Estimation of stress-strength reliability in the inverse Gaussian distribution under progressively type II censored data

The stress-strength parameter R=P(Y<X), as a reliability parameter, is considered in different statistical distributions. In the present paper, the stress-strength reliability is estimated based on progressively type II censored samples, in which X and Y are two independent random variables with inverse Gaussian distributions. The maximum likelihood estimate of R via expectation-maximization algorithm and the Bayes estimate of R are obtained. Furthermore, we obtain the bootstrap confidence intervals, HPD credible interval and confidence intervals based on generalized pivotal quantity for R. Additionally, the performance of point estimators and confidence intervals are evaluated by a simulation study. Finally, the proposed methods are conducted on a set of real data for illustrative purposes.