Double precision rational approximation algorithms for the standard normal first and second order loss functions

Abstract

We present double precision algorithms based upon piecewise rational approximations for the standard normal first and second order loss functions. These functions are used frequently in inventory management. No direct approximation or closed formulation exists for the standard first and second order loss functions. Current state-of-the-art algorithms require intermediate computations of the cumulative normal distribution or tabulations and they do not compute to full double precision. We deal with both these issues and present direct double precision accurate algorithms which are valid in the full range of double precision floating point numbers.