Suppose I have N smarties, each of which is one of C distinct colours.
Suppose further that N is known and largish (10,000) but C is not, and that for each colour C there are $c_i$ smarties of that colour. Whilst the distribution of $c_i$ is unknown, we have the vague assumption that no $c_i$ will be very large or small, eg no one colour will make up more more than 99 or less than 1 percent of the total number of smarties.
If I take a sample of size n and determine that it contains $x_i$ smarties of each colour, how can I produce a good estimate the total number of classes?
Note -> I'm familiar with http://arxiv.org/pdf/0708.2153.pdf and http://www.jstor.org/stable/2290471 but was wondering if anyone had anything else to contibute. Also I'm concerned with the case where N is large but not infinite, which is fairly distinct from the first paper.