Dutta Subhankar, Kayal Suchandan
Department of Mathematics, Bioinformatics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, India.
Department of Mathematics, National Institute of Technology Rourkela, Rourkela, India.
J Appl Stat. 2025 Jan 4;52(10):1871-1903. doi: 10.1080/02664763.2024.2445237. eCollection 2025.
In this article, we consider statistical inference based on dependent competing risks data from Marshall-Olkin bivariate Weibull distribution. The maximum likelihood estimates of the unknown model parameters have been computed by using Newton-Raphson method under adaptive Type II progressive hybrid censoring with partially observed failure causes. Existence and uniqueness of maximum likelihood estimates are derived. Approximate confidence intervals have been constructed via the observed Fisher information matrix using asymptotic normality property of the maximum likelihood estimates. Bayes estimates and highest posterior density credible intervals have been calculated under gamma-Dirichlet prior distribution by using Markov chain Monte Carlo technique. Convergence of Markov chain Monte Carlo samples is tested. In addition, a Monte Carlo simulation is carried out to compare the effectiveness of the proposed methods. Further, three different optimality criteria have been taken into account to obtain the most effective censoring plans. From these simulation study results it has been concluded that Bayesian technique produces superior outcomes. Finally, a real-life data set has been analyzed to illustrate the operability and applicability of the proposed methods.
在本文中，我们考虑基于来自马歇尔 - 奥尔金双变量威布尔分布的相依竞争风险数据进行统计推断。在具有部分观测失效原因的自适应II型渐进混合删失下，通过牛顿 - 拉弗森方法计算了未知模型参数的最大似然估计。推导了最大似然估计的存在性和唯一性。利用最大似然估计的渐近正态性，通过观测费希尔信息矩阵构建了近似置信区间。使用马尔可夫链蒙特卡罗技术，在伽马 - 狄利克雷先验分布下计算了贝叶斯估计和最高后验密度可信区间。检验了马尔可夫链蒙特卡罗样本的收敛性。此外，进行了蒙特卡罗模拟以比较所提出方法的有效性。进一步地，考虑了三种不同的最优性准则以获得最有效的删失方案。从这些模拟研究结果得出结论，贝叶斯技术产生了更优的结果。最后，分析了一个实际数据集以说明所提出方法的可操作性和适用性。
