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Asymptotic behaviour of conditional $\alpha$ diversity for the two-parameterPoisson-Dirichlet partition model and for the normalized generalized Gammamodel has been recently investigated in Favaro et al. (2009, 2011) with a viewto possible applications in Bayesian treatment of species richness estimation.Here we generalize those results to the larger class of mixed Poisson-Kingmanspecies sampling models driven by the stable subordinator (Pitman, 2003).

Conditional $\alpha$-diversity for exchangeable Gibbs partitions driven by the stable subordinator