Parameter and quantile estimation for the generalized Pareto distribution in peaks over threshold framework

Suyeon Kang, Jongwoo Song

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

In this article, we consider six estimation methods for extreme value modeling and compare their performances, focusing on the generalized Pareto distribution (GPD) in the peaks over threshold (POT) framework. Our goal is to identify the best method in various conditions via a thorough simulation study. In order to compare the estimators in the POT sense, we suggest proper strategies for some estimators originally not developed under the POT framework. The simulation results show that a nonlinear least squares (NLS) based estimator outperforms others in parameter estimation, but there is no clear winner in quantile estimation. For quantile estimation, NLS-based methods perform well even when the sample size is small and the Hill estimator comes to the front when the underlying distribution has a very heavy tail. Applications of EVT cover many different fields and researchers on each field may have their own experimental conditions or practical restrictions. We believe that our results would provide guidance on determining proper estimation method on future analysis.

Original languageEnglish
Pages (from-to)487-501
Number of pages15
JournalJournal of the Korean Statistical Society
Volume46
Issue number4
DOIs
StatePublished - Dec 2017

Keywords

  • Generalized Pareto distribution
  • Hill estimator
  • Maximum likelihood estimator
  • Nonlinear least squares
  • Peaks over threshold

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