A full Bayesian approach to generalized maximum likelihood estimation of generalized extreme value distribution

This study develops a full Bayesian GEV distribution estimation method (BAYBETA), which contains a semi-Bayesian framework of generalized maximum likelihood estimator (GMLE), to make full use of several advantages of the Bayesian approach especially in uncertainty analysis. For the full Bayesian framework, the optimal hyperparameter of beta prior distribution on the shape parameter of the GEV distribution is found as (6.4990, 8.7927) through simulation-based analysis. In a performance comparison analysis, the performances of BAYBETA, which adopts beta(6.4990, 8.7927) as prior density on the shape parameter of the GEV distribution, are almost the same as or slightly better than GML, outperforming MOM, ML, and LM in terms of root mean square error (RMSE) and bias when the shape parameter is negative. Also, a case study of two hydrologic extreme value data shows that the traditional uncertainty analysis using asymptotic approximation of ML and GML has limitations in describing the uncertainty in high upper quantiles, while the proposed full Bayesian estimation method BAYBETA provides a consistent and complete description of the uncertainty.