The objective of this research is to delineate both the likelihood and Bayesian estimation techniques applied to the expansion of the power Topp-Leone distribution using progressively Type-II censored samples with random removal. Initially, we focus on the maximum likelihood method to estimate the model parameters. Furthermore, we explore approximate confidence intervals utilizing asymptotic theory. Additionally, employing flexible gamma priors for the shape and scale parameters, along with a non-informative prior, Bayes estimators are derived under the assumption of a squared error loss function. Correspondingly, we determine the associated highest posterior density credible intervals for the parameters. Monte Carlo simulations are conducted to assess the effectiveness of the suggested estimates based on diverse criteria. Additionally, we offer a comparison of sampling techniques, including censored samples and bootstrap sampling, across various competing censoring plans. To demonstrate the practical utility of the proposed methodologies, we scrutinize a material physics data set and an economic growth data set. The numerical findings affirm the satisfactory performance of our proposed methods.