{"title":"A study on the $F$-distribution motivated by Chvátal's theorem","authors":"Qianqian Zhou, Peng Lu, Zechun Hu","doi":"arxiv-2409.09420","DOIUrl":null,"url":null,"abstract":"Let $X_{d_1, d_2}$ be an $F$-random variable with parameters $d_1$ and $d_2,$\nand expectation $E[X_{d_1, d_2}]$. In this paper, for any $\\kappa>0,$ we\ninvestigate the infimum value of the probability $P(X_{d_1, d_2}\\leq \\kappa\nE[X_{d_1, d_2}])$. Our motivation comes from Chv\\'{a}tal's theorem on the\nbinomial distribution.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"91 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09420","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let $X_{d_1, d_2}$ be an $F$-random variable with parameters $d_1$ and $d_2,$
and expectation $E[X_{d_1, d_2}]$. In this paper, for any $\kappa>0,$ we
investigate the infimum value of the probability $P(X_{d_1, d_2}\leq \kappa
E[X_{d_1, d_2}])$. Our motivation comes from Chv\'{a}tal's theorem on the
binomial distribution.
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
