Better-than-average uniform random variables and Eulerian numbers, or: How many candidates should a voter approve?
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914702320205824 |
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| author | Janson, Svante Smith, Warren D. |
| author_facet | Janson, Svante Smith, Warren D. |
| contents | Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but distinct from, the well known fact that the integer part of the sum of independent random numbers uniform on $[0,1]$ has an Eulerian distribution. One motivation for this problem comes from voting theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Better-than-average uniform random variables and Eulerian numbers, or: How many candidates should a voter approve? Janson, Svante Smith, Warren D. Probability Combinatorics 60C05, 05A15, 91B12 Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but distinct from, the well known fact that the integer part of the sum of independent random numbers uniform on $[0,1]$ has an Eulerian distribution. One motivation for this problem comes from voting theory. |
| title | Better-than-average uniform random variables and Eulerian numbers, or: How many candidates should a voter approve? |
| topic | Probability Combinatorics 60C05, 05A15, 91B12 |
| url | https://arxiv.org/abs/2403.02670 |