Characterization of the tail of river flow data by generalized Pareto distribution

Extreme value theory (EVT) is a branch of statistics that seeks to access, from a given ordered sample, the probabilities of events that are more extreme than usually observed. Under very general conditions, EVT’s main results characterize the distribution of the samples maxima or the distribution of values above a given threshold. Thus, two particular approaches exist, block maxima, which divides a time period into equal sections and the maximum of each section is selected. This usually leads to generalized extreme value (GEV) distribution. The second approach is peaks over threshold (POT) which selects every value that exceeds a certain threshold. Threshold excesses follow an approximate distribution within the generalized Pareto family. This study focuses on modeling the tail of a heavy tail distribution by using the threshold approach. The purpose of this study is manifold: firstly, to compare the estimates of the generalized Pareto distribution (GPD) parameters by three estimation techniques, namely, maximum likelihood estimation (MLE), method of moments (MOM), and probability weighted moments (PWM) in the light of a hydrological application; secondly, to select an appropriate model for the Mississippi River flow data by using the model validation and hypothesis testing; thirdly, to introduce the bootstrap re-sampling approach in hydrological applications; lastly, to obtain a required design value with a given return period of exceedance and probabilities of occurring extreme floods using bootstrap sampling.