A simple test for power-law behavior

Carlos Urzúa

Stata Journal, 2020, vol. 20, issue 3, 604-612

Abstract: In this article, I propose a new test for power-law behavior. The statistical test, pwlaw, is locally optimal if the possible alternative distributions are contained in the Pareto type (IV) family. After deriving the test, I examine four classical datasets: the frequency of unique words in an English text (Moby Dick); the human populations of U.S. cities; the frequency of U.S. family names; and the peak gamma-ray intensity of solar flares. I show that in the first case there is no indication of any power-law behavior and that in the second and fourth cases there is evidence in that regard.

Keywords: pwlaw; power-law distribution; Pareto law; Zipf’s law; Pareto (IV) distribution (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:tsj:stataj:v:20:y:2020:i:3:p:604-612

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DOI: 10.1177/1536867X20953571

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