The maximal correlation coefficient associated with the minimum
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915891431604224 |
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| author | Chang, Yinshan Chen, Qinwei |
| author_facet | Chang, Yinshan Chen, Qinwei |
| contents | For independent random variables $(X_i)_{1\leq i\leq n}$, we consider the maximal correlation coefficient $R=R(\min_{i:1\leq i\leq m}X_i,\min_{j:\ell+1\leq j\leq n}X_j)$. If $X_1,X_2,\ldots,X_n$ are identically distributed with the same continuous distribution, we find that $R=(m-\ell)/\sqrt{m(n-\ell)}$. For discrete distributions, we calculate the maximal correlation coefficient $R$ for Bernoulli distributions, geometric distributions, binomial distributions and Poisson distributions. Our paper answers a question in \cite[Section~6]{ChangChen}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The maximal correlation coefficient associated with the minimum Chang, Yinshan Chen, Qinwei Probability For independent random variables $(X_i)_{1\leq i\leq n}$, we consider the maximal correlation coefficient $R=R(\min_{i:1\leq i\leq m}X_i,\min_{j:\ell+1\leq j\leq n}X_j)$. If $X_1,X_2,\ldots,X_n$ are identically distributed with the same continuous distribution, we find that $R=(m-\ell)/\sqrt{m(n-\ell)}$. For discrete distributions, we calculate the maximal correlation coefficient $R$ for Bernoulli distributions, geometric distributions, binomial distributions and Poisson distributions. Our paper answers a question in \cite[Section~6]{ChangChen}. |
| title | The maximal correlation coefficient associated with the minimum |
| topic | Probability |
| url | https://arxiv.org/abs/2512.15135 |