Function to compute the multinomial beta function?

[Gregory Gentlemen]

Dear R-users,

Is there an R function to compute the multinomial beta function? That is, the normalizing constant that arises in a Dirichlet distribution. For example, with three parameters the beta function is Beta(n1,n2,n2) = Gamma(n1)*Gamma(n2)*Gamma(n3)/Gamma(n1+n2+n3)

Thanks in advance for any assisstance.

Regards,
Greg



        [[alternative HTML version deleted]]

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[Matt Shotwell]

How about this?

mbeta <- function(...) {
    exp(sum(lgamma(c(...)))-lgamma(sum(c(...))))
}
 
> gamma(5)*gamma(6)*gamma(7)/gamma(18)
[1] 5.829838e-09
> mbeta(5,6,7)
[1] 5.829838e-09



On Mon, 2010-07-05 at 17:10 -0400, Gregory Gentlemen wrote:

> Dear R-users,
>
> Is there an R function to compute the multinomial beta function? That is, the normalizing constant that arises in a Dirichlet distribution. For example, with three parameters the beta function is Beta(n1,n2,n2) = Gamma(n1)*Gamma(n2)*Gamma(n3)/Gamma(n1+n2+n3)
>
> Thanks in advance for any assisstance.
>
> Regards,
> Greg
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--
Matthew S. Shotwell
Graduate Student
Division of Biostatistics and Epidemiology
Medical University of South Carolina
http://biostatmatt.com

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[Robert A LaBudde]

At 05:10 PM 7/5/2010, Gregory Gentlemen wrote:
>Dear R-users,
>
>Is there an R function to compute the multinomial beta function?
>That is, the normalizing constant that arises in a Dirichlet
>distribution. For example, with three parameters the beta function
>is Beta(n1,n2,n2) = Gamma(n1)*Gamma(n2)*Gamma(n3)/Gamma(n1+n2+n3)

 > beta3<- function (n1, n2, n3)
exp(lgamma(n1)+lgamma(n2)+lgamma(n3)-lgamma(n1+n2+n3))
 > beta3(5,3,8)
[1] 1.850002e-07

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: [hidden email]
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
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Virginia Beach, VA 23464-3239            Fax: [phone]

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[Robin Hankin-2]

It's usually better to build vectorization in to functions:

 > beta3<- function (n1, n2, n3)
exp(lgamma(n1)+lgamma(n2)+lgamma(n3)-lgamma(n1+n2+n3))
 > f <- function(x){exp(sum(lgamma(x))-lgamma(sum(x)))}
 > beta3(5,3,8)
[1] 1.850002e-07
 > f(c(5,3,8))
[1] 1.850002e-07
 >

rksh


On 07/06/2010 01:54 AM, Robert A LaBudde wrote:

> At 05:10 PM 7/5/2010, Gregory Gentlemen wrote:
>> Dear R-users,
>>
>> Is there an R function to compute the multinomial beta function? That
>> is, the normalizing constant that arises in a Dirichlet distribution.
>> For example, with three parameters the beta function is
>> Beta(n1,n2,n2) = Gamma(n1)*Gamma(n2)*Gamma(n3)/Gamma(n1+n2+n3)
>
> > beta3<- function (n1, n2, n3)
> exp(lgamma(n1)+lgamma(n2)+lgamma(n3)-lgamma(n1+n2+n3))
> > beta3(5,3,8)
> [1] 1.850002e-07
>

--
Robin K. S. Hankin
Uncertainty Analyst
University of Cambridge
19 Silver Street
Cambridge CB3 9EP
01223-764877

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