A New Approximation to the Normal Distribution Quantile Function

TL;DR

This paper introduces a faster approximation to the normal distribution quantile function with acceptable accuracy, suitable for applications like financial markets where speed is critical.

Contribution

A new approximation method for the normal quantile function that is faster than previous methods while maintaining sufficient accuracy for practical use.

Findings

Maximum absolute error less than 2.5e-5

Faster computation than Beasley and Springer approximation

Suitable for real-time financial applications

Abstract

We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2.5 \cdot 10^{-5}$. This is less accurate than [3], but still sufficient for many applications. However it is faster than [3]. This is its primary benefit, which can be crucial to many applications, including in financial markets.