Re: generating constrained random vectors - a proof ( i think)

[M. Lang / S. Railsback]

Chris Landauer wrote:
> 
> hihi, all -
> 
> well, the last message worried me, so i worked through a proof of the process
> suggested by several people of incrementally generating the values (i think
> the comment about bias towards small values is actually correct, but 

I think there's a problem with this approach.

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?)

b. Yet if you pick your first value from between 0 and 1 and it turns
out to be 0.99, then you DO have a range of 0,1 (or 0,.99). 

I don't think you can specify the range of the random numbers in advance
and hope for them to be uniformly distributed. So I go with Sven's
approach. If you want the vector to add to 1.0, then I don't think you
can constrain both the range of values and the shape of the
distribution.

steve
-- 
address@hidden
Lang, Railsback & Assoc.
250 California Ave., Arcata CA 95521
707-822-0453; Fax 822-1868


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