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March 2014 Power-law distributions in binned empirical data
Yogesh Virkar, Aaron Clauset
Ann. Appl. Stat. 8(1): 89-119 (March 2014). DOI: 10.1214/13-AOAS710

Abstract

Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has significant consequences for correctly understanding and modeling complex systems. However, statistical evidence for or against the power-law hypothesis is complicated by large fluctuations in the empirical distribution’s tail, and these are worsened when information is lost from binning the data. We adapt the statistically principled framework for testing the power-law hypothesis, developed by Clauset, Shalizi and Newman, to the case of binned data. This approach includes maximum-likelihood fitting, a hypothesis test based on the Kolmogorov–Smirnov goodness-of-fit statistic and likelihood ratio tests for comparing against alternative explanations. We evaluate the effectiveness of these methods on synthetic binned data with known structure, quantify the loss of statistical power due to binning, and apply the methods to twelve real-world binned data sets with heavy-tailed patterns.

Citation

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Yogesh Virkar. Aaron Clauset. "Power-law distributions in binned empirical data." Ann. Appl. Stat. 8 (1) 89 - 119, March 2014. https://doi.org/10.1214/13-AOAS710

Information

Published: March 2014
First available in Project Euclid: 8 April 2014

zbMATH: 06302229
MathSciNet: MR3191984
Digital Object Identifier: 10.1214/13-AOAS710

Keywords: binned data , heavy-tailed distributions , Model selection , Power-law distribution

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.8 • No. 1 • March 2014
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