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There are many types of skewed distribution, one of which is the lognormal distribution that is positively skewed and may contain true zero values. The coefficient of quartile variation is a statistical tool used to measure the dispersion of skewed and kurtosis data. The purpose of this study is to establish confidence and credible intervals for the coefficient of quartile variation of a zero-inflated lognormal distribution. The proposed approaches are based on the concepts of the fiducial generalized confidence interval, and the Bayesian method. Coverage probabilities and expected lengths were used to evaluate the performance of the proposed approaches via Monte Carlo simulation. The results of the simulation studies show that the fiducial generalized confidence interval and the Bayesian based on uniform and normal inverse Chi-squared priors were appropriate in terms of the coverage probability and expected length, while the Bayesian approach based on Jeffreys' rule prior can be used as alternatives. In addition, real data based on the red cod density from a trawl survey in New Zealand is used to illustrate the performances of the proposed approaches. Doi: 10.28991/esj-2021-01289 Full Text: PDF

Coronavirus disease 2019 (COVID-19) has spread rapidly throughout the world and has caused millions of deaths. However, the number of daily COVID-19 deaths in Thailand has been low with most daily records showing zero deaths, thereby making them fit a Zero-Inflated Poisson (ZIP) distribution. Herein, confidence intervals for the Coefficient Of Variation (CV) of a ZIP distribution are derived using four methods: the standard bootstrap (SB), percentile bootstrap (PB), Markov Chain Monte Carlo (MCMC), and the Bayesian-based highest posterior density (HPD), for which using the variance of the CV is unnecessary. We applied the methods to both simulated data and data on the number of daily COVID-19 deaths in Thailand. Both sets of results show that the SB, MCMC, and HPD methods performed better than PB for most cases in terms of coverage probability and average length. Overall, the HPD method is recommended for constructing the confidence interval for the CV of a ZIP distribution. Doi: 10.28991/esj-2021-SPER-05 Full Text: PDF

Herein, we propose the Bayesian approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. For the first case, the Bayesian approach was compared with large-sample, Chi-squared, and approximate fiducial approaches via Monte Carlo simulation. For the second case, the Bayesian approach was compared with the method of variance estimates recovery (MOVER), modified MOVER, and approximate fiducial approaches using Monte Carlo simulation. The results show that the Bayesian approach provided the best approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. To illustrate the performances of the confidence limit construction approaches with real data, they were applied to analyze real PM10 datasets from the Nan and Chiang Mai provinces in Thailand, the results of which are in agreement with the simulation results. Doi: 10.28991/esj-2021-01264 Full Text: PDF

When considering the medical care costs data with a high proportion of zero items of two inpatient groups, comparing them can be estimated using confidence intervals for the ratio of the means of two delta-lognormal distributions. The Bayesian credible interval-based uniform-beta prior (BCIh-UB) is proposed and compared with the generalized confidence interval (GCI), fiducial GCI (FGCI), the method of variance estimates recovery (MOVER), BCIh based on Jeffreys’ rule prior (BCIh-JR), and BCIh based on the normal-gamma prior (BCIh-NG). The coverage probability (CP), average length (AL), and lower and upper error rates were the performance measures applied for assessing the methods through a Monte Carlo simulation. A numerical evaluation showed that BCIh-UB had much better CP and AL than the others even with a large difference between the variances and with a high proportion of zero. Finally, to illustrate the efficacy of BCIh-UB, the methods were applied to two sets of medical care costs data.

Unnatural rainfall fluctuation can result in such severe natural phenomena as drought and floods. This variability not only occurs in areas with unusual natural features such as land formations and drainage but can also be due to human intervention. Since rainfall data often contain zero values, evaluating rainfall change is an important undertaking, which can be estimated via the confidence intervals for the difference between delta-lognormal variances using the highest posterior density-based reference (HPD-ref) and probability-matching (HPD-pm) priors. Simulation results indicate that HPD-pm performances were better than other methods in terms of coverage rates and relative average lengths for the difference in delta-lognormal variances, even with a large difference in variances. To illustrate the efficacy of our proposed methods, we applied them to daily rainfall data sets for the lower and upper regions of northern Thailand.

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.

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.

