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Article

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

by
Man Chen
*,
Zheng Zhang
and
Cen Cui
Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing 100044, China
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2017, 22(1), 19; https://doi.org/10.3390/mca22010019
Submission 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.
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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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. https://doi.org/10.3390/mca22010019

AMA Style

Chen M, Zhang Z, Cui C. On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution. Mathematical and Computational Applications. 2017; 22(1):19. https://doi.org/10.3390/mca22010019

Chicago/Turabian Style

Chen, Man, Zheng Zhang, and Cen Cui. 2017. "On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution" Mathematical and Computational Applications 22, no. 1: 19. https://doi.org/10.3390/mca22010019

APA Style

Chen, M., Zhang, Z., & Cui, C. (2017). On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution. Mathematical and Computational Applications, 22(1), 19. https://doi.org/10.3390/mca22010019

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