The beyondpareto command for optimal extreme-value index estimation
The beyondpareto command for optimal extreme-value index estimation
In this article, we introduce the command beyondpareto, which estimates the extreme-value index for distributions that are Pareto-like, that is, 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. An essential diagnostic tool for evaluating the fit of the estimated extrerme-value index is the Pareto quantile–quantile 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 German wealth and city-size distributions.
Pareto, Zipf’s law, beyondpareto, bias, extreme-value index, heavy tails, pqqplot, rank-size regression, st0770
169-188
König, Johannes
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Schluter, Christian
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Schröder, Carsten
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Retter, Isabella
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Beckmannshagen, Mattis
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König, Johannes
ccd256ac-c174-4f00-ad7b-94d954d27342
Schluter, Christian
ae043254-4cc4-48aa-abad-56a36554de2b
Schröder, Carsten
6c7c08bb-6763-47fd-88bc-29551d469c1c
Retter, Isabella
4a990621-4f93-45a2-a524-7d8f5a1b249f
Beckmannshagen, Mattis
d0868955-a686-47f9-aecc-bd788d3163bd
König, Johannes, Schluter, Christian, Schröder, Carsten, Retter, Isabella and Beckmannshagen, Mattis
(2025)
The beyondpareto command for optimal extreme-value index estimation.
The Stata Journal, 25 (1), .
(doi:10.1177/1536867X251322969).
Abstract
In this article, we introduce the command beyondpareto, which estimates the extreme-value index for distributions that are Pareto-like, that is, 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. An essential diagnostic tool for evaluating the fit of the estimated extrerme-value index is the Pareto quantile–quantile 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 German wealth and city-size distributions.
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konig-et-al-2025-the-beyondpareto-command-for-optimal-extreme-value-index-estimation
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Accepted/In Press date: 7 July 2024
e-pub ahead of print date: 24 March 2025
Keywords:
Pareto, Zipf’s law, beyondpareto, bias, extreme-value index, heavy tails, pqqplot, rank-size regression, st0770
Identifiers
Local EPrints ID: 503528
URI: http://eprints.soton.ac.uk/id/eprint/503528
ISSN: 1536-867X
PURE UUID: bbaf4957-92ba-4962-9d87-8e010a2bf708
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Date deposited: 04 Aug 2025 16:54
Last modified: 21 Aug 2025 05:16
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Contributors
Author:
Johannes König
Author:
Carsten Schröder
Author:
Isabella Retter
Author:
Mattis Beckmannshagen
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