches are recommended to estimate the confidence intervals for the common SNR of two-parameter exponential distributions. Finally, all proposed approaches are employed in the data of the survival days of lung cancer patients for a demonstration. [ABSTRACT FROM AUTHOR]

Precipitation and flood forecasting are difficult due to rainfall variability. The mean of a delta-gamma distribution can be used to analyze rainfall data for predicting future rainfall, thereby reducing the risks of future disasters due to excessive or too little rainfall. In this study, we construct credible and highest posterior density (HPD) intervals for the mean and the difference between the means of delta-gamma distributions by using Bayesian methods based on Jeffrey's rule and uniform priors along with a confidence interval based on fiducial quantities. The results of a simulation study indicate that the Bayesian HPD interval based on Jeffrey's rule prior performed well in terms of coverage probability and provided the shortest expected length. Rainfall data from Chiang Mai province, Thailand, are also used to illustrate the efficacies of the proposed Methods. [ABSTRACT FROM AUTHOR]

Rainfall fluctuation is directly affected by the Earth's climate change. It can be described using the coefficient of variation (CV). Similarly, the ratio of CVs can be used to compare the rainfall variation between two regions. The ratio of CVs has been widely used in statistical inference in a number of applications. Meanwhile, the confidence interval constructed with this statistic is also of interest. In this paper, confidence intervals for the ratio of two independent CVs of lognormal distributions with excess zeros using the fiducial generalized confidence interval (FGCI), Bayesian methods based on the left-invariant Jeffreys, Jeffreys rule, and uniform priors, and the Wald and Fieller log-likelihood methods are proposed. The results of a simulation study reveal that the highest posterior density (HPD) Bayesian using the Jeffreys rule prior method performed the best in terms of the coverage probability and the average length for almost all cases of small sample size and a large sample size together with a large variance and a small proportion of non-zero values. The performance of the statistic is demonstrated on two rainfall datasets from the central and southern regions in Thailand. [ABSTRACT FROM AUTHOR]

Air pollution is a growing concern for the general public in Thailand with PM 2.5 (particulate matter - 2.5 mm) having the greatest impact on health. The inverse Gaussian (IG) distribution is used for examining the frequency of high concentration events and has often been applied to analyze pollution data, with the coefficient of variation (CV) being used to calculate the quantitative difference in PM 2.5 concentrations. Herein, we propose confidence intervals for the CV of an IG distribution based on the generalized confidence interval (GCI), the adjusted generalized confidence interval (AGCI), the bootstrap percentile confidence interval (BPCI), the fiducial confidence interval (FCI), and the fiducial highest posterior density confidence interval (F-HPDCI). The performance of the proposed confidence intervals was evaluated by using their coverage probabilities and average lengths from various scenarios via Monte Carlo simulations. The simulation results indicate that the coverage probabilities of the AGCI and FCI methods were higher than or close to the nominal level in all of test case scenarios. Moreover, FCI outperformed the others for small sample sizes by achieving the shortest average length. The efficacies of the confidence intervals were demonstrated by using PM 2.5 data from the Din Daeng and Bang Khun Thian districts in Bangkok, Thailand. [ABSTRACT FROM AUTHOR]

Natural rainfall is necessary for agriculture in Thailand. Often, rainfall data contain zero and positive right-skewed observations. Within a given region, the mean rainfall can be used to evaluate how rainfall has changed over a period of time, and so, in this article, we propose interval estimates and an adjustment process based on the Bayesian approach to compute the rainfall amount mean. This includes highest posterior density intervals (HPDs) based on the beta (HPD-B), normal inverse chi-squared (HPD-NIC) and uniform (HPD-U) priors, which were compared with the existing methods. Coverage probability and relative average length were used to assess the performance of the methods by comparing their computation. A numerical evaluation showed that for a single mean and even chance of having zero observations, HPD-beta achieved the given target with small to moderate sample sizes, while HPD-U tended to perform very well with large sample size. To compare the difference between two means, HPD-U demonstrated excellent performance in almost all cases. Daily rainfall data from provinces in northern Thailand were used to confirm the efficacy of the new methods. [ABSTRACT FROM AUTHOR]

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 σj2. 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. [ABSTRACT FROM AUTHOR]

Wind energy is an important renewable energy source for generating electricity that has the potential to replace fossil fuels. Herein, we propose confidence intervals for the difference between the coefficients of variation of Weibull distributions constructed using the concepts of the generalized confidence interval (GCI), Bayesian methods, the method of variance estimates recovery (MOVER) based on Hendricks and Robey’s confidence interval, a percentile bootstrap method, and a bootstrap method with standard errors. To analyze their performances, their coverage probabilities and expected lengths were evaluated via Monte Carlo simulation. The simulation results indicate that the coverage probabilities of GCI were greater than or sometimes close to the nominal confidence level. However, when the Weibull shape parameter was small, the Bayesian- highest posterior density interval was preferable. All of the proposed confidence intervals were applied to wind speed data measured at 90-meter wind energy potential stations at various regions in Thailand. [ABSTRACT FROM AUTHOR]

Abstract Herein, we propose eight Bayesian methods (credible and highest posterior density intervals using the Jeffreys rule, independence Jeffreys, uniform, or normal-gamma priors) and one based on the fiducial quantity for constructing confidence intervals for the ratio of the means of zero-inflated gamma distributions. Simulation studies were conducted to evaluate the efficacies of the confidence intervals and compare their performances in terms of coverage probabilities and expected lengths, in which the Bayesian highest posterior density interval using the Jeffreys rule prior performed the best. We also applied the methods to rainfall datasets from northern Thailand to demonstrate their efficacies with real data. [ABSTRACT FROM AUTHOR]

