Re: binocdf inaccuracy in Octave

[Dr. Alexander Klein]

Am 08.07.2013 um 22:10 schrieb Daniel J Sebald:

> We should be a little careful here.  There was a discrepancy at one of the 
> extreme ends of the function.  Your modification may have just moved that 
> discrepancy to the other end of the range, i.e., when the argument is 1e-3 as 
> opposed to 1-1e-3.

Rik and Daniel,

thanks for the hints and the updated file!

As far as I can tell, Rik's new version produces correct results in most 
relevant cases. The one remaining pitfall is that "at the other end of the 
range" [Daniel], there are indeed many wrong results remaining:

- Firstly, as Daniel pointed out already, the new _and_ the old version will 
both produce a long string of ones for binocdf(0:50,50,0.001), but this cannot 
be remedied without resorting to multiple precision arithmetic, and the 
relative error is very small, of course.

- Secondly, the "1 - p"-term introduces a new point where catastrophic 
cancellation can occur, but only when p is _really_ small.

So, I think that Rik's patch should fix the problems for the most part.

Thanks again,

        Alex
-- 
Dr. Alexander Klein, Diplom-Mathematiker
TransMIT-Projektbereich für Mathematische Analysen und Feld-Simulationen
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