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The main objective of this paper is to apply linear and pretest shrinkageestimation techniques to estimating the parameters of two 2-parameter Burr-XIIdistributions. Further more, predictions for future observations are made usingboth classical and Bayesian methods within a joint type-II censoring scheme.The efficiency of shrinkage estimates is compared to maximum likelihood andBayesian estimates obtained through the expectation-maximization algorithm andimportance sampling method, as developed by Akbari Bargoshadi et al. (2023) in"Statistical inference under joint type-II censoring data from two Burr-XIIpopulations" published in Communications in Statistics-Simulation andComputation". For Bayesian estimations, both informative and non-informativeprior distributions are considered. Additionally, various loss functionsincluding squared error, linear-exponential, and generalized entropy are takeninto account. Approximate confidence, credible, and highest probability densityintervals are calculated. To evaluate the performance of the estimationmethods, a Monte Carlo simulation study is conducted. Additionally, two realdatasets are utilized to illustrate the proposed methods.

Shrinkage Estimation and Prediction for Joint Type-II Censored Data from Two Burr-XII Populations