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Estimating the parameters of 3-p Weibull distribution through differential evolution

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  • Örkcü, H. Hasan
  • Aksoy, Ertugˇrul
  • Dogˇan, Mustafa İsa

Abstract

The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering and the estimation of the parameters of this distribution is essential in the most real applications. Maximum likelihood (ML) estimation is a common method, which is usually used to elaborate on the parameter estimation. The working principle of ML estimation method based on maximizing the established likelihood function and maximizing this function formed for the parameter estimation of a three-parameter (3-p) Weibull distribution is a quite challenging problem. In this paper, this problem have been briefly discussed and an effective approach based on the differential evolution (DE) algorithm operators is proposed in order to enhance the estimation accuracy with less system resources. Three explanatory numerical examples are given to show that DE approach which requires significantly less CPU time and exhibits a rapid convergence to the maximum value of the likelihood function in less iterations, provides accurate estimates and is satisfactory for the parameter estimation of the 3-p Weibull distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:211-224
    DOI: 10.1016/j.amc.2014.10.127
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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.
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    5. 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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    1. 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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