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On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution

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  • Jukic, Dragan
  • Bensic, Mirta
  • Scitovski, Rudolf

Abstract

The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data (wi,ti,yi), i=1,...,n, is considered. The part wi>0 of the data stands for the data weights. It is shown that the best least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4502-4511
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    References listed on IDEAS

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    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    2. Demidenko, Eugene, 2006. "Criteria for global minimum of sum of squares in nonlinear regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1739-1753, December.
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    Cited by:

    1. Tibor KPogany, 2018. "On a statistical approximation model of probabilitydensity function of non-negative random variables," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(4), pages 69-72, November.
    2. 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.
    3. 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.
    4. 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.

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