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Author Clauset, Aaron ♦ Shalizi, Cosma Rohilla ♦ Newman, M. E. J.
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Empirical Detection ♦ Accurate Parameter Estimate ♦ Empirical Data ♦ Different Discipline ♦ Scientific Interest ♦ Power-law Data ♦ Data Set ♦ Reasonable Fit ♦ Man-made Phenomenon ♦ Large Fluctuation ♦ Standard Method ♦ Quantitative Measure ♦ Many Situation ♦ Real-world Data Set ♦ Power-law Distribution ♦ Statistical Technique ♦ Maximum Likelihood Method ♦ Power Law ♦ Significant Consequence
Description 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.
ISSN 00361445
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2009-01-01