Estimating reliability parameters for inverse Gaussian distributions under complete and progressively type-II censored samples

Abstract

ABSTRACT In this paper, we study estimation of stress-strength reliability, assuming the stress and strength variables are inverse Gaussian distributed with unknown parameters. When the coefficient of variations of the distributions is unknown but equal, we develop MLE, Bayes estimator, bootstrap interval of the reliability. The profile likelihood Bayes estimator of the coefficient of variation is also derived. When all parameters are different, we derive the MLE, UMVUE, Bayes estimator, bootstrap interval, and highest posterior density credible interval of the stress-strength reliability. The predictive Bayes estimators of the reliability functions are derived. Under progressive type-II censoring, we derive the MLE, Bayes estimator and bootstrap confidence interval. Monte-Carlo simulation results and real data-based examples are also presented. We analyze lung cancer and air pollution data sets as applications of the stress-strength model.