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

Understand

Asymptotic behaviour of conditional $\alpha$ diversity for the two-parameter Poisson-Dirichlet partition model and for the normalized generalized Gamma model has been recently investigated in Favaro et al.

• (2009, 2011) with a view to possible applications in Bayesian treatment of species richness estimation.
• Here we generalize those results to the larger class of mixed Poisson-Kingman species sampling models driven by the stable subordinator (Pitman, 2003).