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A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data

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  • Acitas, Sukru
  • Aladag, Cagdas Hakan
  • Senoglu, Birdal

Abstract

Three-parameter Weibull is one of the most popular and most widely-used distribution in many fields of science. Therefore, many studies have been conducted concerning the statistical inferences of the parameters of Weibull distribution. In general, the maximum likelihood (ML) methodology is used in the estimation process of unknown parameters. In this study, the ML estimation of the parameters of Weibull distribution is considered using particle swarm optimization (PSO). As in other heuristic optimization methods, the performance of PSO is affected by initial conditions. The novelty of this study comes from the fact that we propose a new adaptive search space based on confidence intervals in PSO. The modified maximum likelihood (MML) estimators are utilized for constructing the confidence intervals. MML based confidence intervals allow a narrower search space for the parameters of Weibull distribution than the search space used in the literature. Therefore, the performance of PSO increases, since the search space is wisely narrowed. In order to show the performance of the proposed approach, an extensive Monte-Carlo simulation study is conducted. Simulation results show that the proposed approach works well. In addition, real world data is analyzed to show implementation of the proposed method.

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  • Acitas, Sukru & Aladag, Cagdas Hakan & Senoglu, Birdal, 2019. "A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 116-127.
    • Handle: RePEc:eee:reensy:v:183:y:2019:i:c:p:116-127
    DOI: 10.1016/j.ress.2018.07.024
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    References listed on IDEAS

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    Cited by:

    1. Hassan M. Okasha & Abdulkareem M. Basheer & A. H. El-Baz, 2021. "Marshall–Olkin Extended Inverse Weibull Distribution: Different Methods of Estimations," Annals of Data Science, Springer, vol. 8(4), pages 769-784, December.
    2. Jiang, Renyan & Qi, Faqun & Cao, Yu, 2023. "Relation between aging intensity function and WPP plot and its application in reliability modelling," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    3. Muhammet Burak Kılıç & Yusuf Şahin & Melih Burak Koca, 2021. "Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation," Computational Statistics, Springer, vol. 36(2), pages 1219-1242, June.
    4. Starling, James K. & Mastrangelo, Christina & Choe, Youngjun, 2021. "Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE," Reliability Engineering and System Safety, Elsevier, vol. 211(C).

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