A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution. (English) Zbl 1077.62040

Park, Jeong-Soo

Math. Comput. Simul. 70, No. 4, 227-234 (2005).

Summary: A systematic way of selecting hyperparameters of the prior on the shape parameter of the generalized extreme value distribution (GEVD) is presented. The optimal selection is based on a Monte Carlo simulation in the generalized maximum likelihood estimation (GMLE) framework. A scaled total misfit measure for the accurate estimation of upper quantiles is used for the selection criterion. The performance evaluations for GEVD and non-GEVD show that the GMLE with selected hyperparameters produces more accurate quantile estimates than the MLE, the L-moments estimator, and E. S. Martins and J. R. Stedinger’s GMLE [Water Resource Res. 36, 737–744 (2000)].

MSC:

62G32	Statistics of extreme values; tail inference
65C05	Monte Carlo methods
86A05	Hydrology, hydrography, oceanography
62E15	Exact distribution theory in statistics
62P12	Applications of statistics to environmental and related topics

Keywords:

Beta distribution; Hydrology; Maximum likelihood estimation; L-moment estimation; Penalized likelihood; Shape parameter

Software:

AS 215; bootstrap; LMOMENTS

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