generate normal distribution with exactly N elements in Y bins

Question

I'll probably want to hit myself over the head for not getting this:

How do I generate a vector with the expected height of a normal distribution over Y bins (nbins in the below), of exactly N elements.

Like so, in the below picture:

• Y or nbins = 15
• N or nstat = 77
• ... should return something like: c(1,1,2,4, ...)

I know I could draw rnorm(77), but that'll never be exactly normal, and looping over 10.000 iterations or so seems overkill.

So I tried using qnorm for that purpose, but I have a hunch that:

1. sth is wrong with the below code
2. there has to be an easier, more elegant way

Here is what I got:

nbins <- 15
nstat <- 77

item.pos <- qnorm( # to the left of which value lies...
  1:(nstat) / (nstat+1)# ... the n-statement?
  # using nstat + 1 because we want midpoints, not cutoffs for later
)

bins <- cut(
  x = item.pos,
  breaks = nbins,
  ordered_result = TRUE
)

height <- summary(bins)
height <- as.numeric(bins)

Answer 1

If your range of data is from -2:2 with 15 intervals and the sample size is 77 I would suggest the following to get the expected heights of the 15 intervals:

rn <- dnorm(seq(-2,2, length = 15))/sum(dnorm(seq(-2,2, length = 15)))*77
 [1] 1.226486 2.084993 3.266586 4.716619 6.276462 7.697443 8.700123 9.062576 8.700123 7.697443
[11] 6.276462 4.716619 3.266586 2.084993 1.226486

The barplot of this looks like:

barplot(height = rn, names.arg = round(seq(-2, 2, length = 15), 2))

So, in your sample of 77 you would get the first value of the sequence in 1.226486, the second value in 2.084993 cases, etc. Its difficult to generate a vector as you described at the beginning, because the sequence above does not consist of integers.