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
Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.be/biostat/http://www.student.kuleuven.be/~m0390867/dimitris.htm
----- Original Message -----
From: "Peter Dalgaard" <p.dalgaard at biostat.ku.dk>
To: "Anna Oganyan" <aoganyan at niss.org>
Cc: <r-help at stat.math.ethz.ch>
Sent: Thursday, August 04, 2005 10:05 AM
Subject: Re: [R] multivariate F distribution
Anna Oganyan <aoganyan at 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 .
Thanks in advance.
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.
O__ ---- Peter Dalgaard ??ster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45)
35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45)
35327907
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