Accurate RMM-based approximations for the CDF of the normal distribution

A variation of the RMM error distribution, used to model the exponential distribution, has recently been applied to derive a three-parameter approximation for the standard normal CDF, with a maximum absolute error of order (10)^-5. In this short communication, a simple modification enhances the accuracy to the order of (10)^-6. Another RMM-based approximation, based on the original RMM error distribution, achieves an absolute maximum error of (10)^-7. The simplicity of the new non-polynomial approximations qualifies them to be conveniently integrated into stochastic optimization models (like inventory models) or to be used in applications. That modeling of the exponential distribution via the RMM model could produce such highly accurate approximation for the standard normal CDF seems to lend further validity to the RMM model.