Comments on: Stand-alone normal (Gaussian) distribution function http://www.johndcook.com/blog/2009/01/19/stand-alone-normal-gaussian-distribution-function/ John D. Cook Wed, 22 May 2013 18:07:41 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: ekzept http://www.johndcook.com/blog/2009/01/19/stand-alone-normal-gaussian-distribution-function/comment-page-1/#comment-13413 ekzept Mon, 19 Jan 2009 18:26:12 +0000 http://www.johndcook.com/blog/?p=1296#comment-13413 If high accuracy isn’t essential, there’s also Polya’s approximation to the standard Gaussian c.d.f. which Aludaat and Alotdat have recently improved, at least in a maximum error sense (Applied Mathematical Sciences, Vol. 2, 2008, no. 9, 425 – 429). Polya’s is still of interest, at least to me, because its peak deviations are farther out in number of standard errors than Aludaat & Alodat’s. Both have error which approaches zero as the number of standard errors increases in magnitude beyond two. Polya’s maximum deviation from Gaussian c.d.f. is a tad over 0.003 at just over 1.5 standard errors.

The Polya approximation is: 0.5 +- 0.5 sqrt(1-exp(-2z^2/pi))

The inverse is available by algebra.

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