A NEW PROOF FOR WINITZKI'S APPROXIMATION OF NORMAL CUMULATIVE DISTRIBUTION FUNCTION

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MANSOURI SHAHRAM

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Journal: JOURNAL OF STATISTICAL SCIENCES Year:2017 | Volume:10 | Issue:2 Page(s): 329-344

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Title

A NEW PROOF FOR WINITZKI'S APPROXIMATION OF NORMAL CUMULATIVE DISTRIBUTION FUNCTION

Author(s)

MANSOURI SHAHRAM | Issue Writer Certificate

Keywords

NORMAL CUMULATIVE DISTRIBUTION FUNCTIONQ2

ERROR FUNCTIONQ2

APPROXIMATIONQ2

Abstract

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.

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APA: Copy

MANSOURI, SHAHRAM. (2017). A NEW PROOF FOR WINITZKI'S APPROXIMATION OF NORMAL CUMULATIVE DISTRIBUTION FUNCTION. JOURNAL OF STATISTICAL SCIENCES, 10(2 ), 329-344. SID. https://sid.ir/paper/124156/en

Vancouver: Copy

MANSOURI SHAHRAM. A NEW PROOF FOR WINITZKI'S APPROXIMATION OF NORMAL CUMULATIVE DISTRIBUTION FUNCTION. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2017;10(2 ):329-344. Available from: https://sid.ir/paper/124156/en

IEEE: Copy

SHAHRAM MANSOURI, “A NEW PROOF FOR WINITZKI'S APPROXIMATION OF NORMAL CUMULATIVE DISTRIBUTION FUNCTION,” JOURNAL OF STATISTICAL SCIENCES, vol. 10, no. 2 , pp. 329–344, 2017, [Online]. Available: https://sid.ir/paper/124156/en

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