Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach

2014 ◽  
Vol 69 ◽  
pp. 133-140 ◽  
Author(s):  
S.M. Sadooghi-Alvandi ◽  
A. Malekzadeh
Keyword(s):  
Confidence Intervals ◽  
Parametric Bootstrap ◽  
Simultaneous Confidence Intervals ◽  
Lognormal Distributions ◽  
Bootstrap Approach

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.

Confidence intervals for the ratio of two independent Poisson rates: Parametric bootstrap, modified asymptotic, and approximate-estimate approaches

2019 ◽  
Vol 29 (8) ◽  
pp. 2140-2150
Author(s):  
Mahmood Kharrati-Kopaei ◽  
Raziye Dorosti-Motlagh
Keyword(s):  
Confidence Intervals ◽  
Coverage Probability ◽  
Ad Hoc ◽  
Rare Events ◽  
Average Length ◽  
Parametric Bootstrap ◽  
Asymptotic Results ◽  
Approximate Estimate ◽  
Bootstrap Approach ◽  
Estimate Method

We propose four confidence intervals for the ratio of two independent Poisson rates. We apply a parametric bootstrap approach, two modified asymptotic results, and we propose an ad-hoc approximate-estimate method to construct confidence intervals. We justify the correctness of the proposed methods asymptotically in the case of non-rare events (when the Poisson rates are large). We also compare the proposed confidence intervals with some recommended ones in the case of rare events (when the Poisson rates are small) via an extensive simulation study. The results show that the proposed modified asymptotic and the approximate-estimate confidence intervals perform reasonably well in terms of coverage probability and average length.

scholarly journals On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1212
Author(s):  
Xin Gao ◽  
Frank Konietschke ◽  
Qiong Li
Keyword(s):  
Confidence Intervals ◽  
Delta Method ◽  
Lasso Regression ◽  
Bootstrap Confidence Intervals ◽  
Simultaneous Confidence Intervals ◽  
Multiple Parameters ◽  
Joint Inference ◽  
Smoothed Bootstrap ◽  
Bootstrap Approach ◽  
Percentile Bootstrap

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.

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 Estimating confidence intervals for cerebral autoregulation: a parametric bootstrap approach

2021 ◽  
Author(s):  
Jack Edward Douglas Bryant ◽  
Anthony A Birch ◽  
Ronney B Panerai ◽  
Dragana Nikolic ◽  
Diederik O Bulters ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Cerebral Autoregulation ◽  
Parametric Bootstrap ◽  
Bootstrap Approach

scholarly journals Estimating the average daily rainfall in Thailand using confidence intervals for the common mean of several delta-lognormal distributions

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10758
Author(s):  
Patcharee Maneerat ◽  
Sa-Aat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Average Length ◽  
Daily Rainfall ◽  
Parametric Bootstrap ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Common Mean ◽  
The Common ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

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.

scholarly journals 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 ◽  
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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