Admissibility of the constant-coverage probability estimator for estimating the coverage function of certain confidence interval

1998 ◽  
Vol 36 (4) ◽  
pp. 365-372 ◽  
Author(s):  
Hsiuying Wang
Keyword(s):  
Confidence Interval ◽  
Coverage Probability ◽  
Probability Estimator ◽  
Coverage Function

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.

scholarly journals Confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation

2014 ◽  
Vol 11 (2) ◽  
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Coverage Probability ◽  
Process Capability ◽  
Process Capability Index ◽  
Skewed Distributions ◽  
Monte Carlo Simulation Study ◽  
Nominal Level ◽  
R Language ◽  
Capability Index

This paper proposes a confidence interval for the process capability index based on the bootstrap-t confidence interval for the standard deviation. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval based on the confidence interval for the standard deviation. Simulation results show that the proposed confidence interval performs well in terms of coverage probability in case of more skewed distributions. On the other hand, the existing confidence interval has a coverage probability close to the nominal level for symmetrical or less skewed distributions. The code to estimate the confidence interval in R language is provided.

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 Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Coverage Probability ◽  
Normal Approximation ◽  
Monte Carlo Simulation Study ◽  
Population Mean ◽  
Expected Length ◽  
Simulation Results

This paper presents three confidence intervals for the coefficient of variation in a normal distribution with a known population mean. One of the proposed confidence intervals is based on the normal approximation. The other proposed confidence intervals are the shortest-length confidence interval and the equal-tailed confidence interval. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. Simulation results have shown that all three proposed confidence intervals perform well in terms of coverage probability and expected length.

The Nonparametric Confidence Interval for the Process Capability Index C*pmk

2013 ◽  
Vol 404 ◽  
pp. 520-525 ◽  
Author(s):  
Shu Fei Wu
Keyword(s):  
Confidence Interval ◽  
Coverage Probability ◽  
Process Capability ◽  
Process Capability Index ◽  
The Other ◽  
Interval Estimate ◽  
Jackknife Method ◽  
Capability Index ◽  
Simulation Results ◽  
Bootstrap Interval

The process capability index which is a generalization of is defined by the use of the idea of Chan et al. [ for asymmetric tolerance. In this paper, we proposed a Jackknife confidence interval for and compare its coverage probability with the other three Efron and Tibshiranis [ bootstrap interval estimate techniques. The simulation results show that the Jackknife method has higher chance of reaching the nominal confidence coefficient for all cases considered in this paper. Therefore this method is recommended for used. One numerical example to demonstrate the construction of confidence interval for the process capability index is also given in this paper.

scholarly journals Approximate confidence interval for the reciprocal of a normal mean with a known coefficient of variation

2016 ◽  
Vol 13 (2) ◽  
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Confidence Interval ◽  
Coefficient Of Variation ◽  
Coverage Probability ◽  
Nuclear Physics ◽  
Normal Population ◽  
Taylor Series Expansion ◽  
Monte Carlo Simulation Study ◽  
Normal Mean ◽  
Simulation Results ◽  
Approximate Confidence Interval

An approximate confidence interval for the reciprocal of a normal population mean with a known coefficient of variation is proposed. This has applications in the area of nuclear physics, agriculture and economic when the researcher knows the coefficient of variation. The proposed confidence interval is based on the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval. Simulation results show that the proposed confidence interval performs as well as the existing one in terms of coverage probability. However, the approximate confidence interval is very easy to calculate compared with the exact confidence interval.

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