How to draw 4 random weights that sum up to 1?

On 10.10.2011 18:10, Alexander Engelhardt wrote:

Hey list,

This might be a more general question and not that R-specific.  
Sorry for
that.

I'm trying to draw a random vector of 4 numbers that sum up to 1.
My first approach was something like

a <- runif(1)
b <- runif(1, max=1-a)
c <- runif(1, max=1-a-b)
d <- 1-a-b-c

but this kind of distorts the results, right?
Would the following be a good approach?

w <- sample(1:100, 4, replace=TRUE)
w <- w/sum(w)

Yes, although better combine both ways to

w <- runif(4)
w <- w / sum(w)

For the non-statisticians in the audience like myself who didn't know  
what that distribution might "look like" (it being difficult to  
visualize densities on your 3-dimensional manifold in 4-space),  here  
is my effort to get an appreciation:

  M4 <- matrix(runif(40000), ncol=4)
  M4 <- M4/rowSums(M4)
# just a larger realization of Ligges' advice
  colMeans(M4)
[1] 0.2503946 0.2499594 0.2492118 0.2504342
  plot(density(M4[,1]))
  lines(density(M4[,2]),col="red")
  lines(density(M4[,3]),col="blue")
  lines(density(M4[,4]),col="green")

plot(density(rowSums(M4[,1:2])))

  plot(density(rowSums(M4[,1:3])))
plot(density(rowSums(M4[,2:4])))

# rather kewl results, noting that these are a reflecion around 0.5 of  
the single vector densities.

Uwe Ligges

I'd prefer a general algorithm-kind of answer to a specific R  
function
(if there is any). Although a function name would help too, if I can
sourcedive.

David Winsemius, MD
West Hartford, CT