Eur. Phys. J. B 41, 255-258 (2004)
https://doi.org/10.1140/epjb/e2004-00316-5

Problems with fitting to the power-law distribution

School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK 74078, USA

Corresponding author: ^a gyen@okstate.edu

Received: 2 March 2004
Revised: 18 June 2004
Published online: 12 October 2004

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.