Sample-based non-uniform random variate generation

A sample of n lid random variables with a given unknown density is given. We discuss several issues related to the problem or generating a new sample of lid random variables with almost the same density. In particular, we look at sample independence, consistency, sample indistinguishability, moment matching and generator efficiency. We also introduce the notion of a replacement number, the minimum number of observations in a given sample that have to be replaced to obtain a sample with a given density.