Fiducial Inference on the Right Censored Birnbaum–Saunders Data via Gibbs Sampler

In this article, we implement a flexible Gibbs sampler to make inferences for two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. The Gibbs sampler is applied on the fiducial distributions of the BS parameters derived using the maximum likelihood, methods of moments, and their bias-reduced estimates. A Monte-Carlo study is conducted to make comparisons between these estimates for Type-II right censoring with various parameter settings, sample sizes, and censoring percentages. It is concluded that the bias-reduced estimates outperform the rest with increasing precision. Higher sample sizes improve the overall accuracy of all the estimates while the amount of censoring shows a negative effect. Further comparisons are made with existing methods using two real-world examples.