Jayalath Kalanka P, Chhikara Raj S
Department of Mathematics and Statistics, University of Houston - Clear Lake, Houston, TX, USA.
J Appl Stat. 2020 Oct 3;49(3):656-675. doi: 10.1080/02664763.2020.1828314. eCollection 2022.
This paper describes a comprehensive survival analysis for the inverse Gaussian distribution employing Bayesian and Fiducial approaches. It focuses on making inferences on the inverse Gaussian (IG) parameters and and the average remaining time of censored units. A flexible Gibbs sampling approach applicable in the presence of censoring is discussed and illustrations with Type II, progressive Type II, and random rightly censored observations are included. The analyses are performed using both simulated IG data and empirical data examples. Further, the bootstrap comparisons are made between the Bayesian and Fiducial estimates. It is concluded that the shape parameter ( ) of the inverse Gaussian distribution has the most impact on the two analyses, Bayesian vs. Fiducial, and so does the size of censoring in data to a lesser extent. Overall, both these approaches are effective in estimating IG parameters and the average remaining lifetime. The suggested Gibbs sampler allowed a great deal of flexibility in implementation for all types of censoring considered.
本文描述了一种采用贝叶斯方法和 fiducial 方法对逆高斯分布进行的全面生存分析。它着重于对逆高斯（IG）参数以及删失单元的平均剩余时间进行推断。讨论了一种适用于存在删失情况的灵活吉布斯抽样方法，并包含了对 II 型、渐进 II 型和随机右删失观测值的示例说明。分析使用模拟的 IG 数据和实证数据示例进行。此外，还对贝叶斯估计和 fiducial 估计进行了自助法比较。得出的结论是，逆高斯分布的形状参数（ ）对贝叶斯分析与 fiducial 分析的影响最大，数据中的删失规模在较小程度上也有影响。总体而言，这两种方法在估计 IG 参数和平均剩余寿命方面都是有效的。所建议的吉布斯抽样器在考虑的所有类型删失的实现中都具有很大的灵活性。