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.

Log-normal distribution is used widely in application fields such as economics and finance. This paper considers confidence interval estimates for common signal-to-noise ratio of log-normal distributions based on generalized confidence interval (GCI), adjusted method of variance estimates recovery, and computational approaches. A simulation study is conducted to compare the performance of these confidence intervals. A Monte Carlo simulation is applied to report coverage probability and average length of the confidence intervals. Based on the simulation study, for $$k=$$ 3, the GCI can be used. For $$k=$$ 6, the results of GCI approach perform similarly to the results of computational approach. For $$k=$$ 10, the computational approach can be considered as an alternative to estimate the confidence interval. A numerical example based on real data is presented to illustrate the proposed approaches.

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...

In this article, we propose approaches for constructing confidence intervals for the single signal-to-noise ratio (SNR) of a log-normal distribution and the difference in the SNRs of two log-normal distributions. The performances of all of the approaches were compared, in terms of the coverage probability and average length, using Monte Carlo simulations for varying values of the SNRs and sample sizes. The simulation studies demonstrate that the generalized confidence interval (GCI) approach performed well, in terms of coverage probability and average length. As a result, the GCI approach is recommended for the confidence interval estimation for the SNR and the difference in SNRs of two log-normal distributions.

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.

In this paper, the aim is to propose the confidence interval for the mean of Zero-inflated Poisson distribution. The two methods namely the Markov chain Monte Carlo (MCMC) and the highest posterior density (HPD) are applied to avoid the complex variance of mean of Zero-inflated Poisson distribution. Both the simulation study and the real-life data of the number of new daily COVID-19 cases in Laos are considered. The results show that Markov chain Monte Carlo method perform better than the highest posterior density method.

This paper proposes confidence intervals for a single coefficient of variation (CV) in the inverse gamma distribution, using the score method, the Wald method, and the percentile bootstrap (PB) confidence interval. Mote Carlo simulations were used to investigate the performance of these confidence intervals in terms of coverage probabilities (CP) and expected length (EL). The results showed that the Wald method for the single CVs are better than the other confidence intervals. Finally, these methods applied to determine the confidence interval of a real data from rainfall of Thailand.

There are two main approaches to statistical machine learning. The approaches are frequentist approach and Bayesian approach. The frequentist approach is commonly discussed in statistical inference. This approach assumes that unknown parameters are fixed constants. Frequentist approach uses maximum likelihood estimates of unknown parameters to predict new data points. Bayesian approach treats parameters as random variables. Bayesian approach is an important technique in statistics and mathematical statistics. Bayesian inference has found application in science, medicine, philosophy, and engineering. In this paper, the Bayesian confidence intervals for single mean and difference of two means with unknown coefficients of variation (CVs) of normal distributions are introduced. An evaluation of the performance of the Bayesian confidence intervals compared to frequentist confidence intervals of Thangjai et al. [1] for mean and difference of means with unknown CVs using Monte Carlo simulations is conducted. Simulations showed that the Bayesian approach performs better than the existing approaches when sample sizes are moderate and large. The Bayesian approach and other existing approaches are illustrated using two examples.

Fish dispersal can be used to indicate the abundance of fish populations in a given local environment, and it is also important for understanding the ecology of fish species. The motivation of this research is how to estimate the variation in fish abundance from trawl surveys using interval estimations for the single variance of a delta-lognormal distribution. Our proposed methods are the normal approximation (NA), fiducial generalized confidence interval (FGCI) and the method of variance estimates recovery (MOVER). Monte Carlo simulation was used to assess the performance of the three methods in terms of coverage rate and average width. The findings from the simulation study show that NA and FGCI worked well for small and large variances, respectively. Data on the densities of red cod from trawl surveys were used to illustrate the efficacy of our methods.

The aim of this study is to propose confidence intervals for the difference between the coefficients of variation of inverse Gaussian distributions based on the generalized confidence interval (GCI), the adjusted generalized confidence interval (AGCI), the bootstrap percentile confidence interval (BPCI), and the method of variance estimates recovery (MOVER). The performances of the proposed confidence intervals were evaluated using coverage probabilities and average lengths via Monte Carlo simulation. The results showed that the GCI and AGCI methods were higher than or close to the nominal level in all cases. For small sample sizes, MOVER was better than the other methods because it provided the narrowest average length. The performances of all the approaches were illustrated using two real data examples.

