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.