[R] how to generate a set of random numbers that sum to 1 with uniform distribution of elements

[Albyn Jones]

What uniform distribution do you want for the columns?  The average
value of X_k given \sum X_i = 1 must be 1/n.  If you start with 
X_i ~ U(0,1), the result must be skewed.

If you generate X_i uniformly distributed on (0, 2/n), the conditional
distribution given the sum is 1 will be less skewed.

  U <- matrix(runif(1000*100)/50,nrow=1000)
  s <- apply(U,1,sum)
  V <- U/s
  qqplot(U[,1],V[,1])

albyn

On Wed, Nov 07, 2012 at 05:02:10AM -0800, Bärbel wrote:
> Hi,
> I am looking for a way to generate a matrix of random numbers in a way that
> each row of the matrix would sum to 1 and that the numbers in the columns of
> the matrix would have a uniform distribution. So far I have found several
> ways to create random numbers that would sum to 1, but then the distribution
> of the individual elements is more or less skewed - there are much more
> small numbers than larger ones. 
> Any help and suggestions?
> - Bärbel
> 
> 
> 
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-- 
Albyn Jones
Reed College
jones at reed.edu