Journal of Materials Science

, Volume 43, Issue 6, pp 1914–1919 | Cite as

Unbiased estimates of the Weibull parameters by the linear regression method

  • Murat Tiryakioğlu
  • David Hudak


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.


Monte Carlo Simulation Shape Parameter Scale Parameter Maximum Likelihood Method Unbiased Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Engineering, School of Engineering, Mathematics and ScienceRobert Morris UniversityMoon TownshipUSA
  2. 2.Department of Mathematics, School of Engineering, Mathematics and ScienceRobert Morris UniversityMoon TownshipUSA

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