[R-lang] Fitting a Zipf-Mandelbrot distribution

[Marco Baroni]

Dear Ken,

Routines to fit a Zipf-Mandelbrot (probability) distribution are 
implemented in our zipfR library for R:

http://www.cogsci.uni-osnabrueck.de/~severt/zipfR

The library documentation also points to some literature on the topic 
(most notably, Baayens' 2001 Word Frequency Distributions book).

Regards,

Marco


Ken Williams wrote:
> Hi,
> 
> I've got some data (picture at http://limnus.com/~ken/zipf.jpg ) that seems
> to very obviously follow a Zipf-Mandelbrot distribution, and I'm wondering
> how to best fit the parameters of the distribution given the data.
> 
> I'm using the equation y = P(x + A)^-B as the canonical form of the
> Zipf-Mandelbrot curve.
> 
> As a first attempt, I fixed the two endpoints (x=1 and y=1) to coincide with
> the expected values on the graph, which analytically gives me values for P
> and B as functions of A.  Then I twiddle around with values for A until it
> looks nice.  On the attached graph, this means I end up with A=8.
> 
> This method pretty clearly overfits the endpoints, and is subject to the
> whims of my eyeballs for A.  What would members of this list suggest for
> alternative fitting methods?
> 
> Thanks,
> 
>  -Ken
> 
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-- 
Marco Baroni
CIMeC, University of Trento
http://www.form.unitn.it/~baroni