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

[David Winsemius]

On Nov 7, 2012, at 10:48 AM, Albyn Jones wrote:

> 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])

Couldn't one just do:

 mat <- matrix(runif(1000*10), ncol=10) # mean value per element = 0.5
mat2 <- mat/rowSums(mat)       # mean value of rowSums= 5

-- 
David.


> 
> 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
>> 
>> 
>> 
>> --
>> View this message in context: http://r.789695.n4.nabble.com/how-to-generate-a-set-of-random-numbers-that-sum-to-1-with-uniform-distribution-of-elements-tp4648695.html
>> Sent from the R help mailing list archive at Nabble.com.
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
> 
> -- 
> Albyn Jones
> Reed College
> jones at reed.edu
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
Alameda, CA, USA