Bayesian Inference for the Randomly-Censored Three-Parameter Burr XII Distribution

Authors

Rashad M. EL-Sagheer, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, EgyptFollow
Mohamed A. W. Mahmoud, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, EgyptFollow
Hasaballah M. Hasaballah, Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, we obtain the point and interval estimations for a three-parameter Burr-XII distribution (TPBXIID) based on randomly-censored data. The maximum likelihood (ML) and Bayes estimation method are used to estimate the unknown parameters of the TPBXIID. Furthermore, approximate confidence intervals (ACIs) for the unknown parameters are constructed. Markov chain Monte Carlo (MCMC) method is applied to find the Bayes estimation. Also, highest posterior density (HPD) credible intervals (CRIs) are obtained for the parameters. Gibbs within Metropolis-Hasting samplers are used to generate samples from the posterior density functions. A couple of real data sets are discussed to illustrate the proposed methods. Finally, to compare different estimates proposed in this paper, a Monte Carlo simulation study has been performed.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140210

Recommended Citation

M. EL-Sagheer, Rashad; A. W. Mahmoud, Mohamed; and M. Hasaballah, Hasaballah (2020) "Bayesian Inference for the Randomly-Censored Three-Parameter Burr XII Distribution," Applied Mathematics & Information Sciences: Vol. 14: Iss. 2, Article 10.
DOI: http://dx.doi.org/10.18576/amis/140210
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss2/10