From: <Bill.Venables_at_csiro.au>

Date: Mon 11 Apr 2005 - 09:53:03 EST

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R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Mon Apr 11 09:59:46 2005

Date: Mon 11 Apr 2005 - 09:53:03 EST

For three of the beta distribution functions in R the parameters
defining the distribution are alpha, beta and 'ncp'. Pretty trivially,
there is no bijection between these three and the mean and variance, but
for the special case of ncp = 0, I think there is.

Rather than just write it down, it's probably a good idea to see how to get it.

Note that

mu = alpha/(alpha+beta) s2 = alpha*beta/((alpha+beta)^2*(alpha+beta+1)) = mu*(1-mu)/(alpha+beta+1)

So as an intermediate result put

alpha + beta = mu*(1-mu)/s2 - 1 (= ab, say, which must be positive or you are in trouble)

giving

alpha = mu*ab

beta = (1-mu)*ab

Go forth and write your versions of the (central) beta distribution support functions...

Bill Venables.

-----Original Message-----

From: r-help-bounces@stat.math.ethz.ch

[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Tolga Uzuner
Sent: Monday, 11 April 2005 9:01 AM

To: tolga@coubros.com

Cc: r-help@stat.math.ethz.ch

Subject: [R] Re: beta distribution in terms of it's mean and
standarddeviation

*> Hi,
**>
*

> Is the beta distribution implemented in terms of it's mean and

*> standard deviation, as opposed to alpha and beta, in any R package ?
**>
**> Thanks
**> Tolga
**>
*

Hmm... answering my own question... guess there is no bijection between
{alpha,beta} and {mean,variance} which is why... ocurred to me after I
sent the question, unless someone disagrees.

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide!

http://www.R-project.org/posting-guide.html

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Mon Apr 11 09:59:46 2005

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