Abstract
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.
Highlights
The Birnbaum–Saunders (BS) distribution [1] was originally introduced to model failure time due to the growth of a dominant crack that is subject to cyclic stress that causes a failure when it reaches a threshold level
Our simulation study indicates that the biased reduced maximum likelihood estimation (MLE) and moment estimators (MMEs) estimates are robust against higher censoring percentages and lower sample sizes
The amount of censoring and sample size has a direct impact on the performance of the MLE and MME methods and one may cautiously apply them for smaller to moderate sample size problems
Summary
The Birnbaum–Saunders (BS) distribution [1] was originally introduced to model failure time due to the growth of a dominant crack that is subject to cyclic stress that causes a failure when it reaches a threshold level. Reference [9] introduced modified MLEs that are bias-free to second-order and considered bootstrap bias correction They derived a Bartlett correction that improves the finite-sample performance of the likelihood ratio test in finite samples. Reference [13] suggested a Bayesian estimation method for Type-II censored BS data in the simple step stress accelerated life test with power law accelerated form. They applied a Gibbs sampling procedure to get the Bayesian estimates for shape parameter of BS distribution and parameters of power law–accelerated model.
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