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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

Mathworld seems to treat the terms Extreme Value and Fisher Tippet as
interchangable (see, 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" 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 ;-)


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