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Marshall-Olkin extended weibull distribution and its application to censored data

Author

Listed:
  • M. E. Ghitany
  • E. K. Al-Hussaini
  • R. A. Al-Jarallah

Abstract

In this paper we show that the Marshall-Olkin extended Weibull distribution can be obtained as a compound distribution with mixing exponential distribution. In addition, we provide simple sufficient conditions for the shape of the hazard rate function of the distribution. Moreover, we extend the considered distribution to accommodate randomly right censored data. Finally, application of the extended distribution to a data set representing the remission times of bladder cancer patients is given and its goodness-of-fit is demonstrated.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:32:y:2005:i:10:p:1025-1034
    DOI: 10.1080/02664760500165008
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    Cited by:

    1. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    2. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    3. Gupta, Ramesh C. & Lvin, Sergey & Peng, Cheng, 2010. "Estimating turning points of the failure rate of the extended Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 924-934, April.
    4. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    5. Nadarajah, Saralees & Rocha, Ricardo, 2016. "Newdistns: An R Package for New Families of Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i10).
    6. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    7. 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.
    8. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.
    9. Aliyu Ismail Ishaq & Alfred Adewole Abiodun, 2020. "The Maxwell–Weibull Distribution in Modeling Lifetime Datasets," Annals of Data Science, Springer, vol. 7(4), pages 639-662, December.
    10. García, Victoriano J. & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2014. "On Modelling Insurance Data by Using a Generalized Lognormal Distribution || Sobre la modelización de datos de seguros usando una distribución lognormal generalizada," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 18(1), pages 146-162, December.
    11. 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.
    12. Saralees Nadarajah & Božidar Popović & Miroslav Ristić, 2013. "Compounding: an R package for computing continuous distributions obtained by compounding a continuous and a discrete distribution," Computational Statistics, Springer, vol. 28(3), pages 977-992, June.
    13. Zubair Ahmad, 2020. "The Zubair-G Family of Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 7(2), pages 195-208, June.
    14. Rocha, Ricardo & Nadarajah, Saralees & Tomazella, Vera & Louzada, Francisco, 2017. "A new class of defective models based on the Marshall–Olkin family of distributions for cure rate modeling," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 48-63.
    15. Nanda, Asok K. & Das, Suchismita, 2012. "Stochastic orders of the Marshall–Olkin extended distribution," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 295-302.
    16. 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.
    17. Devendra Kumar & Neetu Jain & Mazen Nassar & Osama Eraki Abo-Kasem, 2021. "Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application," Annals of Data Science, Springer, vol. 8(4), pages 785-811, December.
    18. Mohamed Hussein & Gauss M. Cordeiro, 2022. "A Modified Power Family of Distributions: Properties, Simulations and Applications," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    19. Yolanda M. Gómez & Diego I. Gallardo & Carolina Marchant & Luis Sánchez & Marcelo Bourguignon, 2023. "An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    20. Mehdi Basikhasteh & Iman Makhdoom, 2022. "Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions," 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. 13(2), pages 867-880, April.
    21. Jose K. K. & Sivadas Remya, 2015. "Negative Binomial Marshall–Olkin Rayleigh Distribution and Its Applications," Stochastics and Quality Control, De Gruyter, vol. 30(2), pages 89-98, December.
    22. Gauss Cordeiro & Artur Lemonte, 2013. "On the Marshall–Olkin extended Weibull distribution," Statistical Papers, Springer, vol. 54(2), pages 333-353, May.

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