Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample

In this paper, we investigate classical and Bayesian estimation of stress-strength reliability $\delta = P(X > Y)$ under an adaptive progressive type-Ⅱ censored sample. Assume that $X$ and $Y$ are independent random variables that follow inverse Weibull distribution with the same shape but different scale parameters. In classical estimation, the maximum likelihood estimator and asymptotic confidence interval are deduced. An approximate maximum likelihood estimator approach is used to obtain the explicit form. In Bayesian estimation, the Bayesian estimators are derived based on symmetric entropy loss function and LINEX loss function. Due to the complexity of integrals, we proposed Lindley's approximation to get the approximate Bayesian estimates. To compare the different estimators, we performed Monte Carlo simulations. Under gamma prior, the approximate maximum likelihood estimator performs better than Bayesian estimators. Under non-informative prior, the approximate maximum likelihood estimator has the same behavior as Bayesian estimators. In the end, two data sets are used to prove the effectiveness of the proposed methods.