{"title":"Refined normal approximations for the Student distribution","authors":"Frédéric Ouimet","doi":"10.7153/jca-2022-20-03","DOIUrl":null,"url":null,"abstract":"In this paper, we develop a local limit theorem for the Student distribution. We use it to improve the normal approximation of the Student survival function given in Shafiei & Saberali (2015) and to derive asymptotic bounds for the corresponding maximal errors at four levels of approximation. As a corollary, approximations for the percentage points (or quantiles) of the Student distribution are obtained in terms of the percentage points of the standard normal distribution.","PeriodicalId":73656,"journal":{"name":"Journal of classical analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of classical analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/jca-2022-20-03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In this paper, we develop a local limit theorem for the Student distribution. We use it to improve the normal approximation of the Student survival function given in Shafiei & Saberali (2015) and to derive asymptotic bounds for the corresponding maximal errors at four levels of approximation. As a corollary, approximations for the percentage points (or quantiles) of the Student distribution are obtained in terms of the percentage points of the standard normal distribution.
Young J. Juhn MD, MPH , Hirohito Kita MD , Barbara P. Yawn MD, MSc , Thomas G. Boyce MD, MPH , Kwang H. Yoo MD, PhD , Michaela E. McGree BS , Amy L. Weaver MS , Peter Wollan PhD , Robert M. Jacobson MD
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
