An example of a non-log-concave distribution where the difference has a log-concave density
Probability
2025-12-30 v1
Abstract
By the Pr\'ekopa-Leindler inequality, the difference has a log-concave density provided that has a log-concave density and are independent and identically distributed. We prove that the opposite direction does not always hold true by giving an explicit example.
Cite
@article{arxiv.2512.23179,
title = {An example of a non-log-concave distribution where the difference has a log-concave density},
author = {Min Wang},
journal= {arXiv preprint arXiv:2512.23179},
year = {2025}
}
Comments
2 pages