Quite so. But this is different territory
(and in my view better publicised than Stas implies:
there are many books on the statistics of extremes).
Again, there are several Stata implementations, not
just for the Gumbel, but also for generalized Pareto,
generalized extreme value (includes Gumbel as a special
case), etc.
Nick
[email protected]
Stas Kolenikov
> 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.
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