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# st: RE: Estimating Power law distributions

 From "Nick Cox" To Subject st: RE: Estimating Power law distributions Date Mon, 27 Apr 2009 11:31:05 +0100

```You have at least three main choices:

1. Translate this into a probability density function and estimate using
your method of choice, say maximum likelihood.

2. Use -cumul- to calculate the distribution function and thus the
complement explicit here. Then estimate the parameters e.g. by least
squares after transformation.

3. Use graphs. See for example detailed comments on power laws within

SJ-5-3  gr0018  . . . . . . . . . .  Speaking Stata: The protean
quantile plot
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
J. Cox
Q3/05   SJ 5(3):442--460           (see gr41_3 and gr42_3 for
commands)
discusses quantile and distribution plots as used in
the analysis of species abundance data in ecology

Incidentally, none of these methods requires any kind of normalisation.

Nick
n.j.cox@durham.ac.uk

Emanuele Canegrati, Ph.D.

I have to check if the cumulative distribution of a series, say Sj, is
consistent with a power law, say Prob{S>x} distas x*exp(-aSj). I should
normalize my series by transforming it to zero mean and unit s.d. Then I
should evaluate the value for the exponent aSj. Do you know how to do
it?

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