An accurate approximation for the standard normal distribution function

Abstract

In this paper, a new approximation for the standard normal cumulative distribution function, Φ(z) is proposed. The maximum absolute error (MAE) of the proposed approximation is 9.37935 × 10⁻⁶. Comparisons with some existing approximations based on the MAE and mean absolute error (MEAE) are also given. The results show that the proposed approximation is simple and has an acceptable accuracy.

Subject Classification:

• 62E17

Keywords:

• Normal distribution
• Approximation
• Maximum absolute error
• Mean absolute error