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Power-law distributions in empirical data (2009)
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| Venue: | ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111 |
| Citations: | 581 - 7 self |
BibTeX
@INPROCEEDINGS{Clauset09power-lawdistributions,
author = {Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman},
title = {Power-law distributions in empirical data},
booktitle = {ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111},
year = {2009}
}
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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 empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the tail of the distribution. In particular, standard methods such as least-squares fitting are known to produce systematically biased estimates of parameters for power-law distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law distribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We demonstrate these methods by applying them to twentyfour real-world data sets from a range of different disciplines. Each of the data sets has been conjectured previously 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.
Keyphrases
power-law distribution empirical data power law data set large fluctuation statistical technique real-world data set different discipline significant consequence accurate parameter estimate standard method reasonable fit scientific interest empirical detection quantitative measure power-law data many situation maximum likelihood method man-made phenomenon
