Bayesian inference for Birnbaum-Saunders distribution and its generalization. (English) Zbl 07192070
Summary: We present a Bayesian approach for parameter inference of the Birnbaum-Saunders distribution [Z. W. Birnbaum and S. C. Saunders, J. Appl. Probab. 6, 319–327 (1969; Zbl 0209.49801)], as well as the generalized Birnbaum-Saunders distribution developed by W. J. Owen [“A new three-parameter extension to the Birnbaum-Saunders distribution”, IEEE Trans. Reliab. 55, No. 3, 475–479 (2006; doi:10.1109/TR.2006.879646)], in the presence of random right-censored data. To handle the instance of commonly occurred censored observations, we utilize the data augmentation technique [M. A. Tanner and W. H. Wong, J. Am. Stat. Assoc. 82, 528–541 (1987; Zbl 0619.62029)] to circumvent the arduous expressions involving the censored data in posterior inferences. Simulation studies are carried out to assess performance of these methods under different parameter values, with small and large sample sizes, as well as various degrees of censoring. Two real data are analysed for illustrative purpose.
MSC:
| 62F15 | Bayesian inference |
Keywords:
Birnbaum-Saunders distribution; generalization; data augmentation; Bayesian method; MCMC sampling; estimationSoftware:
BayesDAReferences:
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