A simple wide range approximation of symmetric binomial distributions

TL;DR

This paper introduces a uniform, local approximation for symmetric binomial distributions that improves tail estimates and reduces relative error compared to classical methods.

Contribution

It provides a simple, wide-range approximation of symmetric binomial distributions, refining the de Moivre-Laplace normal approximation for better tail accuracy.

Findings

Enhanced approximation accuracy at distribution tails

Reduced relative error in binomial tail estimates

Applicable across a wide range of parameters

Abstract

The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace normal approximation in order to give an estimate at the tail as well to minimize the relative error.