Generalized fifth-order KdV equation; Cnoidal wave solutions; Solitary wave solutions

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 Martins–Stedinger’s GMLE.