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Math. Comput. Appl. 2017, 22(1), 19; doi:10.3390/mca22010019

On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution

Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China
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Received: 18 September 2016 / Accepted: 20 January 2017 / Published: 15 February 2017
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Abstract

Usually, the parameters of a Weibull distribution are estimated by maximum likelihood estimation. To reduce the biases of the maximum likelihood estimators (MLEs) of two-parameter Weibull distributions, we propose analytic bias-corrected MLEs. Two other common estimators of Weibull distributions, least-squares estimators and percentiles estimators, are also introduced. Based on a comparison of their performances in the simulation study, we strongly recommend the analytic bias-corrected MLEs for the parameters of Weibull distributions, especially when the sample size is small. View Full-Text
Keywords: Weibull distribution; maximum likelihood estimators; bias correction; bootstrap; percentiles; least squares estimators Weibull distribution; maximum likelihood estimators; bias correction; bootstrap; percentiles; least squares estimators
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chen, M.; Zhang, Z.; Cui, C. On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution. Math. Comput. Appl. 2017, 22, 19.

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