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In this paper, Burr-X distribution with unified hybrid censored data is considered. The maximum likelihood method, the Bayesian and the E-Bayesian (the expectation of the Bayesian estimate) approaches are studied for the distribution parameter and the associated reliability function. The Bayesian and the E-Bayesian estimates are derived under LINEX and squared error loss (SEL) functions. We apply Markov chain Monte Carlo (MCMC) techniques to derive the Bayesian and the E-Bayesian estimates. Also, confidence intervals (CIs) of the maximum likelihood estimates, as well as credible intervals (CRIs) of the Bayesian and the E-Bayesian estimates, are computed. On the other hand, an example of a real data set is provided for the purpose of illustration. Finally, a numerical comparison among the proposed methods is performed. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods. [ABSTRACT FROM AUTHOR]