[R] Adding up normally distributed numbers seems to not create a t-distribution

[Kramer, Christian]

Hi there,

I have found a strange behavior in R that puzzles me - maybe it is a bug or a basic scientific misunderstanding of mine… anyway, I would highly appreciate some feedback on this, since I did not find anything on the internet.

I am trying to simulate a t-distribution by adding up normally distributed numbers:

a  <- (rnorm(1000) + rnorm(1000) + rnorm(1000) )/3

However, when I look at the distribution using

qqnorm(a)

this looks more like a normal distribution than a t-distribution:

b <- rt(1000,2)
qqnorm(b)

Is this to be expected? Or is this an issue with the random number generator or something else?

Thanks a lot for replies in advance,
Christian

--------------------------------------------
Dr. Christian Kramer
Theoretical Chemistry
University of Innsbruck
Innrain 82
A-6020 Innsbruck
Tel.: +43 512 507 57103
Homepage: http://homepage.uibk.ac.at/~c72448/kramer.html
Email: Christian.Kramer at uibk.ac.at