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 the Newton-Raphson method under adaptive Type II progressive hybrid censoring with partially observed failure causes. The existence and uniqueness of maximum likelihood estimates are derived. Approximate confidence intervals have been constructed via the observed Fisher information matrix using the 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 the 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. Finally, a real-life data set has been analyzed to illustrate the operability and applicability of the proposed methods.
翻译:在本文中,我们考虑了来自 Marshall-Olkin 双变量 Weibull 分布的依赖竞争风险数据的统计推断问题。使用适应性二型渐进混合截尾并部分观测的失效原因,采用 Newton-Raphson 法计算了未知模型参数的最大似然估计值。推导了最大似然估计存在和唯一性的证明。使用最大似然估计的渐近正态性质,通过观测的 Fisher 信息矩阵构建了近似置信区间。采用马尔科夫链蒙特卡洛方法,使用 Gamma-Dirichlet 先验分布计算贝叶斯估计和最高后验密度可信区间。进行了马尔科夫链蒙特卡洛样本的收敛性测试。此外,进行了 Monte Carlo 模拟,以比较所提出的方法的有效性。进一步考虑了三种不同的最优性标准以获得最有效的截尾计划。最后,分析了一组真实数据,以说明所提出方法的操作性和适用性。