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On the Marshall–Olkin extended Weibull distribution

Author

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  • Gauss Cordeiro
  • Artur Lemonte

Abstract

We study some mathematical properties of the Marshall–Olkin extended Weibull distribution introduced by Marshall and Olkin (Biometrika 84:641–652, 1997 ). We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, reliability and Rényi entropy. We determine the moments of the order statistics. We also discuss the estimation of the model parameters by maximum likelihood and obtain the observed information matrix. We provide an application to real data which illustrates the usefulness of the model. Copyright Springer-Verlag 2013

Suggested Citation

  • Gauss Cordeiro & Artur Lemonte, 2013. "On the Marshall–Olkin extended Weibull distribution," Statistical Papers, Springer, vol. 54(2), pages 333-353, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:333-353
    DOI: 10.1007/s00362-012-0431-8
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.
    2. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
    3. Chrys Caroni, 2010. "Testing for the Marshall–Olkin extended form of the Weibull distribution," Statistical Papers, Springer, vol. 51(2), pages 325-336, June.
    4. H. M. Barakat & Y. H. Abdelkader, 2004. "Computing the moments of order statistics from nonidentical random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(1), pages 15-26, April.
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    Cited by:

    1. Hadeel Klakattawi & Dawlah Alsulami & Mervat Abd Elaal & Sanku Dey & Lamya Baharith, 2022. "A new generalized family of distributions based on combining Marshal-Olkin transformation with T-X family," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-29, February.
    2. Ricardo Rocha & Saralees Nadarajah & Vera Tomazella & Francisco Louzada, 2016. "Two new defective distributions based on the Marshall–Olkin extension," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(2), pages 216-240, April.
    3. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    4. Ali Algarni, 2021. "On a new generalized lindley distribution: Properties, estimation and applications," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-19, February.
    5. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa C. Korkmaz & Gauss M. Cordeiro & Haitham M. Yousof & Munir Ahmad, 2019. "On Burr III Marshal Olkin family: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-21, December.
    6. Harsh Tripathi & Varun Agiwal, 2024. "A new version of univariate Rayleigh distribution: properties, estimation and it’s application," 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. 15(11), pages 5367-5377, November.

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