[R-lang] Fitting a Zipf-Mandelbrot distribution

[Ken Williams]

Excellent!  Thanks for the pointer.

 -Ken


On 5/25/07 5:13 PM, "Marco Baroni" <marco.baroni at unitn.it> wrote:

> 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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>