On the Maximum Entropy of a Sum of Independent Discrete Random Variables

DOI10.1137/S0040585X97T99054XzbMath1479.60029arXiv2008.01138OpenAlexW3209910216MaRDI QIDQ5163530

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Publication date: 4 November 2021

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.01138

zbMATH Keywords

maximum entropybinomial distributionultra-log-concavityBernoulli sumShepp-Olkin theorem

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Probability distributions: general theory (60E05) Measures of information, entropy (94A17)

Cites Work

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• Discrete versions of the transport equation and the Shepp-Olkin conjecture
• Log-concavity and the maximum entropy property of the Poisson distribution
• A proof of the Shepp-Olkin entropy monotonicity conjecture
• A proof of the Shepp-Olkin entropy concavity conjecture
• Maximizing the entropy of a sum of independent bounded random variables
• Maximum Entropy for Sums of Symmetric and Bounded Random Variables: A Short Derivation
• On the Maximum Entropy Properties of the Binomial Distribution
• On the Entropy of the Multinomial Distribution
• Binomial and Poisson distributions as maximum entropy distributions

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