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

Heshan Aravinda

Statistics & Probability Letters, 2025, vol. 223, issue C

Abstract: Jakimiuk et al. (2024) have proved that, if X is an ultra log-concave random variable with integral mean, then maxnP{X=n}≥maxnP{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.

Keywords: Ultra log-concave distributions; Log concavity; Poisson distribution; Maximum (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110418

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