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The exponentiated Weibull distribution: a survey

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  • Saralees Nadarajah
  • Gauss Cordeiro
  • Edwin Ortega

Abstract

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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    2. Shakhawat Hossain & Shahedul A. Khan, 2020. "Shrinkage estimation of the exponentiated Weibull regression model for time‐to‐event data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(4), pages 592-610, November.
    3. Cleanderson R. Fidelis & Edwin M. M. Ortega & Gauss M. Cordeiro, 2024. "Residual Analysis for Poisson-Exponentiated Weibull Regression Models with Cure Fraction," Stats, MDPI, vol. 7(2), pages 1-16, May.
    4. 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.
    5. Fang, Longxiang & Zhang, Xinsheng, 2015. "Stochastic comparisons of parallel systems with exponentiated Weibull components," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 25-31.
    6. Ahmed Zohair Djeddi & Ahmed Hafaifa & Abdellah Kouzou & Salam Abudura, 2017. "Exploration of reliability algorithms using modified Weibull distribution: application on gas turbine," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1885-1894, November.
    7. Haselsteiner, Andreas F. & Thoben, Klaus-Dieter, 2020. "Predicting wave heights for marine design by prioritizing extreme events in a global model," Renewable Energy, Elsevier, vol. 156(C), pages 1146-1157.
    8. Haitham M. Yousof & Mustafa Ç. Korkmaz & Subhradev Sen, 2021. "A New Two-Parameter Lifetime Model," Annals of Data Science, Springer, vol. 8(1), pages 91-106, March.
    9. Tommaso Lando & Lucio Bertoli-Barsotti, 2020. "Stochastic dominance relations for generalised parametric distributions obtained through composition," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 297-311, December.
    10. Hazhir Homei & Saralees Nadarajah, 2018. "On Products and Mixed Sums of Gamma and Beta Random Variables Motivated by Availability," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 799-810, June.

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