Às 14:04 de 14/04/2025, Rui Barradas escreveu:
Às 12:26 de 14/04/2025, Brian Smith escreveu:
Hi,
For my analytical work, I need to draw a sample of certain sample size
from a denied population, where population members are marked by
non-negative integers, such that sum of sample members if fixed. For
example,
Population = 0:100
Sample_size = 10
Sample_Sum = 20
Under this setup if my sample members are X1, X2, ..., X10 then I
should have X1+X2+...+X10 = 20
Sample drawing scheme may be with/without replacement
Is there any R function to achieve this? One possibility is to employ
naive trial-error approach, but this doesnt seem to be practical as it
would take long time to get the final sample with desired properties.
Any pointer would be greatly appreciated.
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Hello,
Use the multinomial distribution. The problem with this is that the
population is not part of the solution. But the sum is Sample_Sum.
Population <- 0:100
Sample_size <- 10
Sample_Sum <- 20
probs <- rep(1/Sample_size, Sample_size)
# one sample
rmultinom(1, Sample_Sum, prob = probs)
# five samples
rmultinom(5, Sample_Sum, prob = probs)
Another way, found on StackOverflow.
# user: https://stackoverflow.com/users/4996248/john-coleman
# answer: https://stackoverflow.com/a/49016614/8245406
rand.nums <- function(a,b,n,k){
#finds n random integers in range a:b which sum to k
while(TRUE){
x <- sample(1:(k - n*a), n - 1, replace = TRUE) #cutpoints
x <- sort(x)
x <- c(x, k - n*a) - c(0, x)
if(max(x) <= b - a) return(a + x)
}
}
rand.nums(0, 100, Sample_size, Sample_Sum)
Hope this helps,
Rui Barradas
Hello,
If you have a vector of ages and want to draw n elements from it adding
up to a fixed value, the following code draws without replacement.
Note that it only works if the ages vector is small. Moderately large
vectors will break ?combn.
set.seed(2025)
age_vec_size <- 20L
age <- sample.int(100L, age_vec_size, TRUE)
target_age_sum <- 400L
n <- 10L
cmb <- combn(age, n)
i <- colSums(cmb) == target_age_sum
cmb[, i] |> t() |> head()
cmb[, i] |> t() |> tail()
cmb[, i] |> table() |> barplot()
Hope this helps,
Rui Barradas
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