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On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods

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  • Yan Shen
  • Ancha Xu

Abstract

Competing risks models are of great importance in reliability and survival analysis. They are often assumed to have independent causes of failure in literature, which may be unreasonable. In this article, dependent causes of failure are considered by using the Marshall–Olkin bivariate Weibull distribution. After deriving some useful results for the model, we use ML, fiducial inference, and Bayesian methods to estimate the unknown model parameters with a parameter transformation. Simulation studies are carried out to assess the performances of the three methods. Compared with the maximum likelihood method, the fiducial and Bayesian methods could provide better parameter estimation.

Suggested Citation

  • Yan Shen & Ancha Xu, 2018. "On the dependent competing risks using Marshall–Olkin bivariate Weibull model: Parameter estimation with different methods," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(22), pages 5558-5572, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:22:p:5558-5572
    DOI: 10.1080/03610926.2017.1397170
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    Cited by:

    1. Ke Wu & Liang Wang & Li Yan & Yuhlong Lio, 2021. "Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    2. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    3. Zhang, Chunfang & Wang, Liang & Bai, Xuchao & Huang, Jianan, 2022. "Bayesian reliability analysis for copula based step-stress partially accelerated dependent competing risks model," Reliability Engineering and System Safety, Elsevier, vol. 227(C).

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