%X The three-parameter Indian buffet process is generalized. T
he possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let L_n be the number of dishes experimented by the first n customers, and let 
{\bar K}_n=(1/n)\sum_{i=1}^n K_i
where K_i is the number of dishes tried by customer i. The asymptotic distributions of L_n and {\bar K}_n, suitably
centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., non generalized) Indian buffet process.
%T Central Limit Theorems for an Indian Buffet Model with Random Weights
%J The Annals of Applied Probability
%L eprints2129
%A Patrizia Berti
%A Irene Crimaldi
%A Luca Pratelli
%A Pietro Rigo
%N  
%D 2014
%O Forthcoming
%I IMT Institute for Advanced Studies Lucca
%K Bayesian nonparametrics, Central limit theorem, Conditional identity in distribution, Indian buffet process, Random measure, Random reinforcement, Stable convergence