On the entropy of the log-normal distribution

Christian Berg; Henrik Laurberg Pedersen

On the entropy of the log-normal distribution

Probability 2026-07-16 v1 Classical Analysis and ODEs

Authors: Christian Berg , Henrik Laurberg Pedersen

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.

Keywords

log-normal distribution maximum entropy moment problem counterexample

Cite

@article{arxiv.2607.14674,
  title  = {On the entropy of the log-normal distribution},
  author = {Christian Berg and Henrik Laurberg Pedersen},
  journal= {arXiv preprint arXiv:2607.14674},
  year   = {2026}
}

Comments

7 pages