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

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

Abstract

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

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    1. 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.
    2. 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, November.
    3. 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.
    4. David A. Griffiths, 1980. "Interval Estimation for the Three‐Parameter Lognormal Distribution Via the Likelihood Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 58-68, March.
    5. 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:

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    3. Ouindllassida Jean-Etienne Ou´edraogo & Edoh Katchekpele & Simplice Dossou-Gb´et´e, 2021. "Marginalized Maximum Likelihood for Parameters Estimation of the Three Parameter Weibull Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 1-62, July.
    4. Ajinkya Shirurkar & Yogesh Patil & D. Davidson Jebaseelan, 2019. "Reliability improvement of fork biasing spring in MCCB mechanism," 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. 10(4), pages 491-498, August.
    5. Santosh B. Rane & Yahya A.M. Narvel & Niloy Khatua, 2017. "Development of mechanism for mounting secondary isolating contacts (SICs) in air circuit breakers (ACBs) with high operational reliability," 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. 8(2), pages 1816-1831, November.
    6. Örkcü, H. Hasan & Aksoy, Ertugˇrul & Dogˇan, Mustafa İsa, 2015. "Estimating the parameters of 3-p Weibull distribution through differential evolution," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 211-224.
    7. Örkcü, H. Hasan & Özsoy, Volkan Soner & Aksoy, Ertugrul & Dogan, Mustafa Isa, 2015. "Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 201-226.

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