[WP34s] A set of new quantile functions

[Dieter]

(05-25-2014 09:40 PM)Dieter Wrote:  I now would like to propose a similar solution for the Chi² quantile. Here things are a bit more complex: a regular Halley iteration can be set up easily, as shown in another earlier thread, but there are issues with large degrees of freedom. Although the first Chi² estimate is only approx. 11% low in the worst case, this can mean that the CDF of this can be off by several orders of magnitude. This leads to very slow convergence in the first 2...10 iterations which essentially apply the same correction until the estimate is sufficiently accurate and rapid convergence starts.

Recent tests showed that a similar behaviour may also occur with the Student quantile function. Up to now I only noticed this in extreme cases out of the SP working range, and here six or seven iterations seem to be sufficient. So the number of allowed iterations initially stored in R01 should be set to 8 for the moment. I will take a closer look at this and see if an approach similar to the Chi² case will eliminate this.

Dieter