Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration

2020 ◽  
Vol 39 (16) ◽  
pp. 2152-2166 ◽  
Author(s):  
Yixuan Zou ◽  
Derek S. Young
Keyword(s):  
Tolerance Intervals ◽  
Coverage Probabilities ◽  
Bootstrap Calibration

Content‐adjusted tolerance intervals via bootstrap calibration

Stat ◽  
2021 ◽  
Author(s):  
Junjun Jiao ◽  
Xu Zhao ◽  
Weihu Cheng
Keyword(s):  
Tolerance Intervals ◽  
Bootstrap Calibration

scholarly journals Tolerance limits and tolerance intervals for ratios of normal random variables using a bootstrap calibration

2017 ◽  
Vol 59 (3) ◽  
pp. 550-566 ◽  
Author(s):  
Marilena Flouri ◽  
Shuyan Zhai ◽  
Thomas Mathew ◽  
Ionut Bebu
Keyword(s):  
Random Variables ◽  
Tolerance Limits ◽  
Tolerance Intervals ◽  
Bootstrap Calibration

Nonparametric Interval Estimators for the Coefficient of Variation

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Dongliang Wang ◽  
Margaret K. Formica ◽  
Song Liu
Keyword(s):  
Empirical Likelihood ◽  
Coefficient Of Variation ◽  
Real Life ◽  
Original Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Empirical Likelihood Method ◽  
Coverage Probabilities ◽  
Bootstrap Calibration ◽  
Interval Estimators

Abstract The coefficient of variation (CV) is a widely used scaleless measure of variability in many disciplines. However the inference for the CV is limited to parametric methods or standard bootstrap. In this paper we propose two nonparametric methods aiming to construct confidence intervals for the coefficient of variation. The first one is to apply the empirical likelihood after transforming the original data. The second one is a modified jackknife empirical likelihood method. We also propose bootstrap procedures for calibrating the test statistics. Results from our simulation studies suggest that the proposed methods, particularly the empirical likelihood method with bootstrap calibration, are comparable to existing methods for normal data and yield better coverage probabilities for nonnormal data. We illustrate our methods by applying them to two real-life datasets.

Tolerance Intervals for True Scores

1985 ◽  
Vol 10 (1) ◽  
pp. 1-17 ◽  
Author(s):  
David Jarjoura
Keyword(s):  
Confidence Intervals ◽  
Practical Implication ◽  
Educational Measurement ◽  
True Score ◽  
Tolerance Intervals ◽  
Observed Score ◽  
True Scores

Issues regarding tolerance and confidence intervals are discussed within the context of educational measurement and conceptual distinctions are drawn between these two types of intervals. Points are raised about the advantages of tolerance intervals when the focus is on a particular observed score rather than a particular examinee. Because tolerance intervals depend on strong true score models, a practical implication of the study is that true score tolerance intervals are fairly insensitive to differences in assumptions among the five models studied.

scholarly journals A Distribution for Instantaneous Failures

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Pedro L. Ramos ◽  
Francisco Louzada
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Mean Residual Life ◽  
Parameter Distribution ◽  
Coverage Probabilities ◽  
Instantaneous Failures ◽  
The Relationship ◽  
Mean Variance ◽  
New Distribution

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

Bounds for coverage probabilities with applications to sequential coverage problems

1974 ◽  
Vol 11 (02) ◽  
pp. 281-293 ◽  
Author(s):  
Peter J. Cooke
Keyword(s):  
Asymptotic Behaviour ◽  
Stopping Rules ◽  
Geometrical Probability ◽  
Coverage Probabilities ◽  
Coverage Problems

This paper discusses general bounds for coverage probabilities and moments of stopping rules for sequential coverage problems in geometrical probability. An approach to the study of the asymptotic behaviour of these moments is also presented.

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