Simple Approximations for the Inverse Cumulative Function, the Density Function and the Loss Integral of the Normal Distribution

Haim Shore

Journal of the Royal Statistical Society Series C, 1982, vol. 31, issue 2, 108-114

Abstract: Simple approximations for the inverse cumulative function, the density function and the loss integral of the Normal distribution are derived, and compared with current approximations. The purpose of these simple approximations is to help in the derivation of closed form solutions to stochastic optimization models. A simple approximation for Mills' ratio is also derived. All of the approximations are expressed in terms of the distribution function. The somewhat reduced accuracy of the new approximations is offset by a high algebraic manipulability. A numerical example from inventory analysis is demonstrated.

Date: 1982
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