# A conditional Berry-Esseen inequality

## TL;DR

This paper extends the central limit theorem by establishing a Berry-Esseen inequality for sums of i.i.d. random variables conditioned on another sum of i.i.d. integer-valued variables, providing quantitative bounds.

## Contribution

It introduces a new Berry-Esseen inequality for conditioned sums, expanding the theoretical understanding of limit theorems under conditioning.

## Key findings

- Established a Berry-Esseen inequality for conditioned sums
- Provided bounds on the rate of convergence in the conditioned CLT
- Extended Janson's central limit theorem to include Berry-Esseen bounds

## Abstract

As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.