On the entropy of the log-normal distribution

2026/07/16 by Christian Berg, Henrik Laurberg Pedersen
#math.PR #math.CA

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Abstract

In a paper by Novi Inverardi and Tagliani from 2024 it is claimed that the log-normal density has maximal entropy in the class of densities having the same moments as the log-normal density. We disprove the claim by finding a family of densities with larger entropy.

Related

• Entropy Moments Characterization of Statistical Distributions
• Generalized Boltzmann factors and the maximum entropy principle
• A strengthened entropy power inequality for log-concave densities
• The use of the logarithm of the variate in the calculation of differential entropy among certain related statistical distributions
• The Distributions in Nature and Entropy Principle