Year: 2025
Type: preprint
Abstract: 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 $\mathbb{E}[X]>1$.
Source: arXiv (Cornell University)
Author: Aravinda, Heshan
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979278024
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