Statistical inference for the exponentiated half logistic distribution based on censored data

Abstract

In this paper, we consider the estimates for the scale parameter of an exponentiated half logistic distribution under progressively Type-II censoring and general progressively Type-II censoring, respectively. Because of the complex form of the traditional maximum likelihood estimator, it is hard to get an explicit solution. Therefore, we propose three new estimation methods based on censored data to obtain approximate estimates of the scale parameter. The first two are approximate maximum likelihood estimation methods based on Taylor expansion and the third is the approximate estimation method based on pivotal quantities we establish. Furthermore, we consider asymptotic confidence intervals based on pivotal quantities. Finally, simulation studies are conducted to compare the performance of the proposed estimators. A real dataset analysis is carried out to illustrate the proposed methods.