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 μ and λ 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 ($\varphi =\lambda /\mu$) 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.

本文描述了采用贝叶斯和基准方法的逆高斯分布的综合生存分析。它侧重于对逆高斯 (IG) 参数μ和λ以及审查单位的平均剩余时间进行推断。讨论了适用于存在删失的灵活吉布斯抽样方法，并包括 II 型、渐进 II 型和随机正确删失观察的说明。使用模拟 IG 数据和经验数据示例进行分析。此外，在贝叶斯估计和基准估计之间进行了自助比较。得出形状参数（$\phi =\lambda /\mu$) 逆高斯分布对贝叶斯与基准这两种分析的影响最大，数据审查的规模也较小。总的来说，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。建议的 Gibbs 采样器在实施所有类型的审查时具有很大的灵活性。