An intermediate-precision approximation of the inverse cumulative normal distribution

Abstract

Accurate methods used to evaluate the inverse of the standard normal cumulative distribution function at probability ρ commonly used today are too cumbersome and/or slow to obtain a large number of evaluations reasonably quickly, e.g., as required in certain Monte Carlo applications. Previously reported simple approximations all have a maximum absolute error ε_m > 10^-4 for a ρ-range of practical concern, such as Min[ρ,l−ρ]≥10₋₆. An 11-term polynomial-based approximationis presented for which ε_m > 10^-6 in this range.

Keywords:

• approximation
• inverse cumulative normal distribution
• inverse error function