[R] Checking if the distribution follow a power law

[David Winsemius]

On Sep 8, 2010, at 10:34 AM, NatsumiYotsumoto wrote:

> Dear all.
>
>
> I'm using igraph package, and do a research about network analysis.
>
> With power.law.fit from igraph package, it seems that we can fit a  
> power law
> distribution to some data.
>
>
> But, I want to know how to judge whether the network distribution  
> follows a
> power law or not.

In order to determine whether something is from distribution A or "not- 
A", one needs to have a sensible way of characterizing or considering  
what would be in the range of distributions in the "not-A".  
Unfortunately for your question, the range of possible distributions  
is infinite. That means it would always be possible to have a "better  
fitting distribution than what ever is distribution A.  If you have  
alternatives to the power-law that you want to "put to the test", then  
now is the time to offer them.

My guess is that you do not, so I will offer alternatives:

Alt A:
a) read the citations in the email you cited, especially Newman then ...
b) set up a histogram of your data using hist with logarithmic or  
geometric progression of the breaks argument.
c) as a check on you exponent estimate, calculate alpha and se(alpha)  
as on pg 4-5 of that citation.

Alt B:
require(sos)
???"fitting pareto"
???"fitting power network"   # and proceed from there

-- 
David.

> Does anyone know the way to do this?
>
> Thanks for any help.
>
> Daigo
>
> p.s.
>
> Also,  I tried several ways such as
>
> http://www.mail-archive.com/r-help@stat.math.ethz.ch/msg62520.html
>
> and I got results like this:
>
> Profiling...
>
>   2.5 %   97.5 %
>
> 2.393297 2.412650
>
> What do these suggest?
>
> please tell me about this if someone knows.

-- 

David Winsemius, MD
West Hartford, CT