%0 Report
%9 Technical Report
%A Berti, Patrizia
%A Crimaldi, Irene
%A Pratelli, Luca
%A Rigo, Pietro
%D 2013
%F eprints:1544
%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
%N  
%T Central Limit Theorems for an Indian Buffet Model with Random Weights
%U http://eprints.imtlucca.it/1544/
%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.
%Z Preprint, Submitted