Graphical Diagnostics for Threshold Selection in Fitting the Generalized Pareto Distribution

Abstract

When fitting the Generalized Pareto distribution (GPD), selecting an appropriate threshold value is important for achieving an effective fit. The main objective of this study is to give five graphical diagnostics for selecting GPD thresholds. The other objective of this study is to examine different graphical methods based on the goodness-of-fit test. Maximum likelihood method was used to estimate the shape of parameter. Finally, use flood data to compare five graphical diagnostics of threshold selection for shape parameter estimate. The results show that, the four graphical diagnostics (threshold choice plot, mean excesses plot, dispersion index plot and quantail quantail plot) yield the same threshold range, with the exception of the Hill plot. On the other hand, threshold choice plot is simple to identify the range of thresholds that should be stable to fit. When compared to other graphical diagnostic, the GP distribution becomes valid because they demand too much subjectivity and make it difficult to define a range threshold from the plots. In other words, graphical diagnostics of the higher are an acceptable option for fitting the GPD model based on the goodness-of-fit test. All statically analyses for the study are performed using R- statistical program.