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Abstract: The main purpose of the paper is to investigate the classical and Bayesian estimation for the unknown parameters of the Weibull-exponential distribution (WED) based on Adaptive Type-II progressive censoring (A-II-PRO-C). Maximum likelihood (ML), percentile bootstrap and Bayes methods are used to estimate the unknown parameters of WED. Moreover, the approximate confidence intervals (ACIs) and asymptotic variance-covariance matrix have been obtained. Markov Chain Monte Carlo (MCMC) technique is applied to estimate the unknown parameters of WED. The Metropolis–Hastings algorithm is the MCMC method that’s to generate samples from the posterior density functions. An example is applied to different estimation methods. Finally, a Monte Carlo simulation study is carried out to compare the performance of the different methods.

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