The coefficient of variation (CV) is wildly used as the index of reliability of measurement. Hence, the problem of comparing two coefficients of variation (CVs) is interesting. Moreover, Birnbaum-Saunders (BS) distribution is frequently used for analysing the lifetime of materials and equipment. In this paper, the generalized confidence interval (GCI) was proposed to make inference about the ratio of two CVs of the BS distribution. A Monte Carlo simulation study was carried out to compare the performance of GCI with the biased-corrected percentile bootstrap (BCPB) confidence interval and the biased-corrected and accelerated (BCa) confidence interval based on the coverage probability and the average length. The simulation results indicate that GCI is recommended. The fatigue life of 6061-T6 aluminum coupons are applied to illustrate the proposed method.

This paper proposes the novel approaches to construct confidence intervals for the common coefficient of variation (CV) of several normal populations using the concepts of the adjusted generalized ...

Statistical estimation of the difference between normal means with known coefficients of variation has been investigated for the first time. This phenomenon occurs normally in environment and agriculture experiments when the scientist knows the coefficients of variation of their experiments. In this paper, we constructed new confidence intervals for the difference between normal means with known coefficients of variation. We also derived analytic expressions for the coverage probability and the expected length of each confidence interval. To confirm our theoretical results, Monte Carlo simulation will be used to assess the performance of these intervals based on their coverage probabilities and their expected lengths and we also show our result to the real problem.

The aim of this paper is to propose the new confidence intervals for single coefficient of variation of Weibull distributions, using the concept of the generalized confidence interval (GCI), the fiducial generalized confidence interval (FGCI), and the bootstrap percentile method. The coverage probabilities and the expected lengths were evaluated via Monte Carlo simulation. The simulation results showed that the coverage probabilities of the GCIs and the FGCIs were greater than or close to the nominal confidence level. Both of them were recommended. The coverage probabilities of confidence intervals based on the bootstrap percentile method were under the nominal confidence level. Regarding the expected lengths, they tended to decrease when the sample size was increased. All proposed confidence intervals were applied to some real world data in this study.

The coefficient of variation is an useful indicator to measure and compare separated data in different units. This paper proposes the new confidence interval for the single coefficient of variation and the difference between coefficients of variation of Inverse Gaussian distribution using the generalized confidence interval (GCI) and the bootstrap percentile confidence interval. A Monte Carlo simulation is used to construct and compare the performance of these confidence intervals based on the coverage probability and average length. The results of the simulation study showed that the GCI is an appropriate method to construct the confidence interval for the single coefficient of variation and the difference between coefficients of variation. The proposed approaches are illustrated based on the real data.

Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.

Since rainfall data series often contain zero values and thus follow a delta-lognormal distribution, the coefficient of variation is often used to illustrate the dispersion of rainfall in a number of areas and so is an important tool in statistical inference for a rainfall data series. Therefore, the aim in this paper is to establish new confidence intervals for a single coefficient of variation for delta-lognormal distributions using Bayesian methods based on the independent Jeffreys’, the Jeffreys’ Rule, and the uniform priors compared with the fiducial generalized confidence interval. The Bayesian methods are constructed with either equitailed confidence intervals or the highest posterior density interval. The performance of the proposed confidence intervals was evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian equitailed confidence interval based on the independent Jeffreys’ prior outperformed the other methods. Rainfall data recorded in national parks in July 2015 and in precipitation stations in August 2018 in Nan province, Thailand are used to illustrate the efficacy of the proposed methods using a real-life dataset.

The daily average natural rainfall amounts in the five regions of Thailand can be estimated using the confidence intervals for the common mean of several delta-lognormal distributions based on the fiducial generalized confidence interval (FGCI), large sample (LS), method of variance estimates recovery (MOVER), parametric bootstrap (PB), and highest posterior density intervals based on Jeffreys’ rule (HPD-JR) and normal-gamma-beta (HPD-NGB) priors. Monte Carlo simulation was conducted to assess the performance in terms of the coverage probability and average length of the proposed methods. The numerical results indicate that MOVER and PB provided better performances than the other methods in a variety of situations, even when the sample case was large. The efficacies of the proposed methods were illustrated by applying them to real rainfall datasets from the five regions of Thailand.

