A simple test for power-law behavior

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.