Inverse cumulative normal distribution

[Dieter]

(01-13-2016 09:54 AM)Pekis Wrote:  I wonder how they found 2^(-22^(1-41^(x/10))) for Phi(x) ... Was it pure brute force ?

Ask the author. ;-)

And keep in mind that there is a reason why all these simple approximations require x≥0: As x increases, Phi(x) approaches 1 and the given error near 1E–4 (absolute or relative) makes the results close to useless. Let x=5 and the logistic approximation returns 0,99999995. Plus or minus 0,00014, i.e. the true result can be anything between 0,99986 and 1. #-)

That's why these approximations are useless as x approaches –infinity. The relation Phi(–x) = 1–Phi(x) makes no sense here. 1–Phi(5) would give 5 E–8 instead of the true result 2,8665 E–7.

That's why designing approximations that can handle such cases is a bit more challenging.

Dieter