Abstract.
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-Smirnov 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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Received: 18 June 2004, Published online: 12 October 2004
PACS:
02.50.Ng Distribution theory and Monte Carlo studies - 05.10.Ln Monte Carlo methods - 89.75.-k Complex systems
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Goldstein, M.L., Morris, S.A. & Yen, G.G. Problems with fitting to the power-law distribution. Eur. Phys. J. B 41, 255–258 (2004). https://doi.org/10.1140/epjb/e2004-00316-5
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DOI: https://doi.org/10.1140/epjb/e2004-00316-5