R help - Oct 2013 - Adding up normally distributed numbers seems to not create a t-distribution

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

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.
---------------------------------------------------------------------------
Jeff Newmiller                        The     .....       .....  Go Live...
DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live
Go...
                                      Live:   OO#.. Dead: OO#..  Playing
Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
/Software/Embedded Controllers)               .OO#.       .OO#.  rocks...1k
--------------------------------------------------------------------------- 
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
>
>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
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide
>http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

Hi :)

Try this with other distributions too... And then search for 'central limit
theorem'.

Cheers,

Tsjerk


On Fri, Oct 25, 2013 at 4:48 PM, Kramer, Christian <
Christian.Kramer@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
>
> 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@uibk.ac.at
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
Tsjerk A. Wassenaar, Ph.D.

	[[alternative HTML version deleted]]