  We obtain some approximation results for the weights appearing in the
exchangeable partition probability function identifying Gibbs partition models
of parameter $\alpha \in (0,1)$, as introduced in Gnedin and Pitman (2006). We
rely on approximation results for central and non-central generalized Stirling
numbers and on known results for conditional and unconditional $\alpha$
diversity. We provide an application to an approximate Bayesian nonparametric
estimation of discovery probability in species sampling problems under
normalized inverse Gaussian priors.
