A study on the $F$-distribution motivated by Chvátal's theorem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913500224290816 |
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| author | Zhou, Qianqian Lu, Peng Hu, Zechun |
| author_facet | Zhou, Qianqian Lu, Peng Hu, Zechun |
| contents | 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 $κ>0,$ we investigate the infimum value of the probability $P(X_{d_1, d_2}\leq κE[X_{d_1, d_2}])$. Our motivation comes from Chvátal's theorem on the binomial distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A study on the $F$-distribution motivated by Chvátal's theorem Zhou, Qianqian Lu, Peng Hu, Zechun Probability 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 $κ>0,$ we investigate the infimum value of the probability $P(X_{d_1, d_2}\leq κE[X_{d_1, d_2}])$. Our motivation comes from Chvátal's theorem on the binomial distribution. |
| title | A study on the $F$-distribution motivated by Chvátal's theorem |
| topic | Probability |
| url | https://arxiv.org/abs/2409.09420 |