[R] fitting a truncated power law

glen_b glnbrntt at gmail.com
Tue Aug 4 10:46:49 CEST 2009

John Sanders-2 wrote:
> How can I fit a truncated power law to a vector? I can't find a function
> to do that. If the function provides an AIC, even better.

Okay, "power law" I understand - f(x) = k.x^a, or on the log-scale log(f(x))
= log(k) + a log(x) (linear)

I was unfamiliar with the term "truncated power law", but after looking on
the internet I see that the term implies what appears to be replacing the
linear fit with a linear spline fit to log(y) in terms of log(x)  - but the
usual application seems to be to fit probability distribution to count data;
in this case you fit essentially a two-part Pareto distribution (or Zipf if
the variable is discrete) - again the log-fitted-density is like a linear
spline in the logs.

Is the vector of data you have counts to which you wish to fit a
distribution, or is it a set of measurements?

If I understand the problem correctly, I think it could probably be done
using linear splines with GLMs, which can be done in a couple of packages.

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