Goldstein, et al. "Problems with fitting to the power-law distribution"

[Steven A. Morris]

Folks on this list may be interested in the paper below that
disccusses estimating power-law exponents. The topic is
not new to the bibliometrics field, having been discussed by Pao,
Nicholls, and Rousseau. However, the paper below contains a new KS
table that is specific to evaluating MLE fits on the zeta distribution.

Thanks,

S. Morris




preprint available at:
http://samorris.ceat.okstate.edu/web/publications/power-law.pdf

PROBLEMS WITH FITTING TO THE POWER-LAW DISTRIBUTION
M. L. Goldstein, S. A. Morris and G. G. Yen
The European Physical Journal B - Condensed Matter
Issue: Volume 41, Number 2
Date:  September 2004
Pages: 255 - 258

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.

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