A comparison of parametric and nonparametric estimators for probability precipitation in Korea

The frequency analyses for the precipitation data in Korea were performed. We used daily maximum series, monthly maximum series, and annual series. In order to select an appropriate distribution, 17 probability density functions were considered for the parametric frequency analyses. They are Gamma II, Gamma III, GEV (Generalized Extreme Value), Gumbel (Extreme Value type I), Log-Gumbel, Log-normal II, Log-normal III, Log-Pearson type III, Weibull II,Weibull III, Exponential, Normal, Pearson type III, Generalized logistic, Generalized Pareto, Kappa and Wakeby distributions. For nonparametric frequency analyses, variable kernel and log-variable kernel estimators were used. Nonparametric methods do not require assumptions about the underlying populations from which the data are obtained. Therefore, they are better suited for multimodal distributions with the advantage of not requiring a distributional assumption. The variable kernel estimates are comparable and are in the middle of the range of the parametric estimates. The variable kernel estimates show a very small probability in extrapolation beyond the largest observed data in the sample. However, the log-variable kernel estimates remedied these defects with the log-transformed data.