Asymptotic Confidence Intervals for MRL and TVaR of the Inverse Weibull Distribution with Type II Censored Data

Abstract

We consider interval estimation for the parameters, the Mean Residual Life (MRL) and the Tail Value at Risk (TVaR) of the inverse Weibull distribution. We constructed the confidence intervals based on the asymptotic normality of the maximum likelihood estimator in addition to intervals based on the asymptotic Chi-Square distribution of the likelihood ratio (LR) statistic under Type II Censoring. The performance of intervals is investigated and compared using the lower, upper, and total error rates, in addition to expected lengths using simulation. We found that LR intervals showed better overall performance and are more accurate than confidence intervals based on the asymptotic normality of maximum likelihood estimator.