Forthcoming

A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic

Accepted - January 2022

Authors

  • Marek Arendarczyk University of Wroclaw
  • Tomasz J. Kozubowski University of Nevada Reno
  • Anna K. Panorska University of Nevada Reno

Keywords:

coefficient of variation, extremes, generalized Pareto distribution, heavy tailed distribution, power law, Peak-over-threshold

Abstract

The generalized Pareto distributions (GPDs) play an important role in the statistics of extremes. We point various problems with the likelihood-based inference for the index parameter α of the GPDs, and develop alternative testing strategies, which do not require parameter estimation. Our test statistic is the Greenwood statistic, which probability distribution is stochastically increasing with respect to α within the GPDs. We compare the performance of our test to a test with maximum-to-sum ratio test statistic Rn. New results on the properties of the Rn are also presented, as well as recommendations for calculating the p-values and illustrative data examples.

Additional Files

Published

2022-01-11

How to Cite

Arendarczyk , M., J. Kozubowski , T., & K. Panorska , A. (2022). A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic: Accepted - January 2022. REVSTAT-Statistical Journal. Retrieved from https://revstat.ine.pt/index.php/REVSTAT/article/view/357

Issue

Section

Forthcoming Paper