On 3/6/07, Nick Cox <[email protected]> wrote:
For my part, I think power laws have been oversold, for a variety of
reasons. Here's one. Often the data that are shown are actually for
the right-hand tail, and not a complete distribution. In many examples,
only the largest cities, the longest rivers, and so forth are readily
available and the other tail may be omitted. Income data are often
better, or so it seems.
There is a whole theory of extreme values leading to the appropriate
asymptotic distributions of sample maxima (and highest order
statistics following it). Some of those laws indeed look pretty
similar to power laws, so they may not be so overrated, in the end
:)).
I couldn't find a good source on that within two minutes of looking at
Google results :(. This is a piece of statistical theory not so well
known even to professional statistical audience. Wikipedia has an
article (http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution)
that is disputed; MathWorld asks for a contribution
(http://mathworld.wolfram.com/ExtremeValueTheory.html). If you
restrict Google to site:unc.edu, you'll see a bunch of book chapters
and presentations by my advisor, Richard Smith, who is a bigger name
than any of the people behind those pages. Here's a couple of his
examples: http://www.stat.unc.edu/faculty/rs/s322/evtsection.pdf,
http://www.stat.unc.edu/faculty/rs/talks/042403.pdf.
--
Stas Kolenikov
http://stas.kolenikov.name
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