Estimating Extreme Quantiles of Unknown Distributions Using the Peak over Thresholds Method

Abstract

The purpose of this paper is to present an analytically easy to use procedure for estimating of extreme quantiles of continuous random variables using the Peak Over Threshold approach, and a statistically sound approach to the problem of threshold selection that needs to be resolved in this context. A web link included in the text points to a ready-to-use implementation of the proposed method in the popular programming language Python.

Keywords

extreme value theory / peak over threshold approach / L-moments

Author Contributions

M.K., S.S.: conceptualization, methodology, software; M.K.: data curation, writing—original draft preparation; M.K.: visualization, investigation; S.S.: supervision; S.S., M.K.: software, validation; S.S.: writing—reviewing and editing. All authors have read and agreed to the published version of the manuscript.

Funding

The project underlying this publication was funded by the German Federal Ministry of Economic Affairs and Climate Action under project funding reference number 01MK21002G.

Informed Consent Statement

Not applicable.

Data Availability Statement

A csv file with the data in use, together with a commented version of the code for implementing the proposed procedure, prepared in the language Python, has been provided on the web at https://drive.google.com/drive/folders/1jfl1w00r0-5pGnJFlyB8MzVkEfUcXwxA?usp=sharing (under the file names: S&P500History.csv and peakOverThreshold.ipnb, respectively).

Conflicts of Interest

The authors declare no conflict of interest.

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