# Estimates for the closeness of convolutions of probability distributions on convex polyhedra

## TL;DR

This paper extends previous results on approximating sums of independent random variables and their convolutions to the setting of probability distributions on convex polyhedra, providing new estimates for their closeness.

## Contribution

It transfers existing approximation and convolution proximity results to probability distributions on convex polyhedra, broadening their applicability.

## Key findings

- Established bounds for convolution closeness on convex polyhedra
- Extended compound Poisson approximation techniques to convex polyhedral distributions
- Provided theoretical estimates for multidimensional distribution convolutions

## Abstract

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent summands by the accompanying compound Poisson laws and the estimates of the proximity of sequential convolutions of multidimensional distributions may be transferred to the estimation of the closeness of convolutions of probability distributions on convex polyhedra.