| Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-law distributions in empirical data | 2007 | misc | DOI URL | |
| Abstract: Power-law distributions occur in many situations of scientific interest and ve significant consequences for our understanding of natural and man-made enomena. Unfortunately, the detection and characterization of power laws is mplicated by the large fluctuations that occur in the tail of the stribution -- the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power-law behavior lds. Commonly used methods for analyzing power-law data, such as ast-squares fitting, can produce substantially inaccurate estimates of rameters for power-law distributions, and even in cases where such methods turn accurate answers they are still unsatisfactory because they give no dication of whether the data obey a power law at all. Here we present a incipled statistical framework for discerning and quantifying power-law havior in empirical data. Our approach combines maximum-likelihood fitting thods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic d likelihood ratios. We evaluate the effectiveness of the approach with tests synthetic data and give critical comparisons to previous approaches. We also ply the proposed methods to twenty-four real-world data sets from a range of fferent disciplines, each of which has been conjectured to follow a power-law stribution. In some cases we find these conjectures to be consistent with the ta while in others the power law is ruled out. |
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BibTeX:
@misc{clauset2007powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-law distributions in empirical data},
year = {2007},
note = {cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/},
url = {http://arxiv.org/abs/0706.1062},
doi = {http://dx.doi.org/10.1137/070710111}
}
|
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