Assume there is a number of labeled urns and every urn holds a number of balls (at least one). You know there are n balls in total but you do not know how many urns there are nor how the balls are distributed between them. You can blindly draw a fraction of the balls (lets say 10%) and can see which urn the ball came from. How do you estimate how many urns there are in total?
To maybe bring some intuition to problem, the real life application for this is the following. Assume you have a number of customers, and each customer can make orders (which most likely follows a power law). Now you only see a subset of orders (e.g. 1,000,000 out of 10,000,000 total). Based on the orders you see, you have to estimate how many customers you have in total.
You might assume that the number of orders per customer follows a power law. But actually I would like to not assume a distribution, but infer it from the sample, and then go from there.