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Maximum likelihood estimation of Burr XII distribution parameters under random censoring

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  • M. E. Ghitany
  • S. Al-Awadhi

Abstract

In this paper, we consider the maximum likelihood estimation of the parameters of Burr XII distribution using randomly right censored data. We provide necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood estimates. Under such conditions, it is shown that the maximum likelihood estimates are strongly consistent for the true values of the parameters and are asymptotically bivariate normal. An application to leukemia free-survival times for allogeneic and autologous transplant patients is given.

Suggested Citation

  • M. E. Ghitany & S. Al-Awadhi, 2002. "Maximum likelihood estimation of Burr XII distribution parameters under random censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 955-965.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:7:p:955-965
    DOI: 10.1080/0266476022000006667
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    References listed on IDEAS

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    1. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
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    Cited by:

    1. Neha Goel & Hare Krishna, 2022. "Different methods of estimation in two parameter Geometric distribution with randomly censored data," 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(4), pages 1652-1665, August.
    2. Abbasi, B. & Hosseinifard, S.Z. & Coit, D.W., 2010. "A neural network applied to estimate Burr XII distribution parameters," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 647-654.
    3. Neha Goel, 2018. "Estimation Methods in Clinical Trials with Randomly Censored Exponential Healing Times and Rayleigh Dropout Times," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(3), pages 61-68, October.
    4. Francisco Louzada & Pedro Luiz Ramos, 2017. "A New Long-Term Survival Distribution," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 1(5), pages 104-109, May.
    5. Ilhan Usta, 2013. "Different estimation methods for the parameters of the extended Burr XII distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 397-414, February.
    6. H. Krishna & N. Goel, 2018. "Classical and Bayesian inference in two parameter exponential distribution with randomly censored data," Computational Statistics, Springer, vol. 33(1), pages 249-275, March.
    7. Zang, Zhaoqi & Xu, Xiangdong & Yang, Chao & Chen, Anthony, 2018. "A closed-form estimation of the travel time percentile function for characterizing travel time reliability," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 228-247.

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