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Double precision rational approximation algorithm for the inverse standard normal second order loss function

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Abstract
We present a double precision algorithm based upon rational approximations for the inverse standard normal second order loss function. This function is used frequently in inventory management. No direct approximation or closed formulation exists for the inverse standard normal second order loss function. Calculations are currently based on root-finding methods and intermediate computations of the cumulative normal distribution or tabulations. Results then depend on the accuracy and valid range of that underlying function. We deal with these issues and present a direct, double precision accurate algorithm valid in the full range of double precision floating point numbers.
Keywords
Inventory system, Rational approximation, Normal integral, Normal distribution, Repeated integrals, Loss function

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Citation

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MLA
De Schrijver, Steven, El-Houssaine Aghezzaf, and Hendrik Vanmaele. “Double Precision Rational Approximation Algorithm for the Inverse Standard Normal Second Order Loss Function.” APPLIED MATHEMATICS AND COMPUTATION 232 (2014): 247–253. Print.
APA
De Schrijver, S., Aghezzaf, E.-H., & Vanmaele, H. (2014). Double precision rational approximation algorithm for the inverse standard normal second order loss function. APPLIED MATHEMATICS AND COMPUTATION, 232, 247–253.
Chicago author-date
De Schrijver, Steven, El-Houssaine Aghezzaf, and Hendrik Vanmaele. 2014. “Double Precision Rational Approximation Algorithm for the Inverse Standard Normal Second Order Loss Function.” Applied Mathematics and Computation 232: 247–253.
Chicago author-date (all authors)
De Schrijver, Steven, El-Houssaine Aghezzaf, and Hendrik Vanmaele. 2014. “Double Precision Rational Approximation Algorithm for the Inverse Standard Normal Second Order Loss Function.” Applied Mathematics and Computation 232: 247–253.
Vancouver
1.
De Schrijver S, Aghezzaf E-H, Vanmaele H. Double precision rational approximation algorithm for the inverse standard normal second order loss function. APPLIED MATHEMATICS AND COMPUTATION. ELSEVIER SCIENCE INC; 2014;232:247–53.
IEEE
[1]
S. De Schrijver, E.-H. Aghezzaf, and H. Vanmaele, “Double precision rational approximation algorithm for the inverse standard normal second order loss function,” APPLIED MATHEMATICS AND COMPUTATION, vol. 232, pp. 247–253, 2014.
@article{5920067,
  abstract     = {We present a double precision algorithm based upon rational approximations for the inverse standard normal second order loss function. This function is used frequently in inventory management. No direct approximation or closed formulation exists for the inverse standard normal second order loss function. Calculations are currently based on root-finding methods and intermediate computations of the cumulative normal distribution or tabulations. Results then depend on the accuracy and valid range of that underlying function. We deal with these issues and present a direct, double precision accurate algorithm
valid in the full range of double precision floating point numbers.},
  author       = {De Schrijver, Steven and Aghezzaf, El-Houssaine and Vanmaele, Hendrik},
  issn         = {0096-3003},
  journal      = {APPLIED MATHEMATICS AND COMPUTATION},
  keywords     = {Inventory system,Rational approximation,Normal integral,Normal distribution,Repeated integrals,Loss function},
  language     = {eng},
  pages        = {247--253},
  publisher    = {ELSEVIER SCIENCE INC},
  title        = {Double precision rational approximation algorithm for the inverse standard normal second order loss function},
  url          = {http://dx.doi.org/10.1016/j.amc.2013.12.192},
  volume       = {232},
  year         = {2014},
}

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