Abstract
It is shown that $\frac{1}{\sqrt{2\pi}} \int_{-x}^x e^{-\frac{1}{2}t^2} dt \geq \lbrack 1 - e^{-(2/\pi)x^2}\rbrack^\frac{1}{2}$ and that the equality is never in error by as much as three-fourths of one percent. Other approximations are discussed.
Citation
J. D. Williams. "An Approximation to the Probability Integral." Ann. Math. Statist. 17 (3) 363 - 365, September, 1946. https://doi.org/10.1214/aoms/1177730951
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