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We obtain some approximation results for the weights appearing in theexchangeable partition probability function identifying Gibbs partition modelsof parameter $\alpha \in (0,1)$, as introduced in Gnedin and Pitman (2006). Werely on approximation results for central and non-central generalized Stirlingnumbers and on known results for conditional and unconditional $\alpha$diversity. We provide an application to an approximate Bayesian nonparametricestimation of discovery probability in species sampling problems undernormalized inverse Gaussian priors.

Stirling's approximations for exchangeable Gibbs weights