(15C)(DM15) - PDF/CDF and Inverse of a Normal Distribution

[Albert Chan]

(11-24-2021 03:37 PM)deetee Wrote:  To calculate the CDF I used some approximating function rather than integrating the PDF,
which offers a accuracy of at least 2 digits (error < 1%) and is much faster.

More like 3 digits, and, formula very compact !

cdf2(z) := 1/(1+exp(-0.07*z^3-1.6*z))

We need an extra term to push it to 4-digits accuracy.

cdf3(z) := 1/(1+exp(0.0008*z^5-0.0743*z^3-1.595*z))

A Sigmoid Approximation of the Standard Normal Integral, by Gary R. Waissi and Donald F. Rossin
Note: link won't work as-is. Remove trailing characters after .pdf, and try again.

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Approximation formula intentionally skipped fitting even powers of z-score.
This made formula matching identity: 1 - cdf(-z) = cdf(z)

1 - 1/(1+exp(-x)) = exp(-x)/(1+exp(-x)) = 1/(1+exp(x))