Non-asymptotic estimation for Bell function, with probabilistic applications

TL;DR

This paper develops non-asymptotic bilateral estimates for moment inequalities of sums of non-negative independent random variables, utilizing Bell functions and Poisson distribution properties, with applications in probability theory.

Contribution

It introduces new non-asymptotic bilateral estimates for moment inequalities based on Bell functions and Poisson distribution, advancing probabilistic analysis methods.

Findings

Derived bilateral estimates for moment inequalities

Connected Bell functions with Poisson distribution properties

Enhanced tools for probabilistic inequalities

Abstract

We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.