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:: Volume 10, Issue 2 (3-2017) ::
J. of Stat. Sci. 2017, 10(2): 329-344 Back to browse issues page
A New Proof for Winitzki's Approximation of Normal Cumulative Distribution Function
Shahram Mansouri
Abstract:   (2668 Views)

Among all statistical distributions, standard normal distribution has been the most important and practical distribution in which calculation of area under probability density function and cumulative distribution function are required. Unfortunately, the cumulative distribution function of this is, in general, expressed as a definite integral with no closed form or analytical solution. Consequently, it has to be approximated. In this paper, attempts have been made for Winitzki's approximation to be proved by a new approach. Then, the approximation is improved with some modifications and shown that the maximum error resulted from this is less than 0.0000584. Finally, an inverse function for computation of normal distribution quantiles has been derived.

Keywords: Normal cumulative distribution function, Error function, Approximation
Full-Text [PDF 505 kb]   (783 Downloads)    
Type of Study: Research | Subject: Probabilty and Applications
Received: 2015/08/14 | Accepted: 2016/05/11 | Published: 2017/03/12
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Mansouri S. A New Proof for Winitzki's Approximation of Normal Cumulative Distribution Function. J. of Stat. Sci.. 2017; 10 (2) :329-344
URL: http://jss.irstat.ir/article-1-390-en.html


Volume 10, Issue 2 (3-2017) Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences
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