Statistical Papers

, Volume 60, Issue 3, pp 761–803 | Cite as

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

  • R. Arabi BelaghiEmail author
  • M. Noori Asl
Regular Article


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.


Bayesian estimation SEM algorithm Importance sampling Tierney–Kadane method Shrinkage pre-test estimation Progressively type-I hybrid censored data 



The authors are thankful the reviewers for their valuable comments and suggestions which significantly improved the earlier version of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesUniversity of TabrizTabrizIran

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