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Abstract
In this paper, we consider fiducial inference for the unknown parameters of the Birnbaum-Saunders distribution. Two generalized fiducial distributions of the parameters are obtained. One is based on the inverse of the structural equation, and the fiducial estimates of the parameters are obtained by a simulation method. The other is based on the method of [Hannig J. Generalized fiducial inference via discretization. Stat. Sinica. 2013;23:489–514], then we use adaptive rejection Metropolis sampling to get the fiducial estimates. We compare the fiducial estimates with the maximum likelihood estimates and Bayesian estimates by simulations. Two real data sets are analysed for illustration.
Acknowledgments
The authors thank the two referees for their helpful comments and suggestions which have led to an improvement of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
The research is supported by Natural Science Foundation of China [11201345], Natural Science Foundation of Zhejiang province [LY15G010006], and China Postdoctoral Science Foundation [2015M572598].