A note on the maximum probability of ultra log-concave distributions

Heshan Aravinda

Jakimiuk et al. (2024) have proved that, if $X$ is an ultra log-concave random variable with integral mean, then $$\underset{n}{\max }\mathbb{P}\{X=n\}\ge \underset{n}{\max }\mathbb{P}\{Z=n\},$$ wher…