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

 From Fabien Bertho 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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