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A consistent method of estimation for the three-parameter Weibull distribution


  • Nagatsuka, Hideki
  • Kamakura, Toshinari
  • Balakrishnan, N.


In this paper, we propose a new method for the estimation of parameters of the three-parameter Weibull distribution. The method is based on a data transformation, which avoids the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely in the entire parameter space, and the estimators also have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs better than some existing methods in terms of bias and root mean squared error (RMSE). Finally, two examples based on real data sets are presented to illustrate the proposed method.

Suggested Citation

  • Nagatsuka, Hideki & Kamakura, Toshinari & Balakrishnan, N., 2013. "A consistent method of estimation for the three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 210-226.
  • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:210-226
    DOI: 10.1016/j.csda.2012.09.005

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    References listed on IDEAS

    1. Balakrishnan, N. & Kateri, M., 2008. "On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2971-2975, December.
    2. Jukic, Dragan & Bensic, Mirta & Scitovski, Rudolf, 2008. "On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4502-4511, May.
    3. 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.
    4. Castillo, Enrique & Hadi, Ali S., 1995. "A method for estimating parameters and quantiles of distributions of continuous random variables," Computational Statistics & Data Analysis, Elsevier, vol. 20(4), pages 421-439, October.
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    Cited by:

    1. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    2. Santosh B. Rane & Yahya A. M. Narvel, 2016. "Reliability assessment and improvement of air circuit breaker (ACB) mechanism by identifying and eliminating the root causes," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(1), pages 305-321, December.
    3. repec:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-017-0678-5 is not listed on IDEAS
    4. repec:eee:apmaco:v:251:y:2015:i:c:p:211-224 is not listed on IDEAS
    5. repec:eee:apmaco:v:268:y:2015:i:c:p:201-226 is not listed on IDEAS


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