Inversion of Tchebychev-Tchernov inequality

TL;DR

This paper develops a method to estimate the lower tail bounds of a distribution by analyzing lower bounds of its moment generating function, providing new insights into distribution tail behavior.

Contribution

It introduces a novel approach to derive lower tail bounds using moment generating functions, advancing the theoretical understanding of distribution tails.

Findings

Established a lower tail bound framework based on MGF estimates

Provided theoretical results linking MGFs to distribution tails

Enhanced understanding of tail behavior in probability distributions

Abstract

We derive in this article the {\it lower} bound for tail of distribution for the random variables (r.v.) through a lower estimate for its moment generating functions (MGF).