Bayesian reliability estimation for the Topp–Leone distribution under progressively type-II censored samples

This study explored the possibility of using the Bayesian estimation for the parameters and reliability characteristics (including reliability function, hazard rate function and reversal hazard rate function) of the two-parametric Topp–Leone distribution when the lifetimes are progressively censored. We assumed the independent gamma prior for the scale parameter and beta prior for the shape parameter of the distribution. Because the expressions for the Bayes estimators for the characteristics under investigation cannot be derived in the closed form, we proposed the Lindley’s approximation and Tierney and Kadane’s approximation for their numerical estimation. The comparison among the proposed estimators was made by analyzing the simulated and real-life datasets, which elucidated that the estimators are consistent. The proposed estimators, however, are insensitive with respect to change in values of hyper-parameters and model parameters. The employment of censoring schemes with tail behavior along with entropy loss function and Tierney and Kadane’s approximation provided the best results, especially in the small-to-moderate samples.