Bayesian analysis of head and neck cancer data using generalized inverse Lindley stress–strength reliability model

ABSTRACT

In this article, we present the analysis of head and neck cancer data using generalized inverse Lindley stress–strength reliability model. We propose Bayes estimators for estimating P(X > Y), when X and Y represent survival times of two groups of cancer patients observed under different therapies. The X and Y are assumed to be independent generalized inverse Lindley random variables with common shape parameter. Bayes estimators are obtained under the considerations of symmetric and asymmetric loss functions assuming independent gamma priors. Since posterior becomes complex and does not possess closed form expressions for Bayes estimators, Lindley’s approximation and Markov Chain Monte Carlo techniques are utilized for Bayesian computation. An extensive simulation experiment is carried out to compare the performances of Bayes estimators with the maximum likelihood estimators on the basis of simulated risks. Asymptotic, bootstrap, and Bayesian credible intervals are also computed for the P(X > Y).

KEYWORDS:

• Bayes estimator
• bootstrap
• generalized inverse Lindley distribution
• maximum likelihood estimator
• stress–strength reliability

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62F10

Acknowledgment

The author would like to thank Editor-in-Chief Professor N. Balakrishnan, associate editor, and two anonymous referees for their constructive suggestions for the improvement of the article. He also thanks Professor Umesh Singh and Professor Sanjay Kumar Singh (Department of Statistics, Banaras Hindu University, Varanasi, India) for their suggestions to the content of the article.