Semi-parametric and Parametric Inference of Extreme Value Models for Rainfall Data

Extreme rainfall events and the clustering of extreme values provide fundamental information which can be used for the risk assessment of extreme floods. Event probability can be estimated using the extreme value index (gamma) which describes the behavior of the upper tail and measures the degree of extreme value clustering. In this paper, various semi-parametric and parametric extreme value index estimators are implemented in order to characterize the tail behavior of long-term daily rainfall time series. The results obtained from different estimators are then used to extrapolate the distribution function of extreme values. Extrapolation can be employed to estimate the occurrence probability of rainfall events above a given threshold. The results indicated that different estimators may result in considerable differences in extreme value index estimates. The uncertainty of the extreme value estimators is also investigated using the bootstrap technique. The analyses showed that the parametric methods are superior to the semi-parametric approaches. In particular, the likelihood and Two-Step estimators are preferred as they are found to be more robust and consistent for practical application.