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

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  • Haim Shore

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.

Suggested Citation

  • Haim Shore, 1982. "Simple Approximations for the Inverse Cumulative Function, the Density Function and the Loss Integral of the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 108-114, June.
    • Handle: RePEc:bla:jorssc:v:31:y:1982:i:2:p:108-114
    DOI: 10.2307/2347972
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    Cited by:

    1. Shore, Haim, 1995. "Fitting a distribution by the first two moments (partial and complete)," Computational Statistics & Data Analysis, Elsevier, vol. 19(5), pages 563-577, May.
    2. De Schrijver, Steven K. & Aghezzaf, El-Houssaine & Vanmaele, Hendrik, 2014. "Double precision rational approximation algorithm for the inverse standard normal second order loss function," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 247-253.
    3. H Shore, 2004. "A general solution for the newsboy model with random order size and possibly a cutoff transaction size," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(11), pages 1218-1228, November.
    4. Shore, Haim, 1999. "Optimal solutions for stochastic inventory models when the lead-time demand distribution is partially specified," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 477-485, March.

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