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Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution

Author

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  • Junru Ren

    (Beijing Jiaotong University)

  • Wenhao Gui

    (Beijing Jiaotong University)

Abstract

This paper considers the statistical inference for the competing risks model from generalized Rayleigh distribution based on progressive Type-II censoring when the parameters of the latent lifetime distributions are different or common. Maximum likelihood estimates are obtained, where the existence of the point estimators are proved, and the confidence intervals are established via the observed Fisher information matrix as well. Bayesian estimates of unknown parameters and reliability characteristics are derived under symmetric and asymmetric loss functions, and Monte Carlo Markov Chain sampling method is used to compute the Bayesian point estimates and the highest posterior density credible intervals. In addition, Bootstrap methods are also considered to obtain bias-corrected point estimates and approximate confidence intervals. Then we carry out hypothesis test using likelihood ratio test statistics. Monte Carlo simulation and a set of real data are presented to assess the performance of our proposed methods. Finally, the optimal censoring scheme issue is studied.

Suggested Citation

  • Junru Ren & Wenhao Gui, 2021. "Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution," Computational Statistics, Springer, vol. 36(1), pages 479-513, March.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01021-y
    DOI: 10.1007/s00180-020-01021-y
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    References listed on IDEAS

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    1. Indrani Basak & N. Balakrishnan, 2017. "Prediction of censored exponential lifetimes in a simple step-stress model under progressive Type II censoring," Computational Statistics, Springer, vol. 32(4), pages 1665-1687, December.
    2. Meintanis, Simos G., 2008. "A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2496-2503, January.
    3. Yao Zhang & William Q. Meeker, 2005. "Bayesian life test planning for the Weibull distribution with given shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 237-249, June.
    4. Cramer, Erhard & Schmiedt, Anja Bettina, 2011. "Progressively Type-II censored competing risks data from Lomax distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1285-1303, March.
    5. 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.
    6. Pareek, Bhuvanesh & Kundu, Debasis & Kumar, Sumit, 2009. "On progressively censored competing risks data for Weibull distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4083-4094, October.
    7. Manoj Chacko & Rakhi Mohan, 2019. "Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals," Computational Statistics, Springer, vol. 34(1), pages 233-252, March.
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    Cited by:

    1. Pao-sheng Shen, 2022. "Nonparametric estimation for competing risks survival data subject to left truncation and interval censoring," Computational Statistics, Springer, vol. 37(1), pages 29-42, March.

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