Problems with Fitting to the Power-Law Distribution

TL;DR

This paper demonstrates that graphical methods for fitting power-law distributions are biased, advocates for maximum likelihood estimation, and introduces a new Kolmogorov-Smirnov test table to improve model assessment.

Contribution

It highlights the bias in graphical fitting methods, promotes MLE for power-law estimation, and provides a new goodness-of-fit testing table for empirical data analysis.

Findings

Graphical methods are biased and inaccurate for power-law fitting.

Maximum likelihood estimation provides a more robust fit.

A new Kolmogorov-Smirnov test table improves goodness-of-fit assessment.

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-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.