Bayesian inference for Birnbaum–Saunders distribution and its generalization

ABSTRACT

We present a Bayesian approach for parameter inference of the Birnbaum–Saunders distribution [Birnbaum ZW, Saunders SC. A new family of life distributions. J Appl Probab. 1969;6:319–327], as well as the generalized Birnbaum–Saunders distribution developed by Owen [A new three-parameter extension to the Birnbaum–Saunders distribution. IEEE Trans Reliab. 2006;55:475–479], in the presence of random right-censored data. To handle the instance of commonly occurred censored observations, we utilize the data augmentation technique [Tanner MA, Wong WH. The calculation of posterior distributions by data augmentation. J Amer Statist Assoc. 1987;82(398):528–540] 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.

KEYWORDS:

• Birnbaum–Saunders distribution
• generalization
• data augmentation
• Bayesian method
• MCMC sampling
• estimation

AMS SUBJECT CLASSIFICATION:

• 62F15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Sha's work was partially supported by NSF CMM-0654417 and NIH NIMHD-2G12MD007592.