powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions =======
powerlaw is a toolbox using the statistical methods developed in Clauset et al. 2007 and Klaus et al. 2011 to determine if a probability distribution fits a power law. Academics, please cite as:
Jeff Alstott, Ed Bullmore, Dietmar Plenz. (2014). powerlaw: a Python package for analysis of heavy-tailed distributions. PLoS ONE 9(1): e85777
Also available at arXiv:1305.0215 [physics.data-an]
For the simplest, typical use cases, this tells you everything you need to know.:
import powerlaw
data = array([1.7, 3.2 ...]) # data can be list or numpy array
results = powerlaw.Fit(data)
print results.power_law.alpha
print results.power_law.xmin
R, p = results.distribution_compare('power_law', 'lognormal')For more explanation, understanding, and figures, see the working paper, which illustrates all of powerlaw's features. For details of the math, see Clauset et al. 2007, which developed these methods.
Paper illustrating all of powerlaw's features, with figures
Code examples from manuscript, as an IPython Notebook Note: Some results involving lognormals will now be different from the manuscript, as the lognormal fitting has been improved to allow for greater numerical precision.
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This code was developed and tested for Python 2.x with the Enthought Python Distribution, and later amended to be compatible with 3.x. The full version of Enthought is available for free for academic use.
Further Development -----------------powerlaw is open for further development. If there's a feature you'd like to see in powerlaw, submit an issue. Pull requests and offers for expansion or inclusion in other projects are welcomed and encouraged. The original author of powerlaw, Jeff Alstott, is now only writing minor tweaks, so contributions are very helpful.
Many thanks to Andreas Klaus, Mika Rubinov and Shan Yu for helpful discussions. Thanks also to Andreas Klaus, Aaron Clauset, Cosma Shalizi, and Adam Ginsburg for making their code available. Their implementations were a critical starting point for making powerlaw.