Sample with a max

Question

If I want to sample numbers to create a vector I do:

set.seed(123)
x <- sample(1:100,200, replace = TRUE)
sum(x)
# [1] 10228

What if I

Answer 1

Another approach, but with floating point numbers, so not exactly what you are looking for, sorry :

randomsum <- function(nb, sum) {
  tmp <- sort(runif(nb-1))
  tmp <- c(min(tmp), diff(tmp), 1-max(tmp))
  as.vector(quantile(0:sum, probs=tmp))
}

Which would give for example :

R> result <- randomsum(10, 1000)
R> result
 [1]  35.282191  66.537308  17.263761 182.837409 120.064363 210.752735
 [7] 143.201079   6.164731  34.936359 182.960064
R> sum(result)
[1] 1000

You could use round on the result to get integers, but then of course the sum could be slightly different from what you want to get. A quick and dirty workaround can be to alter one of the random values to make your vector sum to the number you want :

randomsumint <- function(nb, sum) {
  tmp <- sort(runif(nb-1))
  tmp <- c(min(tmp), diff(tmp), 1-max(tmp))
  res <- as.vector(quantile(0:sum, probs=tmp))
  res <- round(res)
  res[length(res)] <- res[length(res)]+(sum-sum(res))
  res
}

Which would give :

R> result <- randomsumint(10,1000)
R> result
 [1]  42 152   0  11  74 138   9 138 172 264
R> sum(result)
[1] 1000

Not that this is far from perfect, as in some rare cases you could get a negative value in your result.