Fit a power law to empirical data in Python
power-law, python
Solution
As @DSM pointed out, the powerlaw module deals with fitting an exponent to values drawn/generated from a power law distribution, rather than fitting a regression. To help people who might have similar confusions, below is how one should verify the exponent fitting:
## use a proper power law random number generator (or code your own)
from networkx.utils import powerlaw_sequence
pl_sequence = powerlaw_sequence(1000,exponent=2.5)
fitted_pl = powerlaw.Fit(pl_sequence)
fitted_pl.alpha
Out[73]: 2.4709012785346314 ##close enough
Problem
I'm experimenting with fitting a power law to empirical data using the powerlaw module. I have created the following data that follows a power law distribution of exponent 2: ``` x = range(1,1000) y = [] for i in x: y.append(i**(-2)) ``` I'm expecting the fitted power law to have an exponent of 2. However the resulting exponent deviates from the theoretical value a lot: ``` fitted_pl = powerlaw.Fit(y) fitted_pl.alpha Out[115]: 1.4017584065981563 ``` Could you please advise why this happens, or point out what I've done wrong here? Thank you for your kind answer!