I ended up asking here.
My Problem might be familiar with the Coupon collector's problem and related to this post Probability of throwing n different numbers in m throws of a dice but it does not solve my specific problem:
I want to know how many unique values there are after throwing a dice with k sides n times. The Coupon collector's problem asks for a constant number of unique values. It is something like the other way around and or I have a brain fart.
- k be the maximum value in range of iid values [1:k] to appear. i.e. [1:100] (known) so there are 100 unique values possible.
- n number of throws (known)
- u number of unique values after n throws (wanted)
In other words, i want to predict this result if k = [1:100] and n = 80:
length(unique(order(table(floor(runif(80, min=1, max=101)))))) # u will be app. 54 #how to predict?
Edit: Problem is not that trivial. Found answer here... How can I estimate unique occurrence counts from a random sampling of data?