Inequalities between $L^p$-norms for log-concave distributions
Statistics Theory
2019-03-26 v1 Information Theory
Functional Analysis
math.IT
Statistics Theory
Abstract
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space. These inequalities are the generalizations of the upper and lower bound of the differential entropy and are also interpreted as a kind of expansion of the inequality between two Lp-norms on the measurable set with finite measure.
Cite
@article{arxiv.1903.10101,
title = {Inequalities between $L^p$-norms for log-concave distributions},
author = {Tomohiro Nishiyama},
journal= {arXiv preprint arXiv:1903.10101},
year = {2019}
}