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


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Generation of three uniform random variables that sum to one
Date   Thu, 21 Oct 2010 15:24:11 +0100

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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