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.

This paper proposes the new confidence intervals for difference between means and ratio of means of Weibull distributions based upon the generalized confidence interval (GCI) and the method of variance estimates recovery (MOVER) based on Wald confidence interval. The simulation study was conducted using the R statistical package to evaluate the coverage probabilities and expected lengths of the proposed confidence intervals. The simulation results indicated that the coverage probabilities of GCI are greater than or close to the nominal confidence level of 0.95 for the difference between means and ratio of means. The coverage probabilities of MOVER based on Wald confidence interval were under the nominal confidence level for small sample sizes and close to or over than the nominal confidence level when the sample size increased. The expected lengths of the proposed confidence intervals tended to decrease when the sample size increased. All proposed confidence intervals were applied to real data.

This paper investigates the performance of the confidence intervals for a single inverse mean and the difference of two inverse means of normal distributions with unknown coefficients of variation (CVs). The confidence intervals for the inverse mean with unknown coefficient of variation (CV) were constructed based on the generalized confidence interval (GCI) approach and the large sample approach. The generalized confidence interval and large sample confidence interval for the inverse mean with unknown CV were compared with the generalized confidence interval for the inverse mean of Niwitpong and Wongkhao [5]. Moreover, the confidence intervals for the difference of inverse means with unknown CVs were constructed using the GCI approach, large sample approach and method of variance estimates recovery (MOVER) approach and then compared with existing confidence interval for the difference of inverse means based on the GCI approach of Niwitpong and Wongkhao [6]. The coverage probability and average length of the confidence intervals were evaluated by a Monte Carlo simulation. Carrying out the simulation studies, the results showed that the generalized confidence interval provides the best confidence interval for the inverse mean with unknown CV. The generalized confidence interval and the MOVER confidence interval for the difference of inverse means with unknown CVs perform well in terms of the coverage probability and average length. Finally, two real datasets are analyzed to illustrate the proposed confidence intervals.

In this study, estimating the difference in the percentiles of two delta-lognormal independent populations was of interest. We used several parameters in a simulation study to compare two delta-lognormal independent populations in terms of percentiles. By simulation, it was found that the coverage probabilities were sufficiently small with a small sample size (\(n = 10\), \(m = 10\) and \(n = 50\), \(m = 10\)), but when the size of the sample was large, the coverage probabilities increased in all three cases in this study. When applying our method to a real-life weather situation, we found that the rainfall data from the Ping River in Northern Thailand (Fang and Chiang Dao, Chiang Mai province) followed delta-lognormal distribution using the confidence interval of delta-lognormal distribution percentiles and that the coverage probability was well estimated.

Focusing on delta-lognormal distribution, confidence intervals for the mean are proposed in this research. This will be achieved using a method of variance estimates recovery (MOVER) and generalized confidence interval (GCI) based on weighted beta distribution by Hannig, and MOVER based on variance stabilized transformation (VST). These are then compared with GCI based on VST. The coverage probabilities and average lengths are performances from the presented methods, computed via Monte Carlo simulation. Our results showed that MOVER based on VST is the recommended method under situations of slight probability of being zero and large coefficient of variation in small to moderate sample sizes. Ultimately, rainfall data in Chiang Mai was used to illustrate all of the presented methods.

The aim of this paper is to propose confidence intervals using the concepts that include the generalized fiducial interval (GFI) and the method of variance estimates recovery (MOVER). The performance of the proposed approaches were gauged in terms of the coverage probabilities and the expected lengths. Simulation studies shown that GFI outperformed other approaches with small sample sizes together with small variances. For larger sample sizes, GFI and MOVER based on the Jeffreys performed better than the other approaches when the variances were large. Furthermore, the results for the cases of high proportion of non-zero values of large sample sizes indicated that GFI is suited for small variance, and if variances are growing, then MOVER based on the Wilson score should be chosen.

