Re: [boost] Beta Distribution for boost::random

From: Andrew Sutton (asutton_at_[hidden])
Date: 2007-12-14 12:04:43

> 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_at_[hidden]