来自两个Burr-XII总体的联合II型删失数据的收缩估计与预测
Shrinkage Estimation and Prediction for Joint Type-II Censored Data from Two Burr-XII Populations
AI总结：
本文针对两个2参数Burr-XII分布，在联合II型删失方案下应用线性和预检收缩估计技术进行参数估计与预测，并通过Monte Carlo模拟和真实数据集验证了方法性能。
摘要：
本文的主要目标是将线性和预检收缩估计技术应用于两个2参数Burr-XII分布的参数估计。此外，在联合II型删失方案下，使用经典和贝叶斯方法对未来观测值进行预测。收缩估计的效率与通过期望最大化算法和重要性抽样方法获得的最大似然估计和贝叶斯估计进行了比较，这些方法由Akbari Bargoshadi等人（2023）在发表于《Communications in Statistics-Simulation and Computation》的论文“Statistical inference under joint type-II censoring data from two Burr-XII populations”中提出。对于贝叶斯估计，考虑了信息先验分布和非信息先验分布。此外，还考虑了各种损失函数，包括平方误差、线性指数和广义熵。计算了近似置信区间、可信区间和最高概率密度区间。为了评估估计方法的性能，进行了Monte Carlo模拟研究。此外，利用两个真实数据集来说明所提出的方法。
英文摘要：
The main objective of this paper is to apply linear and pretest shrinkage estimation techniques to estimating the parameters of two 2-parameter Burr-XII distributions. Further more, predictions for future observations are made using both classical and Bayesian methods within a joint type-II censoring scheme. The efficiency of shrinkage estimates is compared to maximum likelihood and Bayesian estimates obtained through the expectation-maximization algorithm and importance sampling method, as developed by Akbari Bargoshadi et al. (2023) in "Statistical inference under joint type-II censoring data from two Burr-XII populations" published in Communications in Statistics-Simulation and Computation". For Bayesian estimations, both informative and non-informative prior distributions are considered. Additionally, various loss functions including squared error, linear-exponential, and generalized entropy are taken into account. Approximate confidence, credible, and highest probability density intervals are calculated. To evaluate the performance of the estimation methods, a Monte Carlo simulation study is conducted. Additionally, two real datasets are utilized to illustrate the proposed methods.
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