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Estimation based on progressively type-I hybrid censored data from the Burr XII distribution

Author

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  • R. Arabi Belaghi

    (University of Tabriz)

  • M. Noori Asl

    (University of Tabriz)

Abstract

This study considers the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian frameworks when samples are observed in the presence of progressively type-I hybrid censoring. Under classical approach, we employ EM and stochastic EM algorithm for obtaining the maximum likelihood estimators of model parameters. On the other hand, under Bayesian framework, we obtain Bayes estimators with respect to different symmetric and asymmetric loss functions under non-informative and informative priors. In this regard, we use Tierney–Kadane and importance sampling methods. Asymptotic normality theory and MCMC samples are employed to construct the confidence intervals and HPD credible intervals. To improve the estimation accuracy shrinkage pre-test estimation strategy is also suggested. The relative efficiency of these estimators with respect to both classical and Bayesian estimators are investigated numerically. Our simulation studies reveal that the shrinkage pre-test estimation strategy outperforms the estimation based on classical and Bayesian procedure. Finally, one real data set is analyzed to illustrate the methods of inference discussed here.

Suggested Citation

  • R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:3:d:10.1007_s00362-016-0849-5
    DOI: 10.1007/s00362-016-0849-5
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    References listed on IDEAS

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    1. Manoj Rastogi & Yogesh Tripathi, 2013. "Inference on unknown parameters of a Burr distribution under hybrid censoring," Statistical Papers, Springer, vol. 54(3), pages 619-643, August.
    2. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    3. R. Arabi Belaghi & M. Arashi & S. M. M. Tabatabaey, 2015. "On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 1-23, January.
    4. Abdel-Hamid, Alaa H., 2009. "Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2511-2523, May.
    5. B. Kibria & A. Saleh, 2010. "Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples," Statistical Papers, Springer, vol. 51(4), pages 757-773, December.
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    Cited by:

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    2. Bo-Hong Wu & Hirofumi Michimae & Takeshi Emura, 2020. "Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model," Computational Statistics, Springer, vol. 35(4), pages 1525-1552, December.

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