Estimating the Shape Parameter of Topp–Leone Distribution Based on Progressive Type II Censored Samples

Abstract

In this paper, classical and Bayesian point estimations of the Topp–Leone distribution shape parameter are studied when the sample is progressive Type II censored. The maximum likelihood estimator (MLE) of the unknown parameter is proposed. Since the MLE does not have an explicit form, an approximate MLE has been derived. The Bayes estimate and the associated credible interval are also studied. Lindley’s method is proposed to approximate the Bayes estimate. The importance sampling technique is also proposed to approximate the Bayes estimate and to construct the associated credible interval. Monte Carlo simulations are performed to compare the performances of the proposed methods, and two data sets have been analyzed for illustrative purposes.