In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here.

This paper presents a comprehensive analysis of procedures for the excess hazard model. A common issue with hazard models is estimating the overall hazard rather than the excess hazard, leading to inaccurate parameter estimates. The paper suggests applying various survival models, including the excess hazard model and the multilevel excess hazard model, to enhance the accuracy and reliability of the results. The primary objective of this study is to estimate the excess hazard for both models and conduct a comparative analysis between them. Two statistical criteria, Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC), were utilized to evaluate model accuracy. All calculations were performed using the R software system, specifically R version 4.2.2. The multilevel excess hazard model demonstrated superior performance in terms of AIC and BIC compared to the excess hazard model.