This paper investigates the performance of empirical Bayesian and E-Bayesian estimation of the bathtub-shaped distribution based on the progressive Type-II censored samples. These two estimations overcome the selection of hyperparameters in the Bayesian method. The empirical Bayesian analysis employs the classical approach to determine the hyperparameters. The E-Bayesian estimation uses the prior distribution of hyperparameters to derive the expectation of Bayesian estimates. The estimates of parameters are derived under the squared error loss and LINEX loss functions. The extensive simulations show the results of the empirical Bayesian estimates and the E-Bayesain estimates. Further, the empirical Bayesian estimation is also presented to analyze the parameters of bathtub-shaped distribution based on the general progressive Type-II censored samples. The two datasets from the electromechanical field and medical survival analysis are analyzed using the empirical Bayesian and E-Bayesian methods.

Bootstrap-p methodStep 1: Assume that the original sample under the B-JPC scheme has been obtained in advance, named {(t 1 , m 1 ), ..., (t k , m k )}. Using the sample through the EM and SEM algorithm to estimate θ = (β 1 , β 2 , λ). The MLEs of θ is denoted as θ = β1 , β2 , λ .Step 2: Use θ = β1 , β2 , λ to generate a B-JPC sample with the same predetermined S 1 , S 2 , n 1 , and n 2 , then compute the MLEs β1 p , β1 p and λp .