[Rd] qgamma inaccuracy (PR#12324)

[Prof Brian Ripley]

This is a really extreme usage.  AFAICS the code works well enough down to 
shape=1e-10 or so, e.g.

> qgamma(1e-10, 5e-11, lower.tail=FALSE)
[1] 0.08237203

I would be interested to know what substantive problem you were trying to 
solve here that required such values.

I am pretty sure that a completely different algorithm will be required. 
For completeness we may write that in due course, but for now (R 2.7.2) I 
suggest just issuing a warning for miniscule 'shape'.

On Thu, 7 Aug 2008, skylab.gupta at gmail.com wrote:

> Full_Name:
> Version: 2.7.1 (2008-06-23)
> OS: windows vista
> Submission from: (NULL) (216.82.144.137)
>
>
> Hello,
>
> I have been working with various probability distributions in R, and it seems
> the gamma distribution is inaccurate for some inputs.
>
> For example, qgamma(1e-100, 5e-101, lower.tail=FALSE) gives: 1.0. However, it
> seems this is incorrect; I think the correct answer should be
> 0.082372029620717283. When I check these numbers using pgamma, I get:
>
> pgamma(1,5e-101, lower.tail=FALSE) = 9.1969860292859463e-102
> and
> pgamma(0.082372029620717283,5e-101, lower.tail=FALSE) =
> 1.0000000000000166e-100.
>
> Similarly, for example:
> qgamma(1e-100,0.005,lower.tail=FALSE) = 109.36757177007101
> pgamma(109.36757177007101, 0.005, lower.tail=FALSE) = 1.4787306506694758e-52.
>
> This looks completely wrong. The correct value, I think, should be
> 219.59373661415756. In fact,
> pgamma(219.59373661415756, 0.005, lower.tail=FALSE) = 9.9999999999999558e-101.
>
> In fact, when I do the following in R, the results are completely wrong,
>
> x<-c(5e-1,5e-2,5e-3,5e-4,5e-5,5e-6,5e-7,5e-8,5e-9,5e-10)
> z1 <-qgamma(1e-100,x,lower.tail=FALSE)
> y<-pgamma(z1,x,lower.tail=FALSE)
>
> The value of y that I get should be close to 1e-100, but they are not:
>
>> y
> [1] 1.000000e-100  1.871683e-51  1.478731e-52  1.444034e-53  1.440606e-54
> [6]  1.440264e-55  1.440230e-56  1.440226e-57  1.440226e-58  1.440226e-59
>
> The correct values of z1 should be:
> z1true <- c(226.97154111939946, 222.15218724493326, 219.59373661415756,
> 217.27485383840451, 214.98015408183574, 212.68797118872064, 210.39614286838227,
> 208.10445550564617, 205.81289009100664, 203.52144711679352)
>
> With these values of z1true, we get the expected values:
> y<-pgamma(z1true,x,lower.tail=FALSE)
>> y
> [1] 1e-100 1e-100 1e-100 1e-100 1e-100 1e-100 1e-100 1e-100 1e-100 1e-100
>
>
> I am using the precompiled binary version of R, under Windows Vista.
> -----------
>> version
>    _
> platform       i386-pc-mingw32
> arch           i386
> os             mingw32
> system         i386, mingw32
> status
> major          2
> minor          7.1
> year           2008
> month          06
> day            23
> svn rev        45970
> language       R
> version.string R version 2.7.1 (2008-06-23)
> ------------
>
> So, it seems qgamma is inaccurate for small probability values in the upper
> tail, when the shape parameter is also small.
>
> ______________________________________________
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> 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