How to simulate different sample size for many times and calculate the sum for each sample size

Question

Here is my code :

for (p in 1:10){
sample=rgamma(p,p,1)}

Here is what I get

[1] 1.841629
[1] 2.174076 1.410500
[1] 2.398601 4.674819 2.679830
[1] 2.736786 3.767747 4.546256 3.851677
[1]  4.204808  8.393887 10.312640  2.514957  4.863661

How can I simulate this for 1000 times and sum up the the results for each p.
Eg. for p=2, s=sum=(2.174076 + 1.410500 )
By this, there should be 1000 s value for each p
Thankyou very much.

Answer 1

Using replicate you can repeat a function for n times.

simulate <- function(n) {
  sample <- numeric(n)
  for (p in 1:n){
    sample[p] = sum(rgamma(p,p,1))
  }
  sample
}

res <- t(replicate(1000, simulate(10)))

Answer 2

You can put your random gammas in an upper triangular matrix and sum the columns:

sz <- 1e3L
m <- matrix(0, nrow = sz, ncol = sz)
m[upper.tri(m, diag = TRUE)] <- rgamma((sz^2 + sz)/2, rep(1:sz, 1:sz))
s <- colSums(m)

To verify that each column is getting the correct shape parameter:

sz <- 10L
m <- matrix(nrow = sz, ncol = sz)
m[upper.tri(m, diag = TRUE)] <- rep(1:sz, 1:sz)
> m
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
 [1,]    1    2    3    4    5    6    7    8    9    10
 [2,]   NA    2    3    4    5    6    7    8    9    10
 [3,]   NA   NA    3    4    5    6    7    8    9    10
 [4,]   NA   NA   NA    4    5    6    7    8    9    10
 [5,]   NA   NA   NA   NA    5    6    7    8    9    10
 [6,]   NA   NA   NA   NA   NA    6    7    8    9    10
 [7,]   NA   NA   NA   NA   NA   NA    7    8    9    10
 [8,]   NA   NA   NA   NA   NA   NA   NA    8    9    10
 [9,]   NA   NA   NA   NA   NA   NA   NA   NA    9    10
[10,]   NA   NA   NA   NA   NA   NA   NA   NA   NA    10

Edit: or a slightly faster one-liner:

s <- colSums(replace(matrix(0, sz, sz), sequence(1:sz, seq(1, sz^2 - sz + 1, sz)), rgamma((sz^2 + sz)/2, rep(1:sz, 1:sz))))

Or you can sample the sums directly:

s <- rgamma(sz, (1:sz)^2)