Abstract
Fitting Tails by the Empirical Residual Coefficient of Variation: The ercv Package
Highlights
Introduction and overviewExtreme value theory (EVT) is one of the most important statistical techniques for the applied sciences
This paper shows that the R package ercv, based on the coefficient of variation (CV), is a complement, and often an alternative, to the available software on EVT
The mathematical background is shown in Section Mathematical Background, including threshold models and the relationship between power law distribution and the generalized Pareto distributions (GPD), which is the relationship between the two different approaches followed by the aforementioned R packages evir, or ismev, and poweRlaw
Summary
Extreme value theory (EVT) is one of the most important statistical techniques for the applied sciences. The mathematical background is shown in Section Mathematical Background, including threshold models and the relationship between power law distribution and the generalized Pareto distributions (GPD), which is the relationship between the two different approaches followed by the aforementioned R packages evir, or ismev, and poweRlaw. Section Transformation from heavy to light tails (tdata) shows how the methodology developed in the previous sections can be extended with the tdata function to all GPD distributions, even with no finite moments. This technique is applied to the MobyDick example and to the Danish fire insurance dataset, a highly heavy-tailed, infinite-variance model. Section Fitting PoT parameters and tail plots (fitpot ccdfplot) describes the functions of the R package ercv that allow estimation of the parameters (fitpot) and drawing of the adjustments (ccdfplot) for the peak-over-threshold method
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