### 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 language | English (US) |
---|---|

Pages (from-to) | 2-9 |

Number of pages | 8 |

Journal | IEEE Transactions on Reliability |

Volume | R-19 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1970 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*IEEE Transactions on Reliability*,

*R-19*(1), 2-9. https://doi.org/10.1109/TR.1970.5216370

}

*IEEE Transactions on Reliability*, vol. R-19, no. 1, pp. 2-9. https://doi.org/10.1109/TR.1970.5216370

**Inference on Weibull Percentiles and Shape Parameter from Maximum Likelihood Estimates.** / McCool, John I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Inference on Weibull Percentiles and Shape Parameter from Maximum Likelihood Estimates

AU - McCool, John I.

PY - 1970/1/1

Y1 - 1970/1/1

N2 - 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.

AB - 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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U2 - 10.1109/TR.1970.5216370

DO - 10.1109/TR.1970.5216370

M3 - Article

AN - SCOPUS:0014736114

VL - R-19

SP - 2

EP - 9

JO - IEEE Transactions on Reliability

JF - IEEE Transactions on Reliability

SN - 0018-9529

IS - 1

ER -