Re: st: Beta distribution

[Robert A Yaffee <bob.yaffee@nyu.edu>]

Rob,
   If you call the a and b parameter both shape parameters,  you may fix the mean of the beta distribution with E(x) = a/(a + b) .  If you refer to both the a and b as shape parameters,  you can also compute the variance = (a*b)/(a + b)^2(a + b  + 1).   You can set the mean and variance to whatever you need them to be and then insert those parameters into the rbeta(a,b) function.
 -  Bob

Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2009.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: "Hartman, Rob" <rhartman@mitre.org>
Date: Thursday, January 27, 2011 10:35 pm
Subject: st: Beta distribution
To: "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>


> Hi Listers,
> Is it possible to generate a random beta variable with
> -a fixed/predetermined range of possible values, as well as 
> -a fixed mean, but still have
> -the ability to vary the shape parameters meaningfully?  
> 
> This is more a distributions question in general than a stata question 
> in particular, but I would want to implement using stata.
> 
> I want to test the power of a mean comparison test (with means/mean 
> difference specified a priori) for variables with fixed range of 
> values (0 to 2 in this case) but where the underlying distributions 
> are anyone's guess. That is, I want to be able to experiment w/ 
> different distributional properties while maintaining the mean and range.
> 
> Would appreciate any guidance, including alternative approaches.
> 
> Thanks,
> Rob
> 
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