# [Rd] qgamma inaccuracy (PR#12324)

From: <skylab.gupta_at_gmail.com>
Date: Thu, 07 Aug 2008 12:14:52 +0200 (CEST)

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 Received on Thu 07 Aug 2008 - 12:56:40 GMT

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