plfit
plfit: Fitting power-law distributions to empirical data. This program fits power-law distributions to empirical (discrete or continuous) data, according to the method of Clauset, Shalizi and Newman. 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 distributions – the part of the distributions 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. 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.
Keywords for this software
References in zbMATH (referenced in 239 articles , 1 standard article )
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- Comin, Cesar H.; Viana, Matheus P.; Costa, Luciano da F.: The relationship between structure and function in locally observed complex networks (2013)
- Cui, Qiurong; Rohe, Karl; Zhang, Zhengjun: Discussion of “Estimating the historical and future probabilities of large terrorist events” by Aaron Clauset and Ryan Woodard (2013)
- Fulger, Daniel; Scalas, Enrico; Germano, Guido: Random numbers from the tails of probability distributions using the transformation method (2013)
- Gill, Jeff: Discussion of “Estimating the historical and future probabilities of large terrorist events” by Aaron Clauset and Ryan Woodard (2013)
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- Ihlen, Espen A. F.: The influence of power law distributions on long-range trial dependency of response times (2013)
- Jeff Alstott, Ed Bullmore, Dietmar Plenz: Powerlaw: a Python package for analysis of heavy-tailed distributions (2013) arXiv
- Kuronen, Mikko; Leskelä, Lasse: Hard-core thinnings of germ-grain models with power-law grain sizes (2013)
- Lucas, Andrew: Binary decision making with very heterogeneous influence (2013)