how to generate a set of random numbers that sum to 1 with uniform distribution of elements
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, B?rbel 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? >> - B?rbel >> >> >> >> -- >> 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