A simple test for power-law behavior

• Autores: Carlos M. Urzúa
• Localización: The Stata journal, ISSN 1536-867X, Vol. 20, Nº. 3, 2020, págs. 604-612
• Idioma: inglés
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• Resumen

  • In this article, I propose a new test for power-law behavior. Thestatistical 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.