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

[Bill.Venables@csiro.au]

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 at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Tolga Uzuner
Sent: Monday, 11 April 2005 9:01 AM
To: tolga at coubros.com
Cc: r-help at stat.math.ethz.ch
Subject: [R] Re: beta distribution in terms of it's mean and
standarddeviation


Tolga Uzuner wrote:

> 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.

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