Parametric simultaneous confidence bands for cumulative distributions from censored data

Shuen-Lin Jeng, William Q. Meeker

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This article describes existing methods and develops new methods for constructing simultaneous confidence bands for a cumulative distribution function. Our results are built on extensions of previous work by Cheng and Iles for two-sided and one-sided bands, respectively. Cheng and Iles used Wald statistics with (expected) Fisher information. We consider three alternatives-Wald statistics with observed Fisher information, Wald statistics with local information, and likelihood ratio statistics. We compare standard large-sample approximate methods with simulation or bootstrap-calibrated versions of the same methods. For (log-) location-scale distributions with complete or failure (Type II) censoring, the bootstrap methods have the correct coverage probability. A simulation for the Weibull distribution and time-censored (Type I) data shows that bootstrap methods provide coverage probabilities that are closer to nominal than those based on the usual large-sample approximations. We illustrate the methods with examples from product-life analysis and nondestructive evaluation probability of detection.

Original languageEnglish
Pages (from-to)450-461
Number of pages12
JournalTechnometrics
Volume43
Issue number4
DOIs
Publication statusPublished - 2001 Jan 1

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Simultaneous Confidence Bands
Censored Data
Wald Statistic
Statistics
Fisher Information
Bootstrap Method
Coverage Probability
Weibull distribution
Type II Censoring
Observed Information
Probability of Detection
Likelihood Ratio Statistic
Distribution functions
Cumulative distribution function
Weibull Distribution
Bootstrap
Categorical or nominal
Simulation
Alternatives
Evaluation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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Parametric simultaneous confidence bands for cumulative distributions from censored data. / Jeng, Shuen-Lin; Meeker, William Q.

In: Technometrics, Vol. 43, No. 4, 01.01.2001, p. 450-461.

Research output: Contribution to journalArticle

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