Penalized maximum likelihood estimators for the nonstationary Pearson type 3 distribution

Abstract The climate change and human activities can principally doubt the frequency analysis methods which assume that the hydrological events are stationary. The Pearson type 3 (P3) distribution, which has been widely applied in frequency analysis under the stationary condition, was developed for the nonstationary cases. The distribution parameters can be expressed as exponential or polynomial functions with time or other covariates. Parameter estimation for the nonstationary P3 model was done with the penalized maximum likelihood estimation (PMLE) method in which we applied a restrictive penalty on the location parameter to avoid unreasonable results. The results of the nonstationary P3 model were compared to that of the generalized extreme value (GEV) distribution, in which the generalized maximum likelihood estimation (GMLE) method was applied to estimate the parameters. The Monte Carlo simulations indicated that the nonstationary P3 model provided better results than the nonstationary GEV model for different sample sizes. Both models were also applied in hydrological series with various trends and record lengths to prove the feasibility of the nonstationary P3 model in practical applications. The applications showed that the nonstationary P3 model performed better than the nonstationary GEV model in most of the studied cases.