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- W2608120147 abstract "We describe the distribution of frequencies ordered by sample values in a random sample of size $n$ from the two parameter GEM$(alpha,theta)$ random discrete distribution on the positive integers. These frequencies are a $($size$-alpha)$-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well known identity in distribution due to Donnelly and Tavar'e (1986) for $alpha = 0$ to the case $0 le alpha < 1$. This description extends to sampling from Gibbs$(alpha)$ frequencies obtained by suitable conditioning of the GEM$(alpha,theta)$ model, and yields a value-ordered version of the Chinese Restaurant construction of GEM$(alpha,theta)$ and Gibbs$(alpha)$ frequencies in the more usual size-biased order of their appearance. The proofs are based on a general construction of a finite sample $(X_1,dots,X_n)$ from any random frequencies in size-biased order from the associated exchangeable random partition $Pi_infty$ of $mathbb{N}$ which they generate." @default.
- W2608120147 created "2017-05-05" @default.
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- W2608120147 date "2017-04-16" @default.
- W2608120147 modified "2023-09-23" @default.
- W2608120147 title "Ordered and size-biased frequencies in GEM and Gibbs models for species sampling" @default.
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- W2608120147 doi "https://doi.org/10.48550/arxiv.1704.04732" @default.
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