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 The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e9662
Author(s):  
Noppadon Yosboonruang ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Rainfall Data ◽  
Posterior Density ◽  
Lognormal Distributions ◽  
Coefficients Of Variation ◽  
Coverage Probabilities ◽  
The Difference ◽  
Fiducial Generalized Confidence Interval ◽  
Highest Posterior Density

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.

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.

scholarly journals Reliable confidence intervals for RelTime estimates of evolutionary divergence times

2019 ◽  
Author(s):  
Qiqing Tao ◽  
Koichiro Tamura ◽  
Beatriz Mello ◽  
Sudhir Kumar
Keyword(s):  
Confidence Intervals ◽  
Divergence Time ◽  
Simulated Data ◽  
Molecular Dating ◽  
Divergence Times ◽  
Rate Variation ◽  
Evolutionary Divergence ◽  
Posterior Density ◽  
Divergence Time Estimates ◽  
Highest Posterior Density

AbstractConfidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in these analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density (HPD) intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, i.e., the true time is contained within the CIs with a 95% probability. These developments will encourage broader use of computationally-efficient RelTime approach in molecular dating analyses and biological hypothesis testing.

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.

CONFIDENCE INTERVALS FOR THE COMMON MEAN OF SEVERAL ONE-PARAMETER EXPONENTIAL POPULATIONS

2017 ◽  
Vol 51 (4) ◽  
pp. 245-260
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Common Mean ◽  
The Common ◽  
Exponential Populations

scholarly journals The Bayesian Confidence Interval for Coefficient of Variation of Zero-inflated Poisson Distribution with Application to Daily COVID-19 Deaths in Thailand

2021 ◽  
Vol 5 ◽  
pp. 62-76
Author(s):  
Sunisa Junnumtuam ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Average Length ◽  
Simulated Data ◽  
Posterior Density ◽  
The World ◽  
Bayesian Confidence Interval ◽  
Percentile Bootstrap ◽  
Highest Posterior Density ◽  
Better Than

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

scholarly journals Reliable Confidence Intervals for RelTime Estimates of Evolutionary Divergence Times

2019 ◽  
Vol 37 (1) ◽  
pp. 280-290 ◽  
Author(s):  
Qiqing Tao ◽  
Koichiro Tamura ◽  
Beatriz Mello ◽  
Sudhir Kumar
Keyword(s):  
Confidence Intervals ◽  
Divergence Time ◽  
Simulated Data ◽  
Molecular Dating ◽  
Divergence Times ◽  
Rate Variation ◽  
Evolutionary Divergence ◽  
Posterior Density ◽  
Divergence Time Estimates ◽  
Highest Posterior Density

Abstract Confidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in dating analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, that is, the actual time is contained within the CIs with a 94% probability. These developments will encourage broader use of computationally efficient RelTime approaches in molecular dating analyses and biological hypothesis testing.

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