I found another method to generate this, in the Borg of all Wisdom: http://en.wikipedia.org/wiki/Simplex
Alberto Monteiro --- Section Random Sampling: The second method [[the first method is based on the Dirichlet distribution -- avfm]] to generate a random point on the unit simplex is based on the order statistics of the uniform distribution on the unit interval, and was popularized by Horst Kraemer. The algorithm is as follows: Set p0 = 0 and pK=1. Generate K-1 uniform random draws pi from the open interval (0,1). Sort into ascending order the K+1 points p0, ..., pK. The K coordinates t1, ..., tK of the final point on the unit simplex are given by ti=pi-pi-1. It has been pointed out by Smith and Tromble that the second method is technically only valid if none of the differences pi-p(i-1) are equal to zero. In practice, it is sufficient to merely re-run the algorithm to generate a new set of points if this happens. ______________________________________________ R-help@stat.math.ethz.ch 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.
