CENTRAL LIMIT THEOREMS FOR AN INDIAN BUFFET MODEL WITH RANDOM WEIGHTS

• 成果类型: Article
• 署名作者: Berti, Patrizia; Crimaldi, Irene; Pratelli, Luca; Rigo, Pietro
• 署名单位: Universita di Modena e Reggio Emilia; IMT School for Advanced Studies Lucca; University of Pavia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1002
• 发表日期: 2015
• 页码: 523-547
• 关键词: 2-color

摘要

The three-parameter Indian buffet process is generalized. The 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 (K) over bar (n)= (1/n) Sigma(n)(i=1) K-i where K-i is the number of dishes tried by customer i. The asymptotic distributions of L-n and (K) over bar (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., nongeneralized) Indian buffet process.