REVIEW 6 cited by
Power-law distributions in empirical data
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Power-law distributions in empirical data
read the original 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 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.
Forward citations
Cited by 6 Pith papers
-
Virial-based extraction of structures in numerical simulations: The vibes tool
Vibes is a new algorithm that extracts physically motivated core structures from numerical star formation simulations by applying the virial theorem iteratively around density peaks to determine boundaries from energy...
-
Formalization of the generalized Pareto principle and structural typicality of the 20/80-rule
A formalization of the generalized Pareto principle derives that exponential and normal distributions with 100 to 100,000 samples produce p values near 0.2, close to the 80/20 rule and below prior saturation conjectures.
-
Virial-based extraction of structures in numerical simulations: The vibes tool
Vibes extracts cores in simulations using the virial theorem to define boundaries, yielding more stable and physically motivated structures than density-threshold methods like hop and dendrogram.
-
Automatic Construction of a Legal Citation Graph from 100 Million Ukrainian Court Decisions: Large-Scale Extraction, Topological Analysis, and Ontology-Driven Clustering
A citation graph built from the complete Ukrainian court registry recovers legal domain boundaries via community detection and predicts legislative importance with AUC 0.9984.
-
Global and Local Infall in the ASHES Sample (GLASHES). II. Asymmetric Line Profiles around Dense Cores in 70 $\mu$m Dark Massive Clumps
Blue-asymmetric spectral lines appear in 50-60% of dense cores within massive dark clumps, showing that gravitational collapse operates at core scales from prestellar stages onward and supports hierarchical star formation.
-
MoltGraph: A Longitudinal Temporal Graph Dataset of Moltbook for Coordinated-Agent Detection
MoltGraph is a new longitudinal graph dataset from Moltbook that characterizes heavy-tailed connectivity, short bursty coordination episodes, and substantially higher exposure for coordinated posts.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.