Generalized Fiducial Inference for the GEV Distribution

This paper considers parameter estimation and quantile estimation for the generalized extreme value distribution. When the shape parameter is less than -0.5, the frequentist method does not have the standard asymptotic properties and the confidence intervals are invalid. Meanwhile, the Bayesian method relies on the prior, so a robust and efficient method is needed. In this paper, generalized fiducial inference is used to construct the fiducial distributions of the parameters of interest. Then the generalized fiducial estimates and confidence intervals of the parameters are derived. The proposed method is compared with the frequentist method and the Bayesian approach. The simulation results show that the proposed generalize fiducial method is more suitable for parameter estimation and quantile estimation, especially when the shape parameter is less than -0.5. Finally, the proposed method is applied to a real example to illustrate the estimation procedure.