Non-parametric Estimation of the Number of Zeros in Truncated Count Distributions

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 the construction of new non-parametric estimators of the number of unobserved zeros, which are useful for capture-recapture models, or in areas like epidemiology and literary style analysis. Some of these bounds also lead to the well-known Chao's and Turing's estimators. Several examples of application are analysed and discussed.