[R] Checking Goodness of Fit With Kolmogorov-Smirnov

[Gabor Csardi]

Hi,

this function uses maximum likelihood estimation to fit the exponent, and
returns an mle object. See ?"mle-class" for the details.

Just to give you an example for getting confidence intervals:

library(igraph)
data <- sample (1:100000, 100000, rep=TRUE, prob=(1:100000)^-2.4)
res <- power.law.fit(data)
confint(res)

You may want to check these as well:
http://arxiv.org/abs/cond-mat/0412004
http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf

Hope this helps,
Gabor

On Fri, Apr 28, 2006 at 06:39:01PM +0900, Alex Gutteridge wrote:
> Hi,
> 
> I'm using the power.law.fit function from the igraph package to fit a  
> power law distribution to some data. This function returns the power  
> law exponent as it's only result. I would like to have some sort of  
> goodness-of-fit and/or error estimate of the exponent returned. This  
> paper:
> 
> http://www.edpsciences.org/articles/epjb/pdf/2004/18/b04111.pdf
> 
> suggests using the Kolmogorov-Smirnov test to measure the goodness-of- 
> fit, however after reading the ks.test help page I'm not sure how to  
> proceed. The ks.test help page (and other stats texts) seem to say  
> that for the test to be valid, the parameters of the distribution  
> (the power law exponent in this case) cannot be estimated from the  
> data. If that's the case how do I test how good the fit is? Do I need  
> to use something else instead of KS? I've seen other mentions of  
> using KS to measure the goodness-of-fit to power laws though so  
> perhaps I've misunderstood something basic here (I'm a biologist not  
> a statistician).
> 
> If KS is the right tool to use, how would I go about specifying the  
> continuous distribution function for a power law? The help page only  
> shows how to use it with the built in 'pgamma' function is there an  
> analogous function for power law distributions - I couldn't find one.
> 
> Thanks for any help in steering me in the right direction.
> 
> Dr Alex Gutteridge
> Post-Doctoral Researcher
> 
> Bioinformatics Center
> Institute for Chemical Research
> Kyoto University
> Gokasho, Uji, Kyoto 611-0011
> Japan
> 
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-- 
Csardi Gabor <csardi at rmki.kfki.hu>    MTA RMKI, ELTE TTK