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.

@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 = {10.1137/070710111}, keywords = {data, distribution, distributions, empirical, law, power, powerlaw}, abstract = {Power-law distributions occur in many situations of scientific interest andhave significant consequences for our understanding of natural and man-madephenomena. Unfortunately, the detection and characterization of power laws iscomplicated by the large fluctuations that occur in the tail of thedistribution -- the part of the distribution representing large but rare events-- and by the difficulty of identifying the range over which power-law behaviorholds. Commonly used methods for analyzing power-law data, such asleast-squares fitting, can produce substantially inaccurate estimates ofparameters for power-law distributions, and even in cases where such methodsreturn accurate answers they are still unsatisfactory because they give noindication of whether the data obey a power law at all. Here we present aprincipled statistical framework for discerning and quantifying power-lawbehavior in empirical data. Our approach combines maximum-likelihood fittingmethods with goodness-of-fit tests based on the Kolmogorov-Smirnov statisticand likelihood ratios. We evaluate the effectiveness of the approach with testson synthetic data and give critical comparisons to previous approaches. We alsoapply the proposed methods to twenty-four real-world data sets from a range ofdifferent disciplines, each of which has been conjectured to follow a power-lawdistribution. In some cases we find these conjectures to be consistent with thedata while in others the power law is ruled out.} }

%0 = misc %A = Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J. %B = } %C = %D = 2007 %I = %T = Power-law distributions in empirical data} %U = http://arxiv.org/abs/0706.1062