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

[Rolf Turner]

On 10/26/13 21:20, Tsjerk Wassenaar wrote:
> Of course. But the point is that this would happen with summing 
> samples from any distribution.

***What*** would happen?  You are confused about the t-distribution.  
(And the CLT and probably
a lot of other things.)  Back to the text-books.

     cheers,

     Rolf Turner
>
> Cheers,
>
> Tsjerk
>
>
> On Sat, Oct 26, 2013 at 10:14 AM, Rolf Turner <r.tur...@auckland.ac.nz 
> <mailto:r.tur...@auckland.ac.nz>> wrote:
>
>
>
>     Absolutely nothing to do with the CLT.  If X_1, ..., X_n are
>     i.i.d. N(mu, sigma^2) then
>     Xbar is N(mu,sigma^2/n).  Exactly.  No asymptotics, no
>     approximations, no CLT.
>
>         cheers,
>
>         Rolf Turner
>
>
>     On 10/26/13 20:17, Tsjerk Wassenaar wrote:
>>     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.kra...@uibk.ac.at  <mailto:christian.kra...@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  <tel:%2B43%20512%20507%2057103>
>>>     Homepage: http://homepage.uibk.ac.at/~c72448/kramer.html
>>>     <http://homepage.uibk.ac.at/%7Ec72448/kramer.html> Email:
>>>     christian.kra...@uibk.ac.at <mailto:christian.kra...@uibk.ac.at>
>>>     ______________________________________________
>>>     R-help@r-project.org <mailto: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.
>>
>>
>>     ______________________________________________
>>     R-help@r-project.org  <mailto:R-help@r-project.org>  mailing list
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>>     PLEASE do read the posting 
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>
>
>
>
> -- 
> Tsjerk A. Wassenaar, Ph.D.
>


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