Fast Bayesian Inference for Birnbaum-Saunders Distribution

Mahdi Teimouri ()
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Mahdi Teimouri: Gonbad Kavous University

Computational Statistics, 2023, vol. 38, issue 2, No 2, 569-601

Abstract: Abstract In this work, we propose the Bayesian estimator for parameters of the Birnbaum-Saunders distribution based on conjugate, Jeffreys, and reference priors that can be implemented quite fast through Gibbs sampler. The Bayesian estimator based on conjugate prior for the Birnbaum-Saunders is new. Performance of the proposed Bayesian paradigm, based on three priors, is demonstrated by simulation and analyzing two sets of real data. Furthermore, it is shown through an extra real example that the Bayesian estimator can outperform the maximum likelihood estimator for the BS distribution when data are incomplete due to the progressive type-II censoring scheme. An R package called bibs has been uploaded to comprehensive R archive network (CRAN) at https://cran.r-project.org/web/packages/bibs/index.html for computing the Bayesian estimator, corresponding standard errors, and credible intervals.

Keywords: Generalized inverse Gaussian distribution; Markov chain Monte Carlo method; Mixture model; Progressive type-II censoring scheme; survival analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00180-022-01234-3

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