Non-parametric estimation of the population size using the empirical probability generating function
Pedro Puig · 2017
Several non-parametric methods have been proposed in the literature to estimate the number, or equivalently, the probability of zero for zero-truncated count distributions. Some of the most remarkable and commonly used approaches are Chao&s;s estimator, Zelterman&s;s estimator, the first and second-order jackknife estimators and Turing&s;s estimator. It is important to remark that, in general, it is impossible to know the proportion of zeros from its corresponding zero-truncated distribution, because the probability of zero is not univocally determined. The latent class (LC-class) was first introduced in P. Puig and C. Kokonendji, being a very large family of count distributions containing the Compound-Poisson family, Mixed-Poisson family and others. The LC-class is wider than the class of the union of Compound-and Mixed-Poisson distributions. In particular, the LC-class, is closed under independent addition, that is, given two independent random variables belonging to the LC-class the sum also belongs to the LC-class.