Threshold Selection Using Graphical Methods
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Generalized Pareto Distribution (GPD), Goodness-of-Fit Test, Methods of Threshold Selection, Mean Residual Plot (MRLP), Threshold Choice Plot (TCP).
Abstract
One of the major challenges in Peak over Threshold model (POT) the selection of the best threshold in fitting the Generalized Pareto Distribution (GPD) which is widely used in many applications. The choice of threshold must be a balance between bias and variation. In this paper we comparison between two graphical methods to determine the best threshold in the POT model and estimate the tail index. The results obtained from different estimators used to estimate the shape distribution of GPD by using maximum likelihood (ML). Finally, in this paper we use application on real data to compare the properties of different estimators for estimating tail index. The results show that GPD model with threshold of threshold choice plot (TCP) is a better choice basis on the Deviance and Akaike information test. For the calculations, we will use the R programming with packages POT and ismev for parameter estimation and diagnostic plots.
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