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Suppose a population has infinitely many individuals and is partitioned into unknown N disjoint classes. The sample coverage of a random sample from the population is the total proportion of the classes observed in the sample. This paper uses a nonparametric Poisson mixture model to give new understanding and results for inference on the sample coverage. The Poisson mixture model provides a simplified framework for inferring any general abundance-𝒦 coverage, the sum of the proportions of those classes that contribute exactly k individuals in the sample for some k in 𝒦, with 𝒦 being a set of nonnegative integers. A new moment-based derivation of the well-known Turing estimators is presented. As an application, a gene-categorisation problem in genomic research is addressed. Since Turing's approach is a moment-based method, maximum likelihood estimation and minimum distance estimation are indicated as alternatives for the coverage problem. Finally, it will be shown that any Turing estimator is asymptotically fully efficient.