Reliability Analysis and Optimality for a New Extended Topp-Leone Distribution Based on Progressive Censoring With Binomial Removal

Abstract

In this article, a progressive Type II censoring plan with binomial removal is utilized to overcome the estimation issues associated with the truncated Cauchy power-inverted Topp-Leone distribution (TCPITLD). Using maximum likelihood and Bayesian estimation approaches is a means of estimating the unknown parameter. Bayesian estimators are studied using the likelihood function when observed data are produced. This is done by employing the assumption of an informative prior, a gamma prior, and a symmetric loss function. Both of these assumptions are made. In addition, the discussion also includes the approximate confidence intervals obtained by using both the classical technique and the credible intervals with the most significant posterior density. A detailed simulation experiment that considers a variety of sample sizes and censoring techniques is carried out to evaluate the various estimation procedures. A single actual dataset is investigated to validate the effectiveness of the TCPITLD and the estimators provided during the process. The findings indicate that the Bayesian strategy that uses the gamma prior is preferable to both the maximum likelihood technique and the Bayesian approach that uses the informative prior to acquiring the required estimators.