# [R] fitting a truncated power law

glen_b glnbrntt at gmail.com
Wed Aug 5 03:29:08 CEST 2009

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Hang on, now I'm very confused.  What is the information you have collected?
Is it x and y? k and x? which one is the count?

John Sanders-2 wrote:
>
> The function I'm trying to fit has the form:
>
> P(k)
> ~ k^(-y) exp (– k ⁄ kx)
>
> And deals with count data. I'm a newbie, so any more specific suggestion
> would be greatly appreciated.
>
> 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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> and provide commented, minimal, self-contained, reproducible code.
>
>

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