BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

2004 ◽  
Vol 21 (03) ◽  
pp. 407-419 ◽  
Author(s):  
JAE-HAK LIM ◽  
SANG WOOK SHIN ◽  
DAE KYUNG KIM ◽  
DONG HO PARK
Keyword(s):  
Steady State ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Repairable System ◽  
Bootstrap Confidence Interval ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Methods ◽  
Percentile Bootstrap

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

scholarly journals ON THE NUMBER OF BOOTSTRAP REPETITIONS FOR BCa CONFIDENCE INTERVALS

2002 ◽  
Vol 18 (4) ◽  
pp. 962-984 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Moshe Buchinsky
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
High Probability ◽  
Random Variables ◽  
American Statistical Association ◽  
Bootstrap Confidence Interval ◽  
Statistical Association ◽  
Step Method ◽  
Bootstrap Confidence Intervals ◽  
The Ideal

This paper considers the problem of choosing the number of bootstrap repetitions B to use with the BCa bootstrap confidence intervals introduced by Efron (1987, Journal of the American Statistical Association 82, 171–200). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = ∞. We specify a three-step method of choosing B that ensures that the lower and upper lengths of the confidence interval deviate from those of the ideal bootstrap confidence interval by at most a small percentage with high probability.

scholarly journals Confidence Intervals for the Signal-to-Noise Ratio and Difference of Signal-to-Noise Ratios of Log-Normal Distributions

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 164-173 ◽  
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Normal Distributions ◽  
Noise Ratio ◽  
The Difference ◽  
Log Normal

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.

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

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 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

Accuracy assessment of the joint CloudSat-CALIPSO global cloud amount based on the bootstrap confidence intervals

2021 ◽  
Author(s):  
Andrzej Kotarba ◽  
Mateusz Solecki
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Spatial Resolution ◽  
Confidence Level ◽  
Accuracy Assessment ◽  
Cloud Amount ◽  
Radiation Budget ◽  
Bootstrap Confidence Intervals ◽  
Fine Spatial Resolution ◽  
Interval Width

<p>Vertically-resolved cloud amount is essential for understanding the Earth’s radiation budget. Joint CloudSat-CALIPSO, lidar-radar cloud climatology remains the only dataset providing such information globally. However, a specific sampling scheme (pencil-like swath, 16-day revisit) introduces an uncertainty to CloudSat-CALIPSO cloud amounts. In the research we assess those uncertainties in terms of a bootstrap confidence intervals. Five years (2006-2011) of the 2B-GEOPROF-LIDAR (version P2_R05) cloud product was examined, accounting for  typical spatial resolutions of a global grids (1.0°, 2.5°, 5.0°, 10.0°), four confidence levels of confidence interval (0.85, 0.90, 0.95, 0.99), and three time scales of mean cloud amount (annual, seasonal, monthly). Results proved that cloud amount accuracy of 1%, or 5%, is not achievable with the dataset, assuming a 5-year mean cloud amount, high (>0.95) confidence level, and fine spatial resolution (1º–2.5º). The 1% requirement was only met by ~6.5% of atmospheric volumes at 1º and 2.5º, while more tolerant criterion (5%) was met by 22.5% volumes at 1º, or 48.9% at 2.5º resolution. In order to have at least 99% of volumes meeting an accuracy criterion, the criterion itself would have to be lowered to ~20% for 1º data, or to ~8% for 2.5º data. Study also quantified the relation between confidence interval width, and spatial resolution, confidence level, number of observations. Cloud regime (mean cloud amount, and standard deviation of cloud amount) was found the most important factor impacting the width of confidence interval. The research has been funded by the National Science Institute of Poland grant no. UMO-2017/25/B/ST10/01787. This research has been supported in part by PL-Grid Infrastructure (a computing resources).</p>

scholarly journals A Classroom Approach to Illustrate Transformation and Bootstrap Confidence Interval Techniques Using the Poisson Distribution

2017 ◽  
Vol 6 (2) ◽  
pp. 42 ◽  
Author(s):  
Per Gösta Andersson
Keyword(s):  
Problem Solving ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Learning Process ◽  
Bootstrap Confidence Interval ◽  
New Techniques ◽  
Teacher Student ◽  
Bootstrap Techniques ◽  
Interval Estimator

The Poisson distribution is here used to illustrate transformation and bootstrap techniques in order to construct a confidence interval for a mean. A comparison is made between the derived intervals and the Wald  and score confidence intervals. The discussion takes place in a classroom, where the teacher and the students have previously discussed and evaluated the Wald and score confidence intervals. While step by step  interactively getting acquainted  with new techniques,  the students will learn about the effects of e.g. bias and asymmetry and ways of dealing with such phenomena. The primary purpose of this teacher-student communication is therefore not to find the  best possible interval estimator for this particular case, but rather to provide a study displaying a teacher and her/his students interacting with each other in an efficient and rewarding way. The teacher has a strategy of encouraging the students to take initiatives. This is accomplished by providing the necessary background of the problem and some underlying theory after which the students are confronted with questions and problem solving. From this the learning process starts. The teacher has to be flexible according to how the students react.  The students are supposed to have studied mathematical statistics for at least two semesters. 

A note on coverage error of bootstrap confidence intervals for quantiles

1993 ◽  
Vol 114 (3) ◽  
pp. 517-531 ◽  
Author(s):  
D. De Angelis ◽  
Peter Hall ◽  
G. A. Young
Keyword(s):  
Confidence Intervals ◽  
Present Note ◽  
Normal Approximation ◽  
Poor Performance ◽  
Density Estimator ◽  
Bootstrap Confidence Intervals ◽  
Coverage Error ◽  
Bootstrap Percentile ◽  
Coverage Accuracy ◽  
Percentile Bootstrap

AbstractAn interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size n−½, where n denotes sample size. By way of contrast, the error would be O(n−1) for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to o(n−½) by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error O(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-t are also analysed.

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