Main Article Content

Abstract

This paper deals with a new, simple one-term approximation to the cumulative distribution function (c.d.f) of the standard normal distribution which does not have closed form representation. The accuracy of the proposed approximation measured using maximum absolute error (M.S.E) and the same criteria is used to compare this approximation with the existing one-term approximation approaches available in the literature. Our approximation has a maximum absolute error of about 0.0016 and this accuracy is sufficient for most practical applications.

Keywords

Cumulative Distribution Function (c.d.f) Normal Distribution Maximum Absolute Error (M.A.E.) Approximation

Article Details

How to Cite
Hanandeh, A., & Eidous, O. (2021). A New One-term Approximation to the Standard Normal Distribution. Pakistan Journal of Statistics and Operation Research, 17(2), 381-385. https://doi.org/10.18187/pjsor.v17i2.3556

References

  1. Aludaat, K. M. and Alodat, M. T. (2008). A note on approximating the normal distribution function. Applied Mathematical Science, 2(9), 425-429.
  2. Bailey, B. J. (1981). Alternatives to Hasting's approximation to the inverse of the normal cumulative distribution function. Applied Statistics, 30(3), 275-276.
  3. Bowling, S. R., Khasawneh, M. T., Kaewkuekool, S. and Cho, B. R. (2009). A logistic approximation to the cumulative normal distribution. Journal of Industrial Engineering and Management, 2(1), 114-127.
  4. Eidous, O. M. and Al-Salman, S. A. (2015). One-term approximation for normal distribution function. Mathematics and Statistics, 4(1), 15-18.
  5. Eidous, O. M. and Abu-Shareefa, R. (2020). New approximations for standard normal distribution function. Communications in Statistics - Theory and Methods, 49(6), 1357-1374.
  6. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Continuous univariate distributions. Volume 1, 2nd Edition. John Wiley, New York.
  7. Lin, J. T. (1990). A simpler logistic approximation to the normal tail probability and its inverse. Applied Statistics, 39, 255-257.
  8. Ordaz, M. (1991). A simple approximation to the Gaussian distribution. Structural Safety, 9(4), 315-318.
  9. Polya, G. (1949). Remarks on computing the probability integral in one and two dimensions. Proceedings of the First Berkeley Symposium on Mathematical and Statistical Probability. 63-78.
  10. Tocher, K. D. (1963). The art of simulation. The English Universities Press: London, UK.
  11. Zogheib, B. and Hlynka, M. (2009). Approximations of the standard normal distribution. University of Windsor, Dept. of Mathematics and Statistics, on-line text.