On estimation of R=P(Y<X) for exponential distribution under progressive type-II censoring

Abstract

This paper deals with the estimation of the stress–strength parameter R=P(Y<X), when X and Y are independent exponential random variables, and the data obtained from both distributions are progressively type-II censored. The uniformly minimum variance unbiased estimator and the maximum-likelihood estimator (MLE) are obtained for the stress–strength parameter. Based on the exact distribution of the MLE of R, an exact confidence interval of R has been obtained. Bayes estimate of R and the associated credible interval are also obtained under the assumption of independent inverse gamma priors. An extensive computer simulation is used to compare the performances of the proposed estimators. One data analysis has been performed for illustrative purpose.

Keywords:

• maximum-likelihood estimator
• uniformly minimum variance unbiased estimator
• confidence intervals
• Bayes estimator
• prior distribution
• posterior analysis
• credible intervals

Acknowledgements

The authors would like to thank the two unknown referees and the associate editor for their valuable comments which had helped to improve the paper significantly. Part of the work of the third author has been supported by a grant from the Department of Science and Technology, Government of India.