R help - Jun 2008 - Generate Random Samples

Hi,

I am a newbie to R and I am working with a Mac.

Is there any package that I can use to generate random samples from a  
user defined distribution ?  That is , I define a distribution  
function ( maybe multi dimension ) and I want some random samples  
generated from my this distribution.

Or, there is a more specific problem . If I have a three component  
mixture with each of them being normal distribution( say 3  
dimension ) , is there any package that I can use to generate random  
samples from this mixture . I know I can generate random samples from  
each individual component. However, can I just add them directly????

Thanks.










--------------------------
Peng Jiang
??
Ph.D. Candidate

Antai College of Economics & Management
????????
Department of Mathematics
???
Shanghai Jiaotong University (Minhang Campus)
800 Dongchuan Road
200240 Shanghai
P. R. China

To answer your specific question, you can use mvrnorm (from MASS, i.e.
library(MASS)) to generate each component.
To generate a mixture with three components (Prob(1 st component) = p1,
Prob(2nd component) = p2, Prob(3rd component) = p3, p1+p2+p3=1), you can
generate a uniformly distributed variable X in (0,1) and then generate the 1st
component if X < p1, the 2nd one if p1 <= X < p1+p2 and the 3rd one if
X >=p1+p2.


--- On Fri, 13/6/08, Peng Jiang <jp021 at sjtu.edu.cn> wrote:
> From: Peng Jiang <jp021 at sjtu.edu.cn>
> Subject: [R] Generate Random Samples
> To: r-help at r-project.org
> Received: Friday, 13 June, 2008, 1:24 AM
> Hi,
> 
> I am a newbie to R and I am working with a Mac.
> 
> Is there any package that I can use to generate random
> samples from a  
> user defined distribution ?  That is , I define a
> distribution  
> function ( maybe multi dimension ) and I want some random
> samples  
> generated from my this distribution.
> 
> Or, there is a more specific problem . If I have a three
> component  
> mixture with each of them being normal distribution( say 3 
> 
> dimension ) , is there any package that I can use to
> generate random  
> samples from this mixture . I know I can generate random
> samples from  
> each individual component. However, can I just add them
> directly????
> 
> Thanks.
> 
> 
> 
> 
> 
> 
> 
> 
> 
> 
> --------------------------
> Peng Jiang
> ??
> Ph.D. Candidate
> 
> Antai College of Economics & Management
> ????????
> Department of Mathematics
> ???
> Shanghai Jiaotong University (Minhang Campus)
> 800 Dongchuan Road
> 200240 Shanghai
> P. R. China
> 
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