# On Discrete Gibbs Measure Approximation to Runs

## TL;DR

This paper develops a Stein operator-based approximation method for runs in Bernoulli trials using discrete Gibbs measures, providing new bounds and demonstrating their practical relevance.

## Contribution

It introduces a novel Stein operator for runs as a perturbation of a discrete Gibbs measure operator, enabling improved approximation bounds.

## Key findings

- New bounds for run approximations derived
- Application demonstrating the bounds' practical importance
- Stein method effectively applied to Bernoulli trials

## Abstract

A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli trials are derived via Stein method. The bounds obtained are new and their importance is demonstrated through an interesting application.