Generate 3 random number that sum to 1 in R

Question

I am hoping to create 3 (non-negative) quasi-random numbers that sum to one, and repeat over and over.

Basically I am trying to partition something into three random parts over many trials.

While I am aware of

a = runif(3,0,1)

I was thinking that I could use 1-a as the max in the next runif, but it seems messy.

But these of course don't sum to one. Any thoughts, oh wise stackoverflow-ers?

Answer 1

This question involves subtler issues than might be at first apparent. After looking at the following, you may want to think carefully about the process that you are using these numbers to represent:

## My initial idea (and commenter Anders Gustafsson's):
## Sample 3 random numbers from [0,1], sum them, and normalize
jobFun <- function(n) {
    m <- matrix(runif(3*n,0,1), ncol=3)
    m<- sweep(m, 1, rowSums(m), FUN="/")
    m
}

## Andrie's solution. Sample 1 number from [0,1], then break upper 
## interval in two. (aka "Broken stick" distribution).
andFun <- function(n){
  x1 <- runif(n)
  x2 <- runif(n)*(1-x1)
  matrix(c(x1, x2, 1-(x1+x2)), ncol=3)
}

## ddzialak's solution (vectorized by me)
ddzFun <- function(n) {
    a <- runif(n, 0, 1)
    b <- runif(n, 0, 1)
    rand1 = pmin(a, b)
    rand2 = abs(a - b)
    rand3 = 1 - pmax(a, b)
    cbind(rand1, rand2, rand3)
}

## Simulate 10k triplets using each of the functions above
JOB <- jobFun(10000)
AND <- andFun(10000)
DDZ <- ddzFun(10000)

## Plot the distributions of values
par(mfcol=c(2,2))
hist(JOB, main="JOB")
hist(AND, main="AND")
hist(DDZ, main="DDZ")

Answer 2

just random 2 digits from (0, 1) and if assume its a and b then you got:

rand1 = min(a, b)
rand2 = abs(a - b)
rand3 = 1 - max(a, b)