sample with replacement but constrain the max frequency of each member to be drawn

Question

Is it possible to extend the sample function in R to not return more than say 2 of the same element when replace = TRUE?

Suppose I have a list:

l = c(1,1,2,3,4,5)

To sample 3 elements with replacement, I would do:

sample(l, 3, replace = TRUE)

Is there a way to constrain its output so that only a maximum of 2 of the same elements are returned? So (1,1,2) or (1,3,3) is allowed, but (1,1,1) or (3,3,3) is excluded?

Answer 1

set.seed(0)

The basic idea is to convert sampling with replacement to sampling without replacement.

ll <- unique(l)          ## unique values
#[1] 1 2 3 4 5
pool <- rep.int(ll, 2)   ## replicate each unique so they each appear twice
#[1] 1 2 3 4 5 1 2 3 4 5
sample(pool, 3)          ## draw 3 samples without replacement
#[1] 4 3 5

## replicate it a few times
## each column is a sample after out "simplification" by `replicate`
replicate(5, sample(pool, 3))
#     [,1] [,2] [,3] [,4] [,5]
#[1,]    1    4    2    2    3
#[2,]    4    5    1    2    5
#[3,]    2    1    2    4    1

If you wish different value to appear up to different number of times, we can do for example

pool <- rep.int(ll, c(2, 3, 3, 4, 1))
#[1] 1 1 2 2 2 3 3 3 4 4 4 4 5

## draw 9 samples; replicate 5 times
oo <- replicate(5, sample(pool, 9))
#      [,1] [,2] [,3] [,4] [,5]
# [1,]    5    1    4    3    2
# [2,]    2    2    4    4    1
# [3,]    4    4    1    1    1
# [4,]    4    2    3    2    5
# [5,]    1    4    2    5    2
# [6,]    3    4    3    3    3
# [7,]    1    4    2    2    2
# [8,]    4    1    4    3    3
# [9,]    3    3    2    2    4

We can call tabulate on each column to count the frequency of 1, 2, 3, 4, 5:

## set `nbins` in `tabulate` so frequency table of each column has the same length
apply(oo, 2L, tabulate, nbins = 5)
#     [,1] [,2] [,3] [,4] [,5]
#[1,]    2    2    1    1    2
#[2,]    1    2    3    3    3
#[3,]    2    1    2    3    2
#[4,]    3    4    3    1    1
#[5,]    1    0    0    1    1

The count in all columns meet the frequency upper bound c(2, 3, 3, 4, 1) we have set.

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Would you explain the difference between rep and rep.int?

rep.int is not the "integer" method for rep. It is just a faster primitive function with less functionality than rep. You can get more details of rep, rep.int and rep_len from the doc page ?rep.