Normal distribution on 32E and 21S

[deffunc]

(02-04-2021 05:40 PM)Dave Britten Wrote:  As an aside, anybody happen to know how the 21S handles the F distribution and its inverse? All of the various HP application pacs seem to require that one of the degrees of freedom be even in their implementations of it, but the 21S imposes no such limitation.

I don't know which algorithm is used by the 21S, but a while back I had need for the t-distribution on my 27S. I implemented the continued fraction algorithm for the incomplete beta function recommended in chapter 6 of Numerical Recipes, 2nd Ed., for Q(t) and used Solve when I needed the inverse. Both the t and F distributions are special cases of the incomplete beta function. The method is slow to converge when the degrees of freedom are large, but mine were under 100 so that was never a problem. The 21S was restricted to dof < 200, if I remember correctly.

Numerical Recipes can be read online for free, and the 3rd Ed. explains how to use Halley's method for fast inverse. There is also Abramowitz and Stegun on their site, which lists the series and continued fraction formulae, and also polynomial and rational function approximations.

http://numerical.recipes/oldverswitcher.html