Estimating frequencies of frequencies in finite populations

Given a sample from a finite population partitioned into classes, we consider estimating the distribution of the class frequencies. We propose first to estimate certain moments of this distribution, assuming Poisson sampling with unequal inclusion probabilities, and then to adapt these estimates using modelling assumptions. A simulation study illustrates the bias-robustness of the approach to departures from these assumptions. © 2012 Elsevier B.V..