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 em > 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 em > 10-6 in this range.