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 twenty-four 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.
Comment: 26 pages, 9 figures, 7 tables; code available at
http://www.santafe.edu/~aaronc/powerlaws/
Description
[0706.1062] Power-law distributions in empirical data
%0 Generic
%1 Clauset2007
%A Clauset, Aaron
%A Shalizi, Cosma Rohilla
%A Newman, M. E. J.
%D 2007
%K imported
%T Power-law distributions in empirical data
%U http://arxiv.org/abs/0706.1062
%X 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 twenty-four 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.
Comment: 26 pages, 9 figures, 7 tables; code available at
http://www.santafe.edu/~aaronc/powerlaws/
@misc{Clauset2007,
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 twenty-four 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.
Comment: 26 pages, 9 figures, 7 tables; code available at
http://www.santafe.edu/~aaronc/powerlaws/},
added-at = {2008-10-28T02:55:07.000+0100},
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
biburl = {https://www.bibsonomy.org/bibtex/27da1624e601898dd74df839ce2daeb24/sidney},
description = {[0706.1062] Power-law distributions in empirical data},
interhash = {2e3bc5bbd7449589e8bfb580e8936d4b},
intrahash = {7da1624e601898dd74df839ce2daeb24},
keywords = {imported},
timestamp = {2008-10-28T02:55:07.000+0100},
title = {Power-law distributions in empirical data},
url = {http://arxiv.org/abs/0706.1062},
year = 2007
}