Enhancing the Accuracy of Standard Normal Distribution Approximations
Abstract
In this paper, we introduce a novel approximation for the standard normal distribution function, significantly improving its accuracy. Using the maximum absolute error (Max-AE) and mean absolute error (MAE) as metrics, our approximation achieves a Max-AE of 2.95 × 10−5, outperforming most existing methods. Additionally, we present an approximation for the inverse normal distribution, showing its superiority over many current models. Numerical comparisons validate the efficiency of our methods, making them applicable in fields like statistical analysis, machine learning, and financial modeling.
Fields of Study & Subjects
Mathematical functions and polynomials
Mathematical and Computational Methods
Numerical Methods and Algorithms
Publication details
- Journal / source
- Statistics Optimization & Information Computing
- Volume
- 15
- Issue
- 4
- Pages
- 2819–2828
- Publication date
- 24 January 2026
- Language
- VI