## The Annals of Applied Probability

### Central limit theorems for an Indian buffet model with random weights

#### Abstract

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 $\overline{K}_{n}=(1/n)\sum_{i=1}^{n}K_{i}$ where $K_{i}$ is the number of dishes tried by customer $i$. The asymptotic distributions of $L_{n}$ and $\overline{K}_{n}$, 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., nongeneralized) Indian buffet process.

#### Article information

Source
Ann. Appl. Probab., Volume 25, Number 2 (2015), 523-547.

Dates
First available in Project Euclid: 19 February 2015

https://projecteuclid.org/euclid.aoap/1424355122

Digital Object Identifier
doi:10.1214/14-AAP1002

Mathematical Reviews number (MathSciNet)
MR3313747

Zentralblatt MATH identifier
1314.60015

#### Citation

Berti, Patrizia; Crimaldi, Irene; Pratelli, Luca; Rigo, Pietro. Central limit theorems for an Indian buffet model with random weights. Ann. Appl. Probab. 25 (2015), no. 2, 523--547. doi:10.1214/14-AAP1002. https://projecteuclid.org/euclid.aoap/1424355122

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