基于Dickman从属子的广义Poisson—Dirichlet分布

IF 0.5 4区 数学 Q4 STATISTICS & PROBABILITY Theory of Probability and its Applications Pub Date : 2023-02-01 DOI:10.1137/s0040585x97t991167
R. Maller, S. Shemehsavar
{"title":"基于Dickman从属子的广义Poisson—Dirichlet分布","authors":"R. Maller, S. Shemehsavar","doi":"10.1137/s0040585x97t991167","DOIUrl":null,"url":null,"abstract":"We study exchangeable random partitions based on an underlying Dickman subordinator and the corresponding family of Poisson--Dirichlet distributions. The large sample distribution of the vector representing the block sizes and the number of blocks in a partition of $\\{1,2,\\dots,n\\}$ is shown to be, after norming and centering, a product of independent Poissons and a normal distribution. In a species or gene sampling situation, these quantities represent the abundances and the numbers of species or genes observed in a sample of size $n$ from the corresponding Poisson--Dirichlet distribution. We include a summary of known convergence results concerning the Dickman subordinator in this context.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Poisson--Dirichlet Distributions Based on the Dickman Subordinator\",\"authors\":\"R. Maller, S. Shemehsavar\",\"doi\":\"10.1137/s0040585x97t991167\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study exchangeable random partitions based on an underlying Dickman subordinator and the corresponding family of Poisson--Dirichlet distributions. The large sample distribution of the vector representing the block sizes and the number of blocks in a partition of $\\\\{1,2,\\\\dots,n\\\\}$ is shown to be, after norming and centering, a product of independent Poissons and a normal distribution. In a species or gene sampling situation, these quantities represent the abundances and the numbers of species or genes observed in a sample of size $n$ from the corresponding Poisson--Dirichlet distribution. We include a summary of known convergence results concerning the Dickman subordinator in this context.\",\"PeriodicalId\":51193,\"journal\":{\"name\":\"Theory of Probability and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/s0040585x97t991167\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991167","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0

摘要

我们研究了基于Dickman从属和泊松-狄利克雷分布族的可交换随机分区。在$\{1,2,\dots,n\}$的分区中,表示块大小和块数量的向量的大样本分布表明,在规范化和定心之后,是独立泊松和正态分布的乘积。在物种或基因取样的情况下,这些数量表示从相应的泊松-狄利克雷分布中观察到的物种或基因在大小为$n$的样本中的丰度和数量。在此背景下,我们包括关于Dickman从属子的已知收敛结果的总结。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Generalized Poisson--Dirichlet Distributions Based on the Dickman Subordinator
We study exchangeable random partitions based on an underlying Dickman subordinator and the corresponding family of Poisson--Dirichlet distributions. The large sample distribution of the vector representing the block sizes and the number of blocks in a partition of $\{1,2,\dots,n\}$ is shown to be, after norming and centering, a product of independent Poissons and a normal distribution. In a species or gene sampling situation, these quantities represent the abundances and the numbers of species or genes observed in a sample of size $n$ from the corresponding Poisson--Dirichlet distribution. We include a summary of known convergence results concerning the Dickman subordinator in this context.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Theory of Probability and its Applications
Theory of Probability and its Applications 数学-统计学与概率论
CiteScore
1.00
自引率
16.70%
发文量
54
审稿时长
6 months
期刊介绍: Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
期刊最新文献
Poisson Process with Linear Drift and Related Function Series In Memory of A. M. Vershik (12.28.1933--02.14.2024) Two-sided Estimates for the Sum of Probabilities of Errors in the Multiple Hypothesis Testing Problem with Finite Number of Hypotheses on a Nonhomogeneous Sample On an Example of Expectation Evaluation High Excursion Probabilities for Gaussian Fields on Smooth Manifolds
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1