IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v251y2015icp211-224.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314015021
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2014.10.127?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Paterlini, Sandra & Krink, Thiemo, 2006. "Differential evolution and particle swarm optimisation in partitional clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1220-1247, March.
    3. Chang, Tian Pau, 2011. "Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application," Applied Energy, Elsevier, vol. 88(1), pages 272-282, January.
    4. Bartolucci, Alfred A. & Singh, Karan P. & Bartolucci, Anne D. & Bae, Sejong, 1999. "Applying medical survival data to estimate the three-parameter Weibull distribution by the method of probability-weighted moments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 385-392.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.
    2. Eslam Mohammed Abdelkader & Abobakr Al-Sakkaf & Ghasan Alfalah & Nehal Elshaboury, 2022. "Hybrid Differential Evolution-Based Regression Tree Model for Predicting Downstream Dam Hazard Potential," Sustainability, MDPI, vol. 14(5), pages 1-21, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    3. Chandel, S.S. & Ramasamy, P. & Murthy, K.S.R, 2014. "Wind power potential assessment of 12 locations in western Himalayan region of India," Renewable and Sustainable Energy Reviews, Elsevier, vol. 39(C), pages 530-545.
    4. He, J.Y. & Chan, P.W. & Li, Q.S. & Huang, Tao & Yim, Steve Hung Lam, 2024. "Assessment of urban wind energy resource in Hong Kong based on multi-instrument observations," Renewable and Sustainable Energy Reviews, Elsevier, vol. 191(C).
    5. Pagnini, Luisa C. & Burlando, Massimiliano & Repetto, Maria Pia, 2015. "Experimental power curve of small-size wind turbines in turbulent urban environment," Applied Energy, Elsevier, vol. 154(C), pages 112-121.
    6. Katinas, Vladislovas & Gecevicius, Giedrius & Marciukaitis, Mantas, 2018. "An investigation of wind power density distribution at location with low and high wind speeds using statistical model," Applied Energy, Elsevier, vol. 218(C), pages 442-451.
    7. Chang, Tian-Pau & Ko, Hong-Hsi & Liu, Feng-Jiao & Chen, Pai-Hsun & Chang, Ying-Pin & Liang, Ying-Hsin & Jang, Horng-Yuan & Lin, Tsung-Chi & Chen, Yi-Hwa, 2012. "Fractal dimension of wind speed time series," Applied Energy, Elsevier, vol. 93(C), pages 742-749.
    8. Thiemo Krink & Stefan Mittnik & Sandra Paterlini, 2009. "Differential evolution and combinatorial search for constrained index-tracking," Annals of Operations Research, Springer, vol. 172(1), pages 153-176, November.
    9. Dongbum Kang & Kyungnam Ko & Jongchul Huh, 2018. "Comparative Study of Different Methods for Estimating Weibull Parameters: A Case Study on Jeju Island, South Korea," Energies, MDPI, vol. 11(2), pages 1-19, February.
    10. César Henrique Mattos Pires & Felipe M. Pimenta & Carla A. D'Aquino & Osvaldo R. Saavedra & Xuerui Mao & Arcilan T. Assireu, 2020. "Coastal Wind Power in Southern Santa Catarina, Brazil," Energies, MDPI, vol. 13(19), pages 1-23, October.
    11. Liu, Feng Jiao & Chang, Tian Pau, 2011. "Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment," Energy, Elsevier, vol. 36(3), pages 1820-1826.
    12. Kang, Dongbum & Ko, Kyungnam & Huh, Jongchul, 2015. "Determination of extreme wind values using the Gumbel distribution," Energy, Elsevier, vol. 86(C), pages 51-58.
    13. 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.
    14. Oluseyi O. Ajayi & Richard O. Fagbenle & James Katende & Julius M. Ndambuki & David O. Omole & Adekunle A. Badejo, 2014. "Wind Energy Study and Energy Cost of Wind Electricity Generation in Nigeria: Past and Recent Results and a Case Study for South West Nigeria," Energies, MDPI, vol. 7(12), pages 1-27, December.
    15. Toja-Silva, Francisco & Lopez-Garcia, Oscar & Peralta, Carlos & Navarro, Jorge & Cruz, Ignacio, 2016. "An empirical–heuristic optimization of the building-roof geometry for urban wind energy exploitation on high-rise buildings," Applied Energy, Elsevier, vol. 164(C), pages 769-794.
    16. Shu, Z.R. & Li, Q.S. & Chan, P.W., 2015. "Investigation of offshore wind energy potential in Hong Kong based on Weibull distribution function," Applied Energy, Elsevier, vol. 156(C), pages 362-373.
    17. Guedes, Kevin S. & de Andrade, Carla F. & Rocha, Paulo A.C. & Mangueira, Rivanilso dos S. & de Moura, Elineudo P., 2020. "Performance analysis of metaheuristic optimization algorithms in estimating the parameters of several wind speed distributions," Applied Energy, Elsevier, vol. 268(C).
    18. Andrea Scozzari & Fabio Tardella & Sandra Paterlini & Thiemo Krink, 2013. "Exact and heuristic approaches for the index tracking problem with UCITS constraints," Annals of Operations Research, Springer, vol. 205(1), pages 235-250, May.
    19. Xu, Lei & Wang, Shengwei & Tang, Rui, 2019. "Probabilistic load forecasting for buildings considering weather forecasting uncertainty and uncertain peak load," Applied Energy, Elsevier, vol. 237(C), pages 180-195.
    20. Arslan, Talha & Bulut, Y. Murat & Altın Yavuz, Arzu, 2014. "Comparative study of numerical methods for determining Weibull parameters for wind energy potential," Renewable and Sustainable Energy Reviews, Elsevier, vol. 40(C), pages 820-825.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:211-224. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.