(35S) Statistical Distributions Functions

[Dieter]

(10-29-2015 07:18 AM)Dieter Wrote:  I am not quite happy with the initial guess of the Chi² quantile. This is a very stripped down version of what's implemented in the 34s. But a more sophisticated version that usually converges within 3...5 iterations would require an estimate for the Normal quantile, which is also true for the Student inverse. So this can be done in a unified package that includes all three (or four) distributions.

I now tried this with the Chi² and Student programs. Both calculate a quite good first guess for the quantile which is based on a simple approximation of the Normal quantile. The previous Chi² example (10 dof and p=0,95) converges after just three iterations. The initial estimate was 18,24 with 18,307 being the correct result. In most cases, both for Chi² and Student, merely 3...5 iterations will do. This approach requires one or two additional subroutine(s) for the Normal estimate, and the complete Student program (including the inverse) finally has about 200 steps.

Dieter