Mondal Shuvashree, Kundu Debasis
Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India.
J Appl Stat. 2019 Sep 24;47(6):1084-1108. doi: 10.1080/02664763.2019.1669542. eCollection 2020.
In reliability and survival analysis the inverse Weibull distribution has been used quite extensively as a heavy tailed distribution with a non-monotone hazard function. Recently a bivariate inverse Weibull (BIW) distribution has been introduced in the literature, where the marginals have inverse Weibull distributions and it has a singular component. Due to this reason this model cannot be used when there are no ties in the data. In this paper we have introduced an absolutely continuous bivariate inverse Weibull (ACBIW) distribution omitting the singular component from the BIW distribution. A natural application of this model can be seen in the analysis of dependent complementary risks data. We discuss different properties of this model and also address the inferential issues both from the classical and Bayesian approaches. In the classical approach, the maximum likelihood estimators cannot be obtained explicitly and we propose to use the expectation maximization algorithm based on the missing value principle. In the Bayesian analysis, we use a very flexible prior on the unknown model parameters and obtain the Bayes estimates and the associated credible intervals using importance sampling technique. Simulation experiments are performed to see the effectiveness of the proposed methods and two data sets have been analyzed to see how the proposed methods and the model work in practice.
在可靠性和生存分析中，逆威布尔分布作为一种具有非单调危险函数的重尾分布被广泛使用。最近，文献中引入了一种二元逆威布尔（BIW）分布，其边缘分布具有逆威布尔分布且有一个奇异分量。由于这个原因，当数据中没有平局时，该模型不能使用。在本文中，我们引入了一种绝对连续的二元逆威布尔（ACBIW）分布，它从BIW分布中省略了奇异分量。该模型在相依互补风险数据的分析中有着自然的应用。我们讨论了这个模型的不同性质，并从经典方法和贝叶斯方法两个方面解决了推断问题。在经典方法中，无法明确获得最大似然估计量，我们建议基于缺失值原理使用期望最大化算法。在贝叶斯分析中，我们对未知模型参数使用了非常灵活的先验，并使用重要性抽样技术获得贝叶斯估计和相关的可信区间。进行了模拟实验以检验所提方法的有效性，并分析了两个数据集以了解所提方法和模型在实际中的工作情况。
