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, [EMAIL PROTECTED] 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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--
Brian D. Ripley, [EMAIL PROTECTED]
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
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