IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v118y2013icp71-80.html
   My bibliography  Save this article

Selection of regressand for fitting the extreme value distributions using the ordinary, weighted and generalized least-squares methods

Author

Listed:
  • Hong, H.P.

Abstract

Fitting the extreme value distributions to samples is needed in many reliability analysis problems. The ordinary, weighted and generalized least-squares methods (OL, WL and GL method) are used to fit extreme value distributions based on the moments of order statistics and adopted plotting positions. An analyst may consider the observed ordered sample or the reduced variate as the regressand. The choice of the regressand for the least-squares methods and their corresponding relative accuracy are not always clear. Simulation results are presented in this study to rank the performance of the OL, WL and GL methods in combination with the choice of the regressands to estimate the distribution parameters, quantiles and nonexceedance probability. Analysis results for the OL method are also presented by adopting different plotting positions. The results indicate that the use of the ordered sample as the regressand is preferred. In such a case, the GL method outperforms the OL and WL methods for small sample size; the performance of the OL, WL and GL methods are similar for the sample size greater than about 20. The application of the OL method can be of value, if the adopted plotting position approximates well the mean of order statistics.

Suggested Citation

  • Hong, H.P., 2013. "Selection of regressand for fitting the extreme value distributions using the ordinary, weighted and generalized least-squares methods," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 71-80.
    • Handle: RePEc:eee:reensy:v:118:y:2013:i:c:p:71-80
    DOI: 10.1016/j.ress.2013.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832013000987
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2013.04.003?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. Schoefs, Franck, 2008. "Sensitivity approach for modelling the environmental loading of marine structures through a matrix response surface," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 1004-1017.
    2. Taflanidis, Alexandros A. & Loukogeorgaki, Eva & Angelides, Demos C., 2013. "Offshore wind turbine risk quantification/evaluation under extreme environmental conditions," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 19-32.
    3. Pasanisi, Alberto & Keller, Merlin & Parent, Eric, 2012. "Estimation of a quantity of interest in uncertainty analysis: Some help from Bayesian decision theory," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 93-101.
    4. Zhang, L.F. & Xie, M. & Tang, L.C., 2007. "A study of two estimation approaches for parameters of Weibull distribution based on WPP," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 360-368.
    5. Mir Pirouzi Fard, 2010. "Probability plots and order statistics of the standard extreme value distribution," Computational Statistics, Springer, vol. 25(2), pages 257-267, June.
    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. Li, Xiaoyue & Yang, Yinfei & Li, Liang & Zhao, Guolong & He, Ning, 2020. "Uncertainty quantification in machining deformation based on Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    2. Jiang, R., 2014. "A drawback and an improvement of the classical Weibull probability plot," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 135-142.

    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, Xin & Zhang, Zhaolong & Shi, Xiaoqiang & Ju, Wenbin, 2014. "A review on wind power industry and corresponding insurance market in China: Current status and challenges," Renewable and Sustainable Energy Reviews, Elsevier, vol. 38(C), pages 1069-1082.
    2. Merlin Keller & Guillaume Damblin & Alberto Pasanisi & Mathieu Schumann & Pierre Barbillon & Fabrizio Ruggeri, 2022. "Validation of a Computer Code for the Energy Consumption of a Building, with Application to Optimal Electric Bill Pricing," Post-Print hal-04071903, HAL.
    3. Leimeister, Mareike & Kolios, Athanasios, 2018. "A review of reliability-based methods for risk analysis and their application in the offshore wind industry," Renewable and Sustainable Energy Reviews, Elsevier, vol. 91(C), pages 1065-1076.
    4. Jin, Xin & Ju, Wenbin & Zhang, Zhaolong & Guo, Lianxin & Yang, Xiangang, 2016. "System safety analysis of large wind turbines," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 1293-1307.
    5. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    6. Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.
    7. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    8. Hu, Xiaonong & Fang, Genshen & Yang, Jiayu & Zhao, Lin & Ge, Yaojun, 2023. "Simplified models for uncertainty quantification of extreme events using Monte Carlo technique," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    9. Merlin Keller & Guillaume Damblin & Alberto Pasanisi & Mathieu Schumann & Pierre Barbillon & Fabrizio Ruggeri & Eric Parent, 2022. "Validation of a Computer Code for the Energy Consumption of a Building, with Application to Optimal Electric Bill Pricing," Econometrics, MDPI, vol. 10(4), pages 1-24, November.
    10. Maheri, Alireza, 2014. "A critical evaluation of deterministic methods in size optimisation of reliable and cost effective standalone hybrid renewable energy systems," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 159-174.
    11. Wei, K. & Arwade, S.R. & Myers, A.T. & Hallowell, S. & Hajjar, J.F. & Hines, E.M. & Pang, W., 2016. "Toward performance-based evaluation for offshore wind turbine jacket support structures," Renewable Energy, Elsevier, vol. 97(C), pages 709-721.
    12. Lee, Yeon-Seung & Choi, Byung-Lyul & Lee, Ji Hyun & Kim, Soo Young & Han, Soonhung, 2014. "Reliability-based design optimization of monopile transition piece for offshore wind turbine system," Renewable Energy, Elsevier, vol. 71(C), pages 729-741.
    13. Robinson, Allen C. & Drake, Richard R. & Swan, M. Scot & Bennett, Nichelle L. & Smith, Thomas M. & Hooper, Russell & Laity, George R., 2021. "A software environment for effective reliability management for pulsed power design," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    14. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    15. Charlton, T.S. & Rouainia, M., 2022. "Geotechnical fragility analysis of monopile foundations for offshore wind turbines in extreme storms," Renewable Energy, Elsevier, vol. 182(C), pages 1126-1140.
    16. Rufo, M.J. & Martín, J. & Pérez, C.J., 2014. "Adversarial life testing: A Bayesian negotiation model," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 118-125.
    17. Renyan Jiang, 2022. "A novel parameter estimation method for the Weibull distribution on heavily censored data," Journal of Risk and Reliability, , vol. 236(2), pages 307-316, April.
    18. Jiang, R., 2014. "A drawback and an improvement of the classical Weibull probability plot," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 135-142.
    19. Tianyu Liu & Lulu Zhang & Guang Jin & Zhengqiang Pan, 2022. "Reliability Assessment of Heavily Censored Data Based on E-Bayesian Estimation," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    20. Chabridon, Vincent & Balesdent, Mathieu & Bourinet, Jean-Marc & Morio, Jérôme & Gayton, Nicolas, 2018. "Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 164-178.

    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:reensy:v:118:y:2013:i:c:p:71-80. 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/reliability-engineering-and-system-safety .

    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.