The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings. [ABSTRACT FROM AUTHOR]

The aim of this study is to establish new confidence intervals for the single coefficient of variation of an inversegamma distribution using Bayesian methods based on the Jeffreys, reference, and uniform priors and compare them with the Wald method. The Bayesian methods are constructed with either the credible confidence interval or the highest posterior density (HPD) interval. These concepts were extended to find the difference between the coefficients of variation for two independent inverse-gamma populations. The performances of the proposed confidence intervals were evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian HPD interval based on the reference prior can be recommended for constructing confidence intervals for the coefficient of variation of a single inverse-gamma distribution and the Bayesian HPD interval based on the Jeffreys prior can be recommended for constructing confidence intervals for the difference between the coefficients of variation of two inverse-gamma distributions. Rainfall data from northern Thailand were used to illustrate the efficacies of the proposed methods. [ABSTRACT FROM AUTHOR]

The Birnbaum-Saunders distribution plays a crucial role in statistical analysis, serving as a model for failure time distribution in engineering and the distribution of particulate matter 2.5 (PM2.5) in environmental sciences. When assessing the health risks linked to PM2.5, it is crucial to give significant weight to percentile values, particularly focusing on lower percentiles, as they offer a more precise depiction of exposure levels and potential health hazards for the population. Mean and variance metrics may not fully encapsulate the comprehensive spectrum of risks connected to PM2.5 exposure. Various approaches, including the generalized confidence interval (GCI) approach, the bootstrap approach, the Bayesian approach, and the highest posterior density (HPD) approach, were employed to establish confidence intervals for the percentile of the Birnbaum-Saunders distribution. To assess the performance of these intervals, Monte Carlo simulations were conducted, evaluating them based on coverage probability and average length. The results demonstrate that the GCI approach is a favorable choice for estimating percentile confidence intervals. In conclusion, this article presents the results of the simulation study and showcases the practical application of these findings in the field of environmental sciences., Competing Interests: The authors declare that they have no competing interests., (© 2024 Thangjai et al.)

The Weibull distribution has been used to analyze data from many fields, including engineering, survival and lifetime analysis, and weather forecasting, particularly wind speed data. It is useful to measure the central tendency of wind speed data in specific locations using statistical parameters for instance the mean to accurately forecast the severity of future catastrophic events. In particular, the common mean of several independent wind speed samples collected from different locations is a useful statistic. To explore wind speed data from several areas in Surat Thani province, a large province in southern Thailand, we constructed estimates of the confidence interval for the common mean of several Weibull distributions using the Bayesian equitailed confidence interval and the highest posterior density interval using the gamma prior. Their performances are compared with those of the generalized confidence interval and the adjusted method of variance estimates recovery based on their coverage probabilities and expected lengths. The results demonstrate that when the common mean is small and the sample size is large, the Bayesian highest posterior density interval performed the best since its coverage probabilities were higher than the nominal confidence level and it provided the shortest expected lengths. Moreover, the generalized confidence interval performed well in some scenarios whereas adjusted method of variance estimates recovery did not. The approaches were used to estimate the common mean of real wind speed datasets from several areas in Surat Thani province, Thailand, fitted to Weibull distributions. These results support the simulation results in that the Bayesian methods performed the best. Hence, the Bayesian highest posterior density interval is the most appropriate method for establishing the confidence interval for the common mean of several Weibull distributions., Competing Interests: The authors declare there are no competing interests., (©2023 La-ongkaew et al.)

Weighted percentiles in many areas can be used to investigate the overall trend in a particular context. In this article, the confidence intervals for the common percentile are constructed to estimate rainfall in Thailand. The confidence interval for the common percentile help to indicate intensity of rainfall. Herein, four new approaches for estimating confidence intervals for the common percentile of several delta-lognormal distributions are presented: the fiducial generalized confidence interval, the adjusted method of variance estimates recovery, and two Bayesian approaches using fiducial quantity and approximate fiducial distribution. The Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths via the R statistical program. The proposed confidence intervals are compared in terms of their coverage probabilities and average lengths, and the results of a comparative study based on these metrics indicate that one of the Bayesian confidence intervals is better than the others. The efficacies of the approaches are also illustrated by applying them to daily rainfall datasets from various regions in Thailand., Competing Interests: The authors declare that they have no competing interests., (© 2022 Thangjai et al.)

Rainfall fluctuation makes precipitation and flood prediction difficult. The coefficient of variation can be used to measure rainfall dispersion to produce information for predicting future rainfall, thereby mitigating future disasters. Rainfall data usually consist of positive and true zero values that correspond to a delta-lognormal distribution. Therefore, the coefficient of variation of delta-lognormal distribution is appropriate to measure the rainfall dispersion more than lognormal distribution. In particular, the measurement of the dispersion of precipitation from several areas can be determined by measuring the common coefficient of variation in the rainfall from those areas together. Herein, we compose confidence intervals for the common coefficient of variation of delta-lognormal distributions by employing the fiducial generalized confidence interval, equal-tailed Bayesian credible intervals incorporating the independent Jeffreys or uniform priors, and the method of variance estimates recovery. A combination of the coverage probabilities and expected lengths of the proposed methods obtained via a Monte Carlo simulation study were used to compare their performances. The results show that the equal-tailed Bayesian based on the independent Jeffreys prior was suitable. In addition, it can be used the equal-tailed Bayesian based on the uniform prior as an alternative. The efficacies of the proposed confidence intervals are demonstrated via applying them to analyze daily rainfall datasets from Nan, Thailand., Competing Interests: The authors declare that they have no competing interests., (© 2022 Yosboonruang et al.)