The beyondpareto command for optimal extreme value index estimation • ChristianSchluter

C. Schluter, C. Schröder, I. Retter, M. Beckmannshagen, J. König (2025). “The beyondpareto command for optimal extreme value index estimation.” The Stata Journal, forthcoming.

Abstract: This paper introduces the command beyondpareto, which estimates the extreme value index for distributions that are Pareto-like, i.e. whose upper tails are regularly varying and eventually become Pareto. The estimation is based on rank-size regressions, and the threshold value for the upper order statistics included in the final regression is determined optimally by minimizing the asymptotic mean- squared error (AMSE). An essential diagnostic tool for evaluating the fit of the estimated extreme value index is a Pareto quantile-quantile (QQ) plot, provided in the accompanying command pqqplot. The usefulness of our estimation approach is illustrated in several real-world examples focusing on the upper tail of the German wealth and city size distribution.

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@article{SchluterSJ24,
  title = {The beyondpareto command for optimal extreme value index estimation},
  author={Schluter, Christian and Schr{\"o}der, Carsten, and Retter, Isabella, and Beckmannshagen, Mattis, and K{\"o}nig, Johannes},
  journal = {The Stata Journal},
  volume = {25},
  number = {1},
  pages = {169-188},
  year = {2025},
  doi = {10.1177/1536867X251322969},
  URL = {https://doi.org/10.1177/1536867X251322969}
}