期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2018
卷号：80
期号：2
页码：330-341
DOI：10.1007/s13171-018-0124-z
语种：English
出版社：Indian Statistical Institute
摘要：Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the Poisson-Dirichlet distribution with parameter α ∈ [0,1) and 𝜃 > − α . Given a sample of size n from the population, two important statistics are the number K n of different types in the sample, and the number M l , n of different types with frequency l in the sample. We establish moderate deviation principles for ( K n ) n ≥ 1 and ( M l , n ) n ≥ 1. Corresponding rate functions are explicitly identified, which help in revealing a critical scale and in understanding the exact role of the parameters α and 𝜃 .
关键词：α -diversity ; Large and moderate deviations ; Poisson-Dirichlet distribution ; Random partition
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