Classical and Bayesian estimation of stress-strength reliability in type II censored Pareto distributions

ABSTRACT

In this paper, the stress-strength reliability, R, is estimated in type II censored samples from Pareto distributions. The classical inference includes obtaining the maximum likelihood estimator, an exact confidence interval, and the confidence intervals based on Wald and signed log-likelihood ratio statistics. Bayesian inference includes obtaining Bayes estimator, equi-tailed credible interval, and highest posterior density (HPD) interval given both informative and non-informative prior distributions. Bayes estimator of R is obtained using four methods: Lindley's approximation, Tierney-Kadane method, Monte Carlo integration, and MCMC. Also, we compare the proposed methods by simulation study and provide a real example to illustrate them.

Keywords:

• Bayes estimator
• HPD interval
• MCMC
• Pareto distribution
• Stress-strength reliability
• Type II censoring

MATHEMATICS SUBJECT CLASSIFICATION:

• 62Fxx
• 62Nxx

Acknowledgement

The authors thank the Referees and Editor for their useful comments and suggestions, which lead to an improved version of the paper.