IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v36y2021i2d10.1007_s00180-020-01044-5.html
   My bibliography  Save this article

Genetic algorithm approach with an adaptive search space based on EM algorithm in two-component mixture Weibull parameter estimation

Author

Listed:
  • Muhammet Burak Kılıç

    (Burdur Mehmet Akif Ersoy University)

  • Yusuf Şahin

    (Burdur Mehmet Akif Ersoy University)

  • Melih Burak Koca

    (Burdur Mehmet Akif Ersoy University)

Abstract

A mixture of two Weibull distributions (WW) has a variety of usage area from reliability analysis to wind speed modeling. Maximum likelihood (ML) method is the most frequently used method in parameter estimation of WW. Due to the nonlinear nature of the log-likelihood function of WW, usage of iterative techniques is a necessary process. Conventional iterative techniques such as Newton Raphson (NR) require considerable analytical preparatory to work to obtain gradient and may lead to numerical difficulties such as convergence problems. The aim of this paper is to present a genetic algorithm (GA) with an adaptive search space based on the Expectation–Maximization (EM) algorithm to obtain the ML estimators of the parameters of WW. The simulation study is conducted to compare the performances of ML estimators obtained using NR algorithm, EM algorithm, simulated annealing algorithm, and the proposed GA. Furthermore, real data examples are used to compare the efficiency of proposed GA with the existing methods in the literature. Simulation results and real data examples show that the proposed GA has superiority over other techniques in terms of efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01044-5
    DOI: 10.1007/s00180-020-01044-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-020-01044-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-020-01044-5?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. Aydin Karakoca & Ulku Erisoglu & Murat Erisoglu, 2015. "A comparison of the parameter estimation methods for bimodal mixture Weibull distribution with complete data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(7), pages 1472-1489, July.
    2. Carta, J.A. & Ramírez, P., 2007. "Analysis of two-component mixture Weibull statistics for estimation of wind speed distributions," Renewable Energy, Elsevier, vol. 32(3), pages 518-531.
    3. Akdag, S.A. & Bagiorgas, H.S. & Mihalakakou, G., 2010. "Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean," Applied Energy, Elsevier, vol. 87(8), pages 2566-2573, August.
    4. Jaramillo, O.A. & Borja, M.A., 2004. "Wind speed analysis in La Ventosa, Mexico: a bimodal probability distribution case," Renewable Energy, Elsevier, vol. 29(10), pages 1613-1630.
    5. Scrucca, Luca, 2013. "GA: A Package for Genetic Algorithms in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i04).
    6. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    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. Jin, Jingliang & Zhou, Dequn & Zhou, Peng & Miao, Zhuang, 2014. "Environmental/economic power dispatch with wind power," Renewable Energy, Elsevier, vol. 71(C), pages 234-242.
    2. Chang, Tian Pau, 2011. "Estimation of wind energy potential using different probability density functions," Applied Energy, Elsevier, vol. 88(5), pages 1848-1856, May.
    3. 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.
    4. Jung, Christopher & Schindler, Dirk, 2019. "Wind speed distribution selection – A review of recent development and progress," Renewable and Sustainable Energy Reviews, Elsevier, vol. 114(C), pages 1-1.
    5. Emilio Gómez-Lázaro & María C. Bueso & Mathieu Kessler & Sergio Martín-Martínez & Jie Zhang & Bri-Mathias Hodge & Angel Molina-García, 2016. "Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures," Energies, MDPI, vol. 9(2), pages 1-15, February.
    6. Hu, Qinghua & Wang, Yun & Xie, Zongxia & Zhu, Pengfei & Yu, Daren, 2016. "On estimating uncertainty of wind energy with mixture of distributions," Energy, Elsevier, vol. 112(C), pages 935-962.
    7. Shin, Ju-Young & Ouarda, Taha B.M.J. & Lee, Taesam, 2016. "Heterogeneous mixture distributions for modeling wind speed, application to the UAE," Renewable Energy, Elsevier, vol. 91(C), pages 40-52.
    8. Zhang, Hua & Yu, Yong-Jing & Liu, Zhi-Yuan, 2014. "Study on the Maximum Entropy Principle applied to the annual wind speed probability distribution: A case study for observations of intertidal zone anemometer towers of Rudong in East China Sea," Applied Energy, Elsevier, vol. 114(C), pages 931-938.
    9. Munir Ali Elfarra & Mustafa Kaya, 2018. "Comparison of Optimum Spline-Based Probability Density Functions to Parametric Distributions for the Wind Speed Data in Terms of Annual Energy Production," Energies, MDPI, vol. 11(11), pages 1-15, November.
    10. Estefania Artigao & Antonio Vigueras-Rodríguez & Andrés Honrubia-Escribano & Sergio Martín-Martínez & Emilio Gómez-Lázaro, 2021. "Wind Resource and Wind Power Generation Assessment for Education in Engineering," Sustainability, MDPI, vol. 13(5), pages 1-27, February.
    11. Soukissian, Takvor H. & Karathanasi, Flora E., 2017. "On the selection of bivariate parametric models for wind data," Applied Energy, Elsevier, vol. 188(C), pages 280-304.
    12. Muhammad Fitra Zambak & Catra Indra Cahyadi & Jufri Helmi & Tengku Machdhalie Sofie & Suwarno Suwarno, 2023. "Evaluation and Analysis of Wind Speed with the Weibull and Rayleigh Distribution Models for Energy Potential Using Three Models," International Journal of Energy Economics and Policy, Econjournals, vol. 13(2), pages 427-432, March.
    13. Allouhi, A. & Zamzoum, O. & Islam, M.R. & Saidur, R. & Kousksou, T. & Jamil, A. & Derouich, A., 2017. "Evaluation of wind energy potential in Morocco's coastal regions," Renewable and Sustainable Energy Reviews, Elsevier, vol. 72(C), pages 311-324.
    14. Wais, Piotr, 2017. "A review of Weibull functions in wind sector," Renewable and Sustainable Energy Reviews, Elsevier, vol. 70(C), pages 1099-1107.
    15. Gugliani, Gaurav Kumar & Sarkar, Arnab & Ley, Christophe & Matsagar, Vasant, 2021. "Identification of optimum wind turbine parameters for varying wind climates using a novel month-based turbine performance index," Renewable Energy, Elsevier, vol. 171(C), pages 902-914.
    16. Cabello, M. & Orza, J.A.G., 2010. "Wind speed analysis in the province of Alicante, Spain. Potential for small-scale wind turbines," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(9), pages 3185-3191, December.
    17. Calif, Rudy & Emilion, Richard & Soubdhan, Ted, 2011. "Classification of wind speed distributions using a mixture of Dirichlet distributions," Renewable Energy, Elsevier, vol. 36(11), pages 3091-3097.
    18. 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.
    19. Wais, Piotr, 2017. "Two and three-parameter Weibull distribution in available wind power analysis," Renewable Energy, Elsevier, vol. 103(C), pages 15-29.
    20. 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.

    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:spr:compst:v:36:y:2021:i:2:d:10.1007_s00180-020-01044-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.