Statistical Inference of Weighted Exponential Lifetimes Under Progressive Type-II Censoring Scheme

Abstract

Abstract This paper considers estimation of parameters of weighted exponential (WE) distribution based on the progressively Type-II censored data. First the parameters are estimated by the maximum likelihood (MLE) method. It is observed that the MLE of parameters cannot be obtained in a closed form. So, the approximate maximum likelihood estimates (AMLE) approach is proposed to deal with non-linear expressions resulted from the MLE method. A further point estimation method, Bayes estimation, is utilized which does not result in explicit form for the obtained integrals. We use Lindley’s approximation method to get rid of unsolvable integrals designed for squared error and linex loss functions. Also, the Fisher information matrix is found and used to construct asymptotic confidence interval. The two alternative approximate confidence intervals such as percentile bootstrap and bootstrap-t are also derived. Finally, a simulation study in order to compare the proposed estimators is performed.