Avoiding Problems With Normal Approximation Confidence Intervals for Probabilities

Hong, Yili; Meeker, William Q.; Escobar, Luis A.

doi:10.1198/004017007000000470

Cited by 11 publications

(4 citation statements)

References 9 publications

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“…However, if the SE is large, this CI might not be within the range (0, 1). Instead of the obvious corrective method of pruning the CI to the known range (0, 1), we consider an appropriate transformation method in the following, which was particularly developed for CIs for probabilities (see Hong et al 2008).…”

Section: Wald-type Confidence Interval For F â (T)mentioning

confidence: 99%

Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

et al. 2020

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Doubly-truncated data arise in many fields, including economics, engineering, medicine, and astronomy. This article develops likelihood-based inference methods for lifetime distributions under the log-location-scale model and the accelerated failure time model based on doubly-truncated data. These parametric models are practically useful, but the methodologies to fit these models to doubly-truncated data are missing. We develop algorithms for obtaining the maximum likelihood estimator under both models, and propose several types of interval estimation methods. Furthermore, we show that the confidence band for the cumulative distribution function has closedform expressions. We conduct simulations to examine the accuracy of the proposed methods. We illustrate our proposed methods by real data from a field reliability study, called the Equipment-S data.

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Section: Wald-type Confidence Interval For F â (T)mentioning

confidence: 99%

Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

et al. 2020

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“…Applying Gauss-Hermite quadrature gives 15) where n k2 is the number of quadrature points, q 2,k2 are the evaluation points and w 2,k2 are the weights. The evaluation points are the roots of the Hermite polynomial of degree n k2 , H n k2 (q 2 ), and the weights are…”

Section: Gauss-hermite Quadrature Is a Numerical Integration Techniqumentioning

confidence: 99%

Analysis of Reliability Experiments with Random Blocks and Subsampling

Kensler

Freeman

Vining

2015

Journal of Quality Technology

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Reliability experiments provide important information regarding the life of a product, including how various factors may affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling which is a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches. In some cases one batch may not be large enough to provide materials for the entire experiment and more than one batch must be used. These batches lead to a design involving blocks. This dissertation proposes two methods for analyzing reliability experiments with random blocks and subsampling.The first method is a two-stage method which can be implemented in software used by most practitioners, but has some limitations. Therefore, a more rigorous nonlinear mixed model method is proposed.

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“…They observed that their growth estimator produces intervals that are longer and more variable than the normal approximation. In the censored data context, Hong et al (2008) pointed out that the normal approximation to confidence interval calculations can be poor when the sample size is not large or there is heavy censoring. In the context of approximation of the binomial distribution, Chang et al (2008) made similar observations.…”

Section: Introductionmentioning

confidence: 99%

Applications of information measures to assess convergence in the central limit theorem

Atukorala

King

Sriananthakumar

2015

MAS

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The Central Limit Theorem (CLT) is an important result in statistics and econometrics and econometricians often rely on the CLT for inference in practice. Even though different conditions apply to different kinds of data, the CLT results are believed to be generally available for a range of situations. This paper illustrates the use of the Kullback-Leibler Information (KLI) measure to assess how close an approximating distribution is to a true distribution in the context of investigating how different population distributions affect convergence in the CLT. For this purpose, three different non-parametric methods for estimating the KLI are proposed and investigated. The main findings of this paper are 1) the distribution of the sample means better approximates the normal distribution as the sample size increases, as expected, 2) for any fixed sample size, the distribution of means of samples from skewed distributions converges faster to the normal distribution as the kurtosis increases, 3) at least in the range of values of kurtosis considered, the distribution of means of small samples generated from symmetric distributions is well approximated by the normal distribution, and 4) among the nonparametric methods used, Vasicek's (1976) estimator seems to be the best for the purpose of assessing asymptotic approximations. Based on the results of this paper, recommendations on minimum sample sizes required for an accurate normal approximation of the true distribution of sample means are made.

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Avoiding Problems With Normal Approximation Confidence Intervals for Probabilities

Cited by 11 publications

References 9 publications

Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

Analysis of Reliability Experiments with Random Blocks and Subsampling

Applications of information measures to assess convergence in the central limit theorem

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