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Estimation of the Shape Parameter of a Wear-Out Failure Period for a Three-Parameter Weibull Distribution in a Small Sample

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Listed:
  • Toru Ogura
  • Takatoshi Sugiyama
  • Nariaki Sugiura

Abstract

We propose a method to estimate a shape parameter for a three-parameter Weibull distribution. The proposed method first derives an unbiased estimator for the shape parameter independent of the location and scale parameters and then estimates the shape parameter using a minimum-variance linear unbiased estimator. Since the proposed method is expressed using a hyperparameter, its optimal hyperparameter is searched using Monte Carlo simulations. The recommended hyperparameter used for estimating the shape parameter depends on the sample size, and this causes no problems since the sample size is known when data is obtained. The proposed method is evaluated using a bias and a root mean squared error, and the results are very promising when the population shape parameter is 2 or more in the Weibull distribution representing the wear-out failure period. A numerical dataset is analyzed to demonstrate the practical use of the proposed method.

Suggested Citation

  • Toru Ogura & Takatoshi Sugiyama & Nariaki Sugiura, 2020. "Estimation of the Shape Parameter of a Wear-Out Failure Period for a Three-Parameter Weibull Distribution in a Small Sample," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-39, November.
    • Handle: RePEc:ibn:ijspjl:v:9:y:2020:i:6:p:39
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    References listed on IDEAS

    as
    1. Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729, November.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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