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From: John Maddock (john_at_[hidden])
Date: 2007-12-13 10:46:27

Andrew Sutton wrote:
> So I went back and read a little more carefully. Let me see if I have
> this right... Gumbel, Weibull, and Fisher-Tippet are are all Extreme
> Value distributions. The Fisher-Tippet distribution corresponds to a
> maximum extreme value distribution, and Gumbel, a minimum. Re-reading
> the Wikipedia entry for it, they seem to use the distributions a
> little more interchangeably.

I'm not sure that's correct still and different sources use different
conventions.

Mathworld seems to treat the terms Extreme Value and Fisher Tippet as
interchangable (see
http://mathworld.wolfram.com/ExtremeValueDistribution.html), but if someone
refers colloquially to "The Extreme Value" or "The Fisher Tippet" or "The
Log-Weibul" distribution then it probably means the maximum case of the type
I extreme value dist.

NIST uses "Gumbel Distribution" to refer to both the Extreme Value Type I
distibutions (min ans max cases). Other sources refer to only the minimum
case as "The Gumbel Distribution". Mathworld refers to these as "Gumbel
types" http://mathworld.wolfram.com/GumbelDistribution.html. While
mathematica uses Gumbel to refer to just the minimum case.

So you can call it whatever you like and still be right :-)

BTW I believe the min and max cases are basically just mirror images of each
other about the location parameter?

> As far as code goes, Boost.Math has the Fisher-Tippet variant (as
> extreme_value), but not a true Gumbel distribution, right? That means
> that I've effectively written a Fisher-Tippet variate, but not really
> a true Gumbel variate... I guess I'll just hack away at my new Gumbel
> distribution and rename the number generator.

Well it's a kind of Gumbel distribution, but not what folks normally call
"The Gumbel Distribution": which is the minimum case.

Hope that's now slightly clearer than the proverbial mud ;-)

John.