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Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.


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TL;DR: This article provides an R package ExactCIdiff to implement the exact confidence intervals for the difference of proportions when the sample size is not large, and would be the first available package in R to calculate these intervals.
Abstract: Comparing two proportions through the difference is a basic problem in statistics and has applications in many fields. More than twenty confidence intervals (Newcombe, 1998a,b) have been proposed. Most of them are approximate intervals with an asymptotic infimum coverage probability much less than the nominal level. In addition, large sample may be costly in practice. So exact optimal confidence intervals become critical for drawing valid statistical inference with accuracy and precision. Recently, Wang (2010, 2012) derived the exact smallest (optimal) one-sided 1 - alpha confidence intervals for the difference of two paired or independent proportions. His intervals, however, are computer-intensive by nature. In this article, we provide an R package ExactCIdiff to implement the intervals when the sample size is not large. This would be the first available package in R to calculate the exact confidence intervals for the difference of proportions. Exact two-sided 1 - alpha interval can be easily obtained by taking the intersection of the lower and upper one-sided 1 - alpha/2 intervals. Readers may jump to Examples 1 and 2 to obtain these intervals.

45 citations

Journal ArticleDOI
TL;DR: In this article, a confidence interval for the lOOpth percentile of the Birnbaum-Saunders distribution is constructed, and conservative two-sided tolerance limits are then obtained from the confidence limits.
Abstract: In this paper, a confidence interval for the lOOpth percentile of the Birnbaum-Saunders distribution is constructed. Conservative two-sided tolerance limits are then obtained from the confidence limits. These results are useful for reliability evaluation when using the Birnbaum-Saunders model. A simple scheme for generating Birnbaum-Saunders random variates is derived. This is used for a simulation study on investigating the effectiveness of the proposed confidence interval in terms of its coverage probability.

45 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the cost of using the exact one and two-sided Clopper-Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then in the increase in sample size required to obtain a desired expected length.
Abstract: When computing a confidence interval for a binomial proportion p one must choose between using an exact interval, which has a coverage probability of at least 1-{\alpha} for all values of p, and a shorter approximate interval, which may have lower coverage for some p but that on average has coverage equal to 1-\alpha. We investigate the cost of using the exact one and two-sided Clopper--Pearson confidence intervals rather than shorter approximate intervals, first in terms of increased expected length and then in terms of the increase in sample size required to obtain a desired expected length. Using asymptotic expansions, we also give a closed-form formula for determining the sample size for the exact Clopper--Pearson methods. For two-sided intervals, our investigation reveals an interesting connection between the frequentist Clopper--Pearson interval and Bayesian intervals based on noninformative priors.

45 citations

Journal ArticleDOI
TL;DR: The proposed improved interval estimation for the two-parameter Birnbaum–Saunders distribution is based on the recently developed higher-order likelihood-based asymptotic procedure and those procedures discussed in Ng et al. (2003).

45 citations

Journal ArticleDOI
TL;DR: In this article, a generalized confidence region is derived using the concepts of generalized method based on the generalized p-value for the common mean vector of several multivariate normal populations when the covariance matrices are unknown and possibly unequal.

44 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202363
2022153
2021142
2020151
2019142