# [Rd] qgamma inaccuracy (PR#12324)

skylab.gupta at gmail.com skylab.gupta at gmail.com
Thu Aug 7 12:14:52 CEST 2008

```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
 1.000000e-100  1.871683e-51  1.478731e-52  1.444034e-53  1.440606e-54
  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
 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.

```