Title:      Power-law distributions in empirical data

Authors:    Aaron Clauset, Cosma Shalizi, Mark Newman

Entrydate:  2007-06-11 14:58:13

Keywords:   Power-law distributions, Pareto, Zipf, maximum
likelihood, heavy-tailed distributions, likelihood ratio test, model
selection

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.

http://polmeth.wustl.edu/retrieve.php?id=695