A note on the maximum probability of ultra log-concave distributions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910849712521216 |
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| author | Aravinda, Heshan |
| author_facet | Aravinda, Heshan |
| contents | Jakimiuk et al. (2024) have proved that, if $X$ is an ultra log-concave random variable with integral mean, then $$\max_n \mathbb{P}\{X=n\} \geq \max_n \mathbb{P} \{Z=n\}\,,$$ where $Z$ is a Poisson random variable with the parameter $\mathbb{E}[X]$. In this note, we show that this inequality does not always hold true when $X$ is ultra log-concave with $\mathbb{E}[X]>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the maximum probability of ultra log-concave distributions Aravinda, Heshan Probability 60E05, 60E15 Jakimiuk et al. (2024) have proved that, if $X$ is an ultra log-concave random variable with integral mean, then $$\max_n \mathbb{P}\{X=n\} \geq \max_n \mathbb{P} \{Z=n\}\,,$$ where $Z$ is a Poisson random variable with the parameter $\mathbb{E}[X]$. In this note, we show that this inequality does not always hold true when $X$ is ultra log-concave with $\mathbb{E}[X]>1$. |
| title | A note on the maximum probability of ultra log-concave distributions |
| topic | Probability 60E05, 60E15 |
| url | https://arxiv.org/abs/2502.20486 |