Inference on Weibull Percentiles and Shape Parameter from Maximum Likelihood Estimates

John I. McCool

Research output: Contribution to journalArticle

53 Citations (Scopus)

Abstract

Four functions of the maximum likelihood estimates of the Weibull shape parameter and any Weibull percentile are found. The sampling distributions are independent of the population parameters and depend only upon sample size and the degree of (Type II) censoring. These distributions, once determined by Monte Carlo methods, permit the testing of the following hypotheses: 1) that the Weibull shape parameter is equal to a specifiedvalue; 2) that a Weibull percentile is equal to a specified value; 3) that the shape parameters of two Weibull populations are equal; and 4) that a specified percentile of two Weibull populations are equal given that the shape parameters are. The OC curves of the various tests are shown to be readily computed. A by-product of the determination of the distribution of the four functions are the factors required for median unbiased estimation of 1) the Weibull shape parameter, 2) a Weibull percentile, 3) the ratio of shape parameters of two Weibull distributions, and 4) the ratio of a specified percentile of two Weibull distributions.

Original languageEnglish (US)
Pages (from-to)2-9
Number of pages8
JournalIEEE Transactions on Reliability
VolumeR-19
Issue number1
DOIs
StatePublished - Jan 1 1970

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Weibull distribution
Maximum likelihood
Byproducts
Monte Carlo methods
Sampling
Testing

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Electrical and Electronic Engineering

Cite this

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abstract = "Four functions of the maximum likelihood estimates of the Weibull shape parameter and any Weibull percentile are found. The sampling distributions are independent of the population parameters and depend only upon sample size and the degree of (Type II) censoring. These distributions, once determined by Monte Carlo methods, permit the testing of the following hypotheses: 1) that the Weibull shape parameter is equal to a specifiedvalue; 2) that a Weibull percentile is equal to a specified value; 3) that the shape parameters of two Weibull populations are equal; and 4) that a specified percentile of two Weibull populations are equal given that the shape parameters are. The OC curves of the various tests are shown to be readily computed. A by-product of the determination of the distribution of the four functions are the factors required for median unbiased estimation of 1) the Weibull shape parameter, 2) a Weibull percentile, 3) the ratio of shape parameters of two Weibull distributions, and 4) the ratio of a specified percentile of two Weibull distributions.",
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Inference on Weibull Percentiles and Shape Parameter from Maximum Likelihood Estimates. / McCool, John I.

In: IEEE Transactions on Reliability, Vol. R-19, No. 1, 01.01.1970, p. 2-9.

Research output: Contribution to journalArticle

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