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

Jeff Newmiller jdnewmil at dcn.davis.CA.us
Sat Oct 26 07:25:13 CEST 2013

That would be an expected result. Recommend that you hit the books or use a search engine as basic theory like this is off topic here.
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Sent from my phone. Please excuse my brevity.

"Kramer, Christian" <Christian.Kramer at uibk.ac.at> wrote:
>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
>this looks more like a normal distribution than a t-distribution:
>b <- rt(1000,2)
>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,
>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
>R-help at r-project.org mailing list
>PLEASE do read the posting guide
>and provide commented, minimal, self-contained, reproducible code.

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