  In Bayesian nonparametric inference, random discrete probability measures are
commonly used as priors within hierarchical mixture models for density
estimation and for inference on the clustering of the data. Recently, it has
been shown that they can also be exploited in species sampling problems: indeed
they are natural tools for modeling the random proportions of species within a
population thus allowing for inference on various quantities of statistical
interest. For applications that involve large samples, the exact evaluation of
the corresponding estimators becomes impracticable and, therefore, asymptotic
approximations are sought. In the present paper, we study the limiting
behaviour of the number of new species to be observed from further sampling,
conditional on observed data, assuming the observations are exchangeable and
directed by a normalized generalized gamma process prior. Such an asymptotic
study highlights a connection between the normalized generalized gamma process
and the two-parameter Poisson-Dirichlet process that was previously known only
in the unconditional case.
