Problems with Fitting to the Power-Law Distribution

Details Problems with Fitting to the Power-Law Distribution Problems with Fitting to the Power-Law Distribution

2004-02-11

arxiv.org/abs/cond-mat/0402322v3

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure, 2 tables

Scientific paper

10.1140/epjb/e2004-00316-5

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data.

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