I wonder how I can address the following scenario:
I am sampling from a given discrete distribution with $n$ categories/coupons (not necessarily uniform). Let $U_k$ represents the number of unique values seen after $k$ samples. I would like to estimate the confidence interval of $U_k$.
The closest paper I could find was:
Shank, N.B. and Yang, H., 2013. Coupon collector problem for non-uniform coupons and random quotas. the electronic journal of combinatorics, 20(2), p.P33.
But it finds the expected k for having at least one of each type of coupon been selected.