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?
So names aside, it's all the extreme value distribution, but there are minimum and maximum variations of it. After doing more math than I've done in some time, I'll agree to that :) Actually, the min/max case are so similar that it might be worth considering generalizing the extreme value distribution to handle both cases. It comes down to adding a third parameter, c which is either 1 or -1. Naturally, 1 for max, -1 for min. c(x) = (c * (a - x)) / b pdf(x) = exp(c(x) - exp(cx)) if c == 1, then it's the maximum case. If c == -1, then it's the minimum because (a - x) becomes (x - a). Unfortunately, the cdf's are a little different... cdf(x) = { exp(-exp(c(x)), for c == 1 1 - exp(-exp(c(x)), for c== -1 } Which is kind of fun because the cdf for the minimum is the complement of the cdf for the maximum (and vice versa for respective complements). The characteristics (outside the mean) are all the same. The mean can be redefined given as: mean = a + c * b * euler I don't know what the effect on the quantile functions would be, since I'm not sure how to compute those. I spent the last hour rewriting the extreme_value_distribution to accept a sign argument, allowing it to act as either the min or max case of the distribution. It defaults to the max. I also figured out how to tweak the random number generator to generate numbers for both cases (also taking the additional parameter). The code is here and here: http://warhol.sdml.cs.kent.edu/trac/miniboost/browser/trunk/boost/ math/distributions/extreme_value.hpp http://warhol.sdml.cs.kent.edu/trac/miniboost/browser/trunk/boost/ random/extreme_value_distribution.hpp Thoughts? Andrew Sutton asutton@cs.kent.edu