[Rd] (PR#13999) Extreme values of non-central chisq (was Accuracy)

[Prof Brian Ripley]

You crossed the value ncp = 80: the help page warned you of 
cancellation there, and at p = 1 - 1e-12, that is what you got 
(badly).

On Sun, 11 Oct 2009, witkovsky at savba.sk wrote:

> Full_Name: Viktor Witkovsky
> Version: 2.9.2
> OS: Windows XP
> Submission from: (NULL) (78.98.89.227)
>
>
> Hello,
>
> I have found strange behavior of the function qchisq (the non-central qchisq is
> based on inversion of pchisq, which is further based on pgamma). The function
> gives wrong results without any warning. For example:
>
> qchisq(1e-12,1,8.94^2,lower.tail=FALSE) gives 255.1840972465858 (notice that
> here the correct value should be 255.1841334848075),
> but
> qchisq(1e-12,1,8.95^2,lower.tail=FALSE) gives 1249.681320136836
> Here, the correct value should be 255.5037231613135.
>
> So, it seems that qchisq is inaccurate for small probability values and larger
> non/centrality parameter.

Actually, for probability values near 1, and it does say so in the 
documentation.  But see

> qchisq(1e-12, 1, 81, lower.tail=FALSE)
[1] 1258.412
> qchisq(1-1e-12, 1, 81)
[1] 257.1488

which I suggest gives you a workaround -- we'll look into giving a 
warning from the code.

>
> I am using the precompiled binary version of R, under Windows XP.
>
>               _
> platform       i386-pc-mingw32
> arch           i386
> os             mingw32
> system         i386, mingw32
> status
> major          2
> minor          9.2
> year           2009
> month          08
> day            24
> svn rev        49384
> language       R
> version.string R version 2.9.2 (2009-08-24)
>
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595