Comparisons of Approximate Confidence Intervals for Distributions Used in Life-Data Analysis

Doganaksoy, Necip; Schmee, Josef

doi:10.1080/00401706.1993.10485039

Cited by 29 publications

(15 citation statements)

References 18 publications

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“…Our ndings for the normal approximation and likelihood ratio procedures are consistent with results in Ostrouchov and Meeker (1988), Doganaksoy and Schmee (1993a), and Doganaksoy (1995). This paper, however, focuses more on the asymmetry of coverage probability for one-sided CIs as well as cases with heavy censoring and a small expected number of failures.…”

Section: Other Results Conclusion and Recommendationssupporting

confidence: 80%

“…UCBs (LCBs) are conservative when p < p f (p > p f ) and are anti-conservative when p > p f (p < p f ) except that when p is close to p f , both are conservative. This change as one crosses p f was also noted in the results of Ostrouchov and Meeker (1988) and Doganaksoy and Schmee (1993a) and will be explored further in the discussion in Section 7. Figure 4, for p f = :1, gives CPs for bootstrap procedure for and several quantiles for E(r) = 15, the point at which some of the bootstrap procedures begin to perform well.…”

Section: One-sided Cbsmentioning

confidence: 90%

“…Vander Wiel and Meeker (1990) showed that for Type I censored Weibull data from accelerated life tests, LLR based CIs have c o verage probabilities closer to nominal than those from the TNORM procedure. Doganaksoy and Schmee (1993a) compared four procedures for Type I censored data from Weibull and lognormal distributions. They are NORM, LLR, the standardized LLR, and the LLR with Bartlett correction (LLRBART).…”

Section: Related Workmentioning

confidence: 99%

“…In general one must substitute an estimate for E(W) computed from one's data. For complicated problems (e.g., those involving censoring) it is necessary to estimate of E(W ) b y using simulation, as described by Doganaksoy and Schmee (1993a). Then, similar to the LLR procedure, the LLRBART CI procedure uses the two roots of W ( 1 )=E(W) ; 2 (1; 1) = 0 as the lower and upper con dence bounds, respectively.…”

Section: Likelihood Ratio Proceduresmentioning

confidence: 99%

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Comparisons of Approximate Confidence Interval Procedures for Type I Censored Data

Jeng¹,

Meeker²

2000

Technometrics

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This article compares different procedures to compute confidence intervals for parameters and quantiles of the Weibull, lognormal, and similar log-location-scale distributions from Type I censored data that typically arise from life-test experiments. The procedures can be classified into three groups. The first group contains procedures based on the commonly used normal approximation for the distribution of studentized (possibly after a transformation) maximum likelihood estimators. The second group contains procedures based on the likelihood ratio statistic and its modifications. The procedures in the third group use a parametric bootstrap approach, including the use of bootstrap-type simulation, to calibrate the procedures in the first two groups. The procedures in all three groups are justified on the basis of large-sample asymptotic theory. We use Monte Carlo simulation to investigate the finite-sample properties of these procedures. Details are reported for the Weibull distribution. Our results show, as predicted by asymptotic theory, that the coverage probabilities of one-sided confidence bounds calculated from procedures in the first and second groups are further away from nominal than those of two-sided confidence intervals. The commonly used normal-approximation procedures are crude unless the expected number of failures is large (more than 50 or 100). The likelihood ratio procedures work much better and provide adequate procedures down to 30 or 20 failures. By using bootstrap procedures with caution, the coverage probability is close to nominal when the expected number of failures is as small as 15 to 10 or less, depending on the particular situation. Exceptional cases, caused by discreteness from Type I censoring, are noted. KeywordsBartlett correction, Bias-corrected accelerated bootstrap, Bootstrap-t, Life data, Likelihood ratio, Maximum likelihood, Parametric bootstrap, Type I censoring Disciplines Statistics and Probability CommentsThis preprint has been published in Technometrics 42 (2000) J u n e 6 , 1 9 9 9 Abstract This paper compares di erent procedures to compute con dence intervals for parameters and quantiles of the Weibull, lognormal, and similar log-location-scale distributions from Type I censored data that typically arise from life test experiments. The procedures can be classi ed into three groups. The rst group contains procedures based on the commonlyused normal approximation for the distribution of studentized (possibly after a transformation) maximum likelihood estimators. The second group contains procedures based on the likelihood ratio statistic and its modi cations. The procedures in the third group use a parametric bootstrap approach, including the use of bootstrap-type simulation, to calibrate the procedures in the rst two groups. The procedures in all three groups are justi ed on the basis of large-sample asymptotic theory. We use Monte Carlo simulation to investigate the nite sample properties of these procedures. Details are reported for the Weibull distribution. ...

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Section: Other Results Conclusion and Recommendationssupporting

confidence: 80%

Section: One-sided Cbsmentioning

confidence: 90%

Section: Related Workmentioning

confidence: 99%

Section: Likelihood Ratio Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Comparisons of Approximate Confidence Interval Procedures for Type I Censored Data

Jeng¹,

Meeker²

2000

Technometrics

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show abstract

“…While the maximum likelihood estimator based interval is often preferred because of the simplicity in calculation, the signed log-likelihood ratio method is invariant to reparametrization and the maximum likelihood estimator based method is not. Doganaksoy and Schmee [13], showed that the signed log-likelihood ratio statistic based interval has better coverage property than the maximum likelihood estimator based interval in cases they considered. In recent years, various adjustments to the signed log-likelihood ratio statistic have been proposed to improve the accuracy of the signed log-likelihood ratio statistic.…”

Section: Likelihood-based Inference For Any Scalar Parameter Of Interestmentioning

confidence: 99%

A Penalized Likelihood Approach to Parameter Estimation with Integral Reliability Constraints

Smith

Wang

Zhou

2015

Entropy

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Stress-strength reliability problems arise frequently in applied statistics and related fields. Often they involve two independent and possibly small samples of measurements on strength and breakdown pressures (stress). The goal of the researcher is to use the measurements to obtain inference on reliability, which is the probability that stress will exceed strength. This paper addresses the case where reliability is expressed in terms of an integral which has no closed form solution and where the number of observed values on stress and strength is small. We find that the Lagrange approach to estimating constrained likelihood, necessary for inference, often performs poorly. We introduce a penalized likelihood method and it appears to always work well. We use third order likelihood methods to partially offset the issue of small samples. The proposed method is applied to draw inferences on reliability in stress-strength problems with independent exponentiated exponential distributions. Simulation studies are carried out to assess the accuracy of the proposed method and to compare it with some standard asymptotic methods.

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Overview of Maximum Likelihood Estimation

Harrell

2015

Regression Modeling Strategies

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Comparisons of Approximate Confidence Intervals for Distributions Used in Life-Data Analysis

Cited by 29 publications

References 18 publications

Comparisons of Approximate Confidence Interval Procedures for Type I Censored Data

Comparisons of Approximate Confidence Interval Procedures for Type I Censored Data

A Penalized Likelihood Approach to Parameter Estimation with Integral Reliability Constraints

Overview of Maximum Likelihood Estimation

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