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

2016/09/21 by Christos Pelekis, Pelekis, Christos
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #math.PR

paper · pdf · doi:10.48550/arxiv.1609.06651

13 pages, 6 figures. Some typos are corrected and the results are extended to the Poisson case

openalex publication_date 2016/09/21 · arxiv created 2017/12/06 · arxiv updated 2017/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Central Binomial Tail Bounds

Related

• A lower bound on the probability that a binomial random variable is exceeding its mean
• Nearly tight universal bounds for the binomial tail probabilities
• On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables
• Tight Lower Bound on the Probability of a Binomial Exceeding its Expectation
• Some inequalities on Binomial and Poisson probabilities