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

[deetee]

(11-25-2021 01:27 PM)Albert Chan Wrote:  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))

Thanks for sharing this information and link.

I developed my formula spending many hours with excel varying as few and simple parameters as possible.

After reading your document and doing some research I found a similar result from Bowling et al (2009) with a maximal error of 1.4x10-4:

CDF = 1/(1+exp(-0.07056*z^3-1.5976*z))

Despite there are many efforts from 1946 (Polya) to 2016 (Eidous and Al-Salman) it seems that no one has really solved this problem (simple formula, simple parameters, high accuracy) ...

Regards
deetee