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Approximations to the Normal Distribution Function and An Extended Table for the Mean Range of the Normal Variables

Kiani, M and Panaretos, J and Psarakis, S and Saleem, M (2008): Approximations to the Normal Distribution Function and An Extended Table for the Mean Range of the Normal Variables. Published in: Journal of the Iranian Statistical Society , Vol. 7, No. 1-2 (2008): pp. 57-72.

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Abstract

This article presents a formula and a series for approx¬imating the normal distribution function. Over the whole range of the normal variable z, the proposed formula has the greatest absolute error less than 6.5e - 09, and series has a very high accuracy. We examine the accuracy of our proposed formula and series for various values of z’s. In the sense of accuracy, our formula and series are su¬perior to other formulae and series available in the literature. Based on the proposed formula an extended table for the mean range of the normal variables is established.

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