Fiducial inference for Birnbaum-Saunders distribution. (English) Zbl 1510.62415
Summary: 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 J. Hannig [Stat. Sin. 23, No. 2, 489–514 (2013; Zbl 1379.62002)], 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.
MSC:
| 62N05 | Reliability and life testing |
| 62F25 | Parametric tolerance and confidence regions |
| 62F10 | Point estimation |
| 62F15 | Bayesian inference |
Citations:
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