Algorithm for Estimating Number of Unique Monthly Visitors
After digging into this for a bit, I came across this paper which provides a solution. The paper gives an approach to estimating the number of new species that will be observed given an initial sampling period. It models observing a given species as a Poisson distribution. It gives the following estimator for the number of new species that will be discovered:
$$
\hat{\Psi}(t)=\sum_{k=1}^{k_{m a x}} N_{k} e^{-k}-\sum_{k=1}^{k_{m a x}} N_{k} e^{-k(1+t)}
$$
where $N_{k}$ is the number of species that were observed $k$ times and $t$ is the length of the second sample relative to the initial sample.