Best (and Newest?) Approximations for Popular Inverse Distributions

[Dieter]

(03-16-2019 07:16 AM)Thomas Klemm Wrote:  

(03-15-2019 01:02 PM)Pekis Wrote:  Perhaps this one ?

These are programs for the HP-42S:

Yes, these are very simple approximations of the Normal Integral that can be directly inverted so that you get the inverse, the Normal quantile. But the error is larger than in the old 1950s approximations Namir mentioned, and they do not work well for probabilities close to 0 or 1. So I wonder if this is what Namir had in mind when he wrote he was looking for "the best ... approximations".

I think in this regard other methods are much more suited. Most of them use rational approximations. Various of such approximations have been published: by Odeh and Evans, Beasley, Moro and Springer, Wichura, Acklam and others.

But you don't have to rely on the results of others. Rational approximations can be developed in Mathematica or Maple, you can even do it in Excel. Just state the domain (down to 1E–99? More? Less?) and the accepted error level, and do your own custom approximation.

Dieter