The POT model described by the generalized Pareto distribution with Poisson arrival rate

Abstract

The use of the peaks over threshold (POT) model described by the generalized Pareto distribution with Poisson arrival rate, which results in the generalized extreme value (GEV) distribution for the annual maximum (AM) series for flood frequency analysis, is discussed. Estimation of the generalized Pareto distribution by the method of probability weighted moments (PWM) is formulated for both known and unknown thresholds. The effect of raising the threshold of the POT series on high quantile estimation is investigated. A comparison of the efficiencies of the POT and AM models in high quantile estimation is made. It is shown that the threshold of the POT series can be raised to a reasonably high level without affecting the efficiency of high quantile estimation. This property is useful in practice. When one cannot be certain that both small and large values in a sample are well described by a single simple distribution or that peaks are independent of each other, a relatively high threshold can be introduced to overcome these difficulties without reduction in efficiency. It is also shown that the POT and AM models are of similar efficiency even when a relatively high threshold is used for the POT series. It is suggested that there is no theoretical reason to use the AM model in preference to the POT model.