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Cited by 8,019Complex Systems and Time Series AnalysisStatistical Mechanics and EntropyStatistical Distribution Estimation and Applications

Power-Law Distributions in Empirical Data

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Clauset, Aaron, Shalizi, Cosma Rohilla, Newman, M. E. J.·2009·SIAM Review
DOI 10.1137/070710111
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Abstract

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.

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  • According to the method suggested by Clauset et al. (2009), all the networks are not scale-free, but their tails are.

    “In our examination according to the standard least-square fitting method, only the natural IVG was a scale free, while according to the method suggested by Clauset et al. (2009) all the networks are not scale-free, but their tails are.”

    From A Network Approach to Link Visibility and Urban Activity Location (2018) · cites this paper as Clauset et al. (2009)

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Authors
Clauset, A., Shalizi, C. R., & Newman, M. E. J.
ORCID
Newman, M. E. J.
Venue
SIAM Review
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2009-11
Volume
51
Issue
4
Pages
661-703
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
DOI
10.1137/070710111
OpenAlex
W2000042664
Cited by
8,019
References
0
Citations by year
2026: 416 · 2025: 476 · 2024: 425 · 2023: 485 · 2022: 537 · 2021: 588 · 2020: 576 · 2019: 552 · 2018: 595 · 2017: 531 · 2016: 545 · 2015: 521 · 2014: 504 · 2013: 425 · 2012: 349
FWCI
615.37
Type
journal article
Language
en
Open access
Locations
  • SIAM Review (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords
power-law distribution, maximum likelihood fitting, goodness-of-fit tests, Kolmogorov-Smirnov statistic, likelihood ratios, parameter estimation, empirical data analysis

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