# Re: [R] multivariate F distribution

From: Dimitris Rizopoulos <dimitris.rizopoulos_at_med.kuleuven.be>
Date: Thu 04 Aug 2005 - 18:43:15 EST

Well, there is a way for constructing a "multivariate F" (i.e., a multivariate distribution with F marginals), using copulas, thanks to Jun Yan's copula package. For instance, in for the bivariate case

library(copula)
x <- mvdc(claytonCopula(2), c("f", "f"),

list(list(df1 = 8, df2 = 9), list(df1 = 8, df2 = 9))) x
contour(x, dmvdc, xis = seq(1e-04, 2, len = 51), yis = seq(1e-04, 2, len = 51))

x.samp <- rmvdc(x, 1000)
hist(x.samp[, 1])
hist(x.samp[, 2])

Regarding the "correlation", the Clayton copula for theta = 2 gives Kendall's tau = 0.5, e.g.,

cor(x.samp, method = "kendall")

Best,
Dimitris

Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

```Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.be/biostat/
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```
• Original Message ----- From: "Peter Dalgaard" <p.dalgaard@biostat.ku.dk> To: "Anna Oganyan" <aoganyan@niss.org> Cc: <r-help@stat.math.ethz.ch> Sent: Thursday, August 04, 2005 10:05 AM Subject: Re: [R] multivariate F distribution

Anna Oganyan <aoganyan@niss.org> writes:

> Dear List,
>
> Is there any function in R to generate multivariate F distribution
> with
> given correlation/covariance matrix?
>
> Actually, I just want to generate some 2-dimentional non-normal data
> sets (skewed) for low (may be around 0.3 cor coeff.) negatively and
> also
> positively correlated variables .
>
>
> Anna

Er, what is "multivariate F"? I have a guess (solve(A,B) where A and B have independent Wishart distributions with the same covariance matrix -- the matrix that gets summarized into Wilk's Lambda, Pillai's trace, etc.) but Googling also pops up something about "inverted Dirichlet" which may or may not be equivalent.

Wishart variates can be generate from (multivariate) normals in a brute-force way using crossprod(). Some may have thought up a more efficient way.

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