Lower bounds on binomial and Poisson tails: an approach via tail conditional expectations

TL;DR

This paper develops upper bounds on tail conditional expectations for binomial and Poisson variables, enabling non-asymptotic lower bounds on probabilities of large deviations from the mean.

Contribution

It introduces a novel approach using tail conditional expectations to derive explicit lower bounds on tail probabilities for binomial and Poisson distributions.

Findings

Derived upper bounds on tail conditional expectations

Established non-asymptotic lower bounds on tail probabilities

Applicable to large deviation analysis of binomial and Poisson variables

Abstract

We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the aforementioned random variables are significantly larger than their expectation.