Power-Law Distributions in Empirical Data

Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-Law Distributions in Empirical Data. SIAM Review, 51(4), 661-703.

Type

Journal article

Intellectual base

Primary research

Year

2009

DOI

10.1137/070710111

Link

https://doi.org/10.1137/070710111

Cited from

mathematics, physics

Cited by

3 citations across 3 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Fractal Geometry
  • Are the apparent power laws in the data robust to rigorous statistical testing

    This sourceMaximum-likelihood-plus-KS-plus-likelihood-ratio framework for rigorously identifying power-law distributions; showed many previously-claimed power laws fail proper goodness-of-fit testing (bibliography + inline; supports the T3 power-law-over-fitting failure mode and the Abstract Reasoning / Notes cautions).

• Scale Invariance
  • - T1 — Claimed Power Laws Are Often Not Power Laws: Visual inspection of log-log plots can deceive; formal statistical testing

    This sourceComprehensive guide to statistical methods for identifying and testing power-law hypotheses; establishes rigorous standards for power-law claims.

Mechanisms

• Log-Log Scaling Plot
  • Its notorious failure is the spurious power law

    This sourceShows that non-power-law distributions can look roughly straight on log-log axes, so a visual proclamation of a power law must be subjected to formal goodness-of-fit testing that can reject it.

Verification

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