R: Getting around periodic random numbers

Question

I'm building a distribution of proportions of random values lower than a specified threshold.

ret = c(); thr = 0.5; n = 15; reps = 10000
for (x in 1:reps) {
  prop = sum(runif(n, 0, 1) < thr) / n
  ret = c(ret, prop)
}
plot(density(ret), main=NA)

The resulting density distribution is highly periodic and is not something one would theoretically expect:

I presume this has something to do with the periodicity of the random number generator. Is there any way around this?

Answer 1

Your distribution is discrete, and hence a kernel density estimate isn't the right tool. Instead you should be plotting the frequencies, as indicated by @nicola and other commenters.

i.e.

plot(table(ret))

gives:

Or, if you want probabilities, you could do:

plot(table(ret) / length(ret))