I would like to estimate the distribution of a very large population of known size but unknown mean and variance.
I cannot assume anything about the shape of the underlying distribution. However, I am certain that the values in the population are non-negative, non-zero integers. I believe that the distribution is naturally lumped in some way discretely rather than being continuously distributed over the entire range. I cannot sample the entire population but I would like to estimate the probability density function. I would also like some level of assurance of the correctness of the estimated distribution.
What is the best way to go about this?
