AI 中文总结
本文针对斑胸草雀生存现象，研究Gompertz分布下改进自适应II型逐步删失数据的竞争风险模型，推导参数估计、构造区间并通过模拟与真实数据验证方法性能。
AI 中文摘要
本文以不同食物可获得性条件下特定鸟类（斑胸草雀）的生存情况为研究对象，针对该现象研究改进自适应II型逐步删失方案（IAT-II PCS）下的竞争风险模型。考虑两个相互独立的竞争失效原因，假设其失效寿命服从含未知尺度和形状参数的Gompertz分布，推导未知参数的极大似然估计（MLE）并证明其唯一存在性；利用MLE的渐近正态性构造渐近置信区间（ACI），在不同损失函数下针对无信息先验和有信息先验分别获取贝叶斯估计，计算最高后验密度（HPD）可信区间；开展蒙特卡洛模拟研究以比较所提估计的性能，研究三种最优性准则以获取最优删失方案；最后对真实数据集进行分析以作进一步说明。
英文摘要
This paper studies survival of certain bird species (Zebra Finches) under different food availability conditions. A competing risks model is studied under improved adaptive type-II progressive censoring scheme (IAT-II PCS) referring to this phenomena. Two independent competing causes of failure are considered where lifetime of these failures are assumed to follow Gompertz distribution with unknown scale and shape parameters. Maximum likelihood estimators (MLEs) of the unknown parameters are derived. It is established that they exist uniquely. Asymptotic confidence intervals (ACIs) are also constructed using asymptotic normality property of the MLE. Bayes estimates are obtained with respect to both non-informative and informative priors under different loss functions. Highest posterior density (HPD) credible intervals are calculated. A Monte Carlo simulation study is conducted to compare the performance of the proposed estimates. Three optimality criteria are studied to obtain the optimal censoring scheme. Finally, a real life data set is analyzed for further illustrations.
Comments37 pages, 5 figures
