Bayesian inference for the randomly censored Burr-type XII distribution

ABSTRACT

The article presents the Bayesian inference for the parameters of randomly censored Burr-type XII distribution with proportional hazards. The joint conjugate prior of the proposed model parameters does not exist; we consider two different systems of priors for Bayesian estimation. The explicit forms of the Bayes estimators are not possible; we use Lindley's method to obtain the Bayes estimates. However, it is not possible to obtain the Bayesian credible intervals with Lindley's method; we suggest the Gibbs sampling procedure for this purpose. Numerical experiments are performed to check the properties of the different estimators. The proposed methodology is applied to a real-life data for illustrative purposes. The Bayes estimators are compared with the Maximum likelihood estimators via numerical experiments and real data analysis. The model is validated using posterior predictive simulation in order to ascertain its appropriateness.

KEYWORDS:

• Log-concave density function
• Gibbs sampling
• Lindley's method
• posterior predictive p-value
• MCMC

Acknowledgements

The authors thank the referees and the associate editor for their useful suggestions to improve the article.

Disclosure statement

No potential conflict of interest was reported by the authors.