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Unbiased estimates of the Weibull parameters by the linear regression method

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Abstract

For sample sizes from 5 to 100, the bias of the scale parameter was investigated for probability estimators, P = (i − a)/(n + b), which yield unbiased estimates of the shape parameter. A class of unbiased estimators for both the shape and scale parameters was developed for each sample size. In addition, the percentage points of the distribution of unbiased estimate of the shape parameter were determined for all sample sizes. The distribution of the scale parameter was found to be normal by using the Anderson-Darling goodness-of-fit test. How the results can be used to establish confidence intervals on both the shape and scale parameters are demonstrated in the paper.

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Authors and Affiliations

  1. Department of Engineering, School of Engineering, Mathematics and Science, Robert Morris University, 6001 University Boulevard, Moon Township, PA, 15108, USA

    Murat Tiryakioğlu

  2. Department of Mathematics, School of Engineering, Mathematics and Science, Robert Morris University, 6001 University Boulevard, Moon Township, PA, 15108, USA

    David Hudak

Authors
  1. Murat Tiryakioğlu
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  2. David Hudak
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Correspondence to Murat Tiryakioğlu.

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Tiryakioğlu, M., Hudak, D. Unbiased estimates of the Weibull parameters by the linear regression method. J Mater Sci 43, 1914–1919 (2008). https://doi.org/10.1007/s10853-008-2457-9

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  • DOI: https://doi.org/10.1007/s10853-008-2457-9

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