{"title":"关于无限多方框占用问题的注解:一般渐近性和幂律*","authors":"A. Gnedin, Ben B. Hansen, J. Pitman","doi":"10.1214/07-PS092","DOIUrl":null,"url":null,"abstract":"This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in sam- ples from populations with infinitely many species. We present moments of this random variable, discuss asymptotic relations among them and with re- lated random variables, and draw connections with regular variation, which appears in various manifestations. AMS 2000 subject classifications: Primary 60F05, 60F15; secondary","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2007-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/07-PS092","citationCount":"165","resultStr":"{\"title\":\"Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws ∗\",\"authors\":\"A. Gnedin, Ben B. Hansen, J. Pitman\",\"doi\":\"10.1214/07-PS092\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in sam- ples from populations with infinitely many species. We present moments of this random variable, discuss asymptotic relations among them and with re- lated random variables, and draw connections with regular variation, which appears in various manifestations. AMS 2000 subject classifications: Primary 60F05, 60F15; secondary\",\"PeriodicalId\":46216,\"journal\":{\"name\":\"Probability Surveys\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2007-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1214/07-PS092\",\"citationCount\":\"165\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Surveys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/07-PS092\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Surveys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/07-PS092","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws ∗
This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in sam- ples from populations with infinitely many species. We present moments of this random variable, discuss asymptotic relations among them and with re- lated random variables, and draw connections with regular variation, which appears in various manifestations. AMS 2000 subject classifications: Primary 60F05, 60F15; secondary
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