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

2025/02/27 by Aravinda, Heshan
#60E05 #60E15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2502.20486

Abstract

Jakimiuk et al. (2024) have proved that, if X is an ultra log-concave random variable with integral mean, then max_n ℙ\X=n\ ≥ max_n ℙ \Z=n\ , where Z is a Poisson random variable with the parameter 𝔼[X]. In this note, we show that this inequality does not always hold true when X is ultra log-concave with 𝔼[X]>1.

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