Numerical study of robust Bayesian analysis of generalized inverted family of distributions based on progressive type II right censoring

Abstract

In this article, we have developed the robust Bayesian inference for the generalized inverted family of distributions (GIFD) under an $ϵ$-contamination class of prior distributions for the shape parameter α, with different possibilities of known and unknown scale parameter, based on progressive type II censoring. We have derived the ML-II Bayes estimators of the parameters, reliability function and hazard function under the general entropy loss function (GELF) and linear exponential loss function (LLF). Results under squared error loss functions (SELF) are derived as a special case of GELF. We have also presented simulation study and analysis of a real data set.

Keywords:

• GIFD
• $ϵ$-contamination class of prior distributions
• ML-II posterior density
• Reliability function
• Hazard function
• SELF
• GELF
• LLF
• Progressive type II censoring
• Markov Chain Monte Carlo (MCMC) procedure
• Metropolis-Hastings algorithm
• Gibbs sampling technique

Acknowledgments

The authors are extremely thankful to the editor and referees for their comments and useful suggestions which helped in the improvement of this paper.