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Best (and Newest?) Approximations for Popular Inverse Distributions
03-15-2019, 04:27 PM (This post was last modified: 03-15-2019 05:14 PM by Dieter.)
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RE: Best (and Newest?) Approximations for Popular Inverse Distributions
(03-15-2019 12:48 PM)Namir Wrote:  I am looking for better approximations that the ones appearing the HP 65/65 Stat Pacs.

I assume that virtually anything is better that the good old Hastings approximation. ;-)

As far as I can tell the de-facto standard for the inverse Normal distribution is the Wichura algorithm from 1988, published in Applied Statistics as algorithm AS241. It works over the whole IEEE double precision domain and has a relative error less than 1 E-16.

I strongly recommend reading the papers by William T. Shaw, both w.r.t. the inverse Normal as well as other distributions. There is a lot of valuable info to be found.

For my part I prefer a less complex approximation which is then refined in a second step. The HP67/97 program in the Software Library here works this way.

Dieter
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RE: Best (and Newest?) Approximations for Popular Inverse Distributions - Dieter - 03-15-2019 04:27 PM



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