[R-lang] Fitting a Zipf-Mandelbrot distribution

[Ken Williams]

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