Novel approaches were proposed for constructing simultaneous confidence intervals for all differences of coefficients of variation of log-normal distributions, using the method of variance estimates recovery (MOVER) approach and the computational approach. They are then compared with the fiducial generalized confidence interval (FGCI) approach which was presented by (W. Thangjai, S. Niwitpong and S. Niwitpong, Simultaneous fiducial generalized confidence intervals for all differences of coefficients of variation of log-normal distributions, Lecture Notes in Artificial Intelligence, 2016). A Monte Carlo simulation was conducted to compare the performances of these simultaneous confidence intervals based on the coverage probability and average length. Simulation results show that the MOVER approach is satisfactory performances for all sample case ($k$) and sample size ($n$). Moreover, the computational approach performs as well as the MOVER approach when the sample size is large. Our approaches are applied to an analysis of a real data set from rainfall in regions of Thailand.

This paper investigates confidence intervals for the ratio of means in the delta-lognormal distribution. The method of variance estimates recovery (MOVER) based on the variance stabilizing transformation, Wilson score method and Jeffreys method were proposed to establish confidence intervals for the ratio of delta-lonormal means. These confidence intervals were compared with the existing confidence interval based on the generalized confidence interval (GCI). The coverage probabilities and average lengths were the performance of these proposed confidence intervals which were evaluated via Monte Carlo simulation. The simulation results showed that the three MOVERs’ performance is similar to the GCI in terms of coverage probability for all sample sizes except when the probability \(\delta \) of having zero is close to zero and the coefficient of variation gets large. However, the MOVER based on Jeffreys provides the minimal average lengths when the coefficient of variation are small for all sample sizes. Finally, two data sets are used to illustrate examples of using the proposed confidence intervals.

This paper proposes confidence intervals for the coefficient of variation of the delta-lognormal distribution which are based on the generalized confidence interval (GCI) method, it is compared with the modified Fletcher method. The coverage probabilities and the expected lengths are used for assessing the performance of these confidence interval. Simulation results show that the GCI method perform best in term of the coverage probability and expected length.

For constructing simultaneous confidence intervals for the differences of means of several two-parameter exponential distributions, generalized confidence interval (GCI) approach and method of variance estimates recovery (MOVER) approach are proposed. The performance of the proposed approaches is compared with parametric bootstrap (PB) approach. Simulation studies showed that the MOVER approach performs better than the other approaches: its coverage probability is close to the nominal confidence level and average length is shorter than the other approaches. Three approaches are illustrated using an example.

This paper examines confidence intervals for the single signal-to-noise ratio (SNR), the difference of signal-to-noise ratios (SNRs), and the common SNR of normal distributions, using the generalized confidence interval (GCI) approach, large-sample approach, and method of variance estimates recovery (MOVER) approach. The coverage probability and average width of these confidence intervals were evaluated by Monte Carlo simulation. The simulation results indicated that the MOVER approach performs better than the other approaches in terms of coverage probability for the single SNR and the difference of SNRs. Furthermore, the coverage probabilities of the adjusted MOVER approach are satisfactory for the common SNR. We also illustrate our confidence intervals using three examples.

This paper presents new confidence intervals for the common mean of lognormal distributions by transforming the lognormal data. Three approaches were based on generalized confidence intervals (GCI) and adjusted method of variance estimates recovery (adjusted MOVER). A Monte Carlo simulation was used to assess the coverage probability and average length. The simulation study found that the adjusted MOVER approach based on Angus’s conservative method (AM2) is appropriate and had the smallest coverage error in all of the scenarios. The generalized confidence interval approach (GCI) had the second smallest coverage error and had the smallest average lengths among the three approaches when the coverage probabilities were close to nominal level 0.95. Real data examples illustrate this approach.

This paper presents a procedure for simultaneous confidence interval estimation for the differences of means of several normal populations with unknown coefficients of variation. The proposed approaches are a generalized confidence interval approach (GCI approach) and method of variance estimates recovery approach (MOVER approach). A Monte Carlo simulation was used to evaluate the performance in terms of coverage probability, average width and standard error. The simulation results indicated that the GCI and MOVER approaches are satisfactory in terms of the coverage probability, but the average widths of the MOVER approach are slightly shorter than the average widths of the GCI approach. The proposed approaches are illustrated by an example.