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September, 1946 An Approximation to the Probability Integral
J. D. Williams
Ann. Math. Statist. 17(3): 363-365 (September, 1946). DOI: 10.1214/aoms/1177730951


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.


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J. D. Williams. "An Approximation to the Probability Integral." Ann. Math. Statist. 17 (3) 363 - 365, September, 1946.


Published: September, 1946
First available in Project Euclid: 28 April 2007

zbMATH: 0061.28307
MathSciNet: MR16706
Digital Object Identifier: 10.1214/aoms/1177730951

Rights: Copyright © 1946 Institute of Mathematical Statistics

Vol.17 • No. 3 • September, 1946
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