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# Re: st: Beta distribution

 From Robert A Yaffee To statalist@hsphsun2.harvard.edu Subject Re: st: Beta distribution Date Thu, 27 Jan 2011 23:20:14 -0500

```Rob,
You might want to take the a and b parameters of the beta distribution and
compute the mean of the distribution = a /(a + b) for each combination.

You might find the following program of use:

set more off
set obs 2000
gen a = .
gen b = .

forv i=1/9 {
forv j=1/9 {
gen beta`i'`j'=.
replace beta`i'`j' = rbeta(`i',`j')
save beta`i'`j', replace
}
}

forv i=1/9 {
forv j=1/9 {
qui summ beta`i'`j'
hist beta`i'`j', normal ///
title(" beta(a ,b) distribution a = `i' and b = `j'") ///
subtitle("Mean = a/(a+b)= `i'/(`i'+`j')")
}
}

I hope this helps.
- 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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```

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