Re: generating constrained random vectors

[Sven N. Thommesen]

At 06:17 PM 10/8/1999 -0700, you wrote:
> M. Lang / S. Railsback writes:
> >
> > a. It seems impossible to have a vector of N values that are uniformly
> > random between 0,1 and yet add up to 1. The constraint that they add up
> > to one excludes a lot of values from the distribution. (How can they be
> > uniformly distributed between 0 and 1 if it is impossible for 0.6 and
> > 0.5 to both be in the vector?)
>
> This makes sense, but it addresses a different problem than the original.
> The question was not how to generate a N-element vector with each
> element uniformly distributed over [0,1] such that the sum of elements
> is 1, but rather how to randomly generate a N-element vector with each
> entry between [0,1] such that the sum of elements is 1 and the vectors
> generated are uniformly distributed over the N-dimensional simplex.
>
> Jason

Well, so much for jumping in before thinking ;-\

My original "easy" solution does seem to have the property that it merely 
scales down a "big" hypercube to a smaller one, thus leaving out the 
corners of the simplex. It seems Steve Upton's solution is likely to be better.

And on a practical note, if you need uniform doubles between 0.0 and 1.0, 
you don't need the uniformDouble distribution object; any generator will 
give you that.

Sven



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