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Re: st: RE: RE: Generation of three uniform random variables that sum to one


From   Fabien Bertho <fabien.bertho@sciences-po.org>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: RE: Generation of three uniform random variables that sum to one
Date   Thu, 21 Oct 2010 17:14:32 +0200 (CEST)

Thank you.

> ----------------------------------------
> From: Nick Cox <n.j.cox@durham.ac.uk>
> Sent: Thu Oct 21 16:24:11 CEST 2010
> To: 'statalist@hsphsun2.harvard.edu' <statalist@hsphsun2.harvard.edu>
> Subject: st: RE: RE: Generation of three uniform random variables that sum to one
> 
> 
> I may be being stupid, but I think your conditions can not be satisfied. 
> 
> If 
> 
> a + b + c = 1 
> 
> then 
> 
> E(a) + E(b) + E(c) = 1 
> 
> And as a, b and c have the same distribution their means must be equal at 1/3. 
> 
> (This problem is familiar to me as data that "fill" a triangular plot, as e.g. -triplot- from SSC.) 
> 
> Nick 
> n.j.cox@durham.ac.uk 
> 
> Fabien Bertho
> 
> Thank you for this.
> 
> Actually, I would like that the three random variables have an uniform distribution too. If their distributions were uniform, means would be .5 and standard deviations .28
> 
> But, with the formula you suggest means = .33 and standard deviations = .16
> 
> What do you think? What can I do?
> 
> Nick Cox <n.j.cox@durham.ac.uk>
>  
> > foreach v in a b c { 
> > 	gen `v' = runiform()
> > }
> > gen total = a + b + c 
> > foreach v in a b c { 
> > 	replace `v' = `v' / total 
> > }
> > 
> > Nick 
> > n.j.cox@durham.ac.uk 
> > 
> > Fabien Bertho
> > 
> > I would like to generate three uniform random variables. And, the sum of these three variables equals to one.
> > 
> 
> *
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