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The exponentiated Weibull distribution: a survey


  • Saralees Nadarajah


  • Gauss Cordeiro
  • Edwin Ortega


A review is given of the exponentiated Weibull distribution, the first generalization of the two-parameter Weibull distribution to accommodate nonmonotone hazard rates. The properties reviewed include: moments, order statistics, characterizations, generalizations and related distributions, transformations, graphical estimation, maximum likelihood estimation, Bayes estimation, other estimation, discrimination, goodness of fit tests, regression models, applications, multivariate generalizations, and computer software. Some of the results given are new and hitherto unknown. It is hoped that this review could serve as an important reference and encourage developments of further generalizations of the two-parameter Weibull distribution. Copyright Springer-Verlag 2013

Suggested Citation

  • Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
  • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:839-877 DOI: 10.1007/s00362-012-0466-x

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    References listed on IDEAS

    1. Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Cancho, Vicente G. & Cordeiro, Gauss M., 2010. "The log-exponentiated Weibull regression model for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1017-1035, April.
    2. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    3. Chansoo Kim & Jinhyouk Jung & Younshik Chung, 2011. "Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring," Statistical Papers, Springer, vol. 52(1), pages 53-70, February.
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    5. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
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    7. Fawziah Alshunnar & Mohammad Raqab & Debasis Kundu, 2010. "On the comparison of the Fisher information of the log-normal and generalized Rayleigh distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 391-404.
    8. Cid, Juan Esteban Ramirez & Achcar, Jorge Alberto, 1999. "Bayesian inference for nonhomogeneous Poisson processes in software reliability models assuming nonmonotonic intensity functions," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 147-159, December.
    9. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
    10. Saralees Nadarajah, 2009. "Bathtub-shaped failure rate functions," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(5), pages 855-863, September.
    11. Amit Choudhury, 2005. "A Simple Derivation of Moments of the Exponentiated Weibull Distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 17-22, September.
    12. repec:eee:reensy:v:95:y:2010:i:9:p:981-988 is not listed on IDEAS
    13. Barreto-Souza, Wagner & Cribari-Neto, Francisco, 2009. "A generalization of the exponential-Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2493-2500, December.
    14. Manisha & M. MASOOM ALI & JUNGSOO WOO, 2006. "Exponentiated Weibull distribution," Statistica, Department of Statistics, University of Bologna, vol. 66(2), pages 139-147.
    15. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    16. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    17. Meintanis, Simos G., 2008. "A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2496-2503, January.
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    Cited by:

    1. Barmalzan, Ghobad & Najafabadi, Amir T. Payandeh & Balakrishnan, Narayanaswamy, 2015. "Stochastic comparison of aggregate claim amounts between two heterogeneous portfolios and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 235-241.
    2. Fang, Longxiang & Zhang, Xinsheng, 2015. "Stochastic comparisons of parallel systems with exponentiated Weibull components," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 25-31.
    3. repec:spr:ijsaem:v:8:y:2017:i:2:d:10.1007_s13198-016-0480-9 is not listed on IDEAS


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