Improved nonparametric estimation of the number of zeros and illustrations

In this talk we present some lower bounds for the probability of zero for the class of count distributions having a log-convex probability generating function, which includes Compound and Mixed Poisson distributions. These lower bounds allow to construct non-parametric estimators of the non-observed number of zeros, which are useful in capture-recapture models. Some of these bounds lead to the well known Chao's and Turing's estimators. Several examples of application are analyzed and discussed.