Fitting to the Power-Law Distribution

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  • 11 February 2004
Abstract
This paper reviews and compares methods of fitting power-law distributions and methods to test goodness-of-fit of power-law models. It is shown that the maximum likelihood estimation (MLE) and Bayesian methods are far more reliable for estimation than using graphical fitting on log-log transformed data, which is the most commonly used fitting technique. The Kolmogorov-Smirnoff (KS) goodness-of-fit test is explained and a table of KS values designed for the power-law distribution is given. 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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