R: Convert (Rho) Matrices to and From Parameter Vectors
p2P
R Documentation
Convert (Rho) Matrices to and From Parameter Vectors
Description
p2P() creates a matrix from a given
vector of parameters. P2p() creates a
numeric vector from a given matrix,
currently useful for elliptical copulas.
getSigma() returns the d * d symmetric
matrix Σ which is called “Rho” as well, written
(capital Greek rho !) as P (and hence sometimes
erronously pronounced "Pee").
Note that getSigma() works for all elliptical copulas and uses
p2P() for the “unstuctured” case, dispstr = "un".
Usage
p2P(param, d)
P2p(P)
getSigma(copula)
Arguments
param
a parameter vector.
d
dimension of the resulting matrix.
P
matrix which should be converted to a vector.
copula
an elliptical copula, i.e., an object (extending)
class ellipCopula; typically resulting from
tCopula() or normalCopula().
Details
These auxiliary functions are often used when working with
elliptical copulas.
Value
p2P:
a symmetric matrix with ones on the
diagonal and the values of param filled column-wise below the
diagonal (which corresponds to row-wise filling above the diagonal).
P2p:
vector of column-wise below-diagonal
entries of P (equal to the row-wise above-diagonal entries in
case of a symmetric matrix).
getSigma:
matrix as from p2P()
for all cases of elliptical copulas.
See Also
ellipCopula, tCopula, normalCopula.
Examples
## display the definitions
p2P
P2p
param <- (2:7)/10
tC <- tCopula(param, dim = 4, dispstr="un", df = 3)
## consistency of the three functions :
P <- p2P(param, d=4)
stopifnot(identical(param, P2p(P)),
identical(P, getSigma(tC)))
## Toeplitz case:
(tCt <- tCopula((2:6)/10, dim = 6, disp = "toep"))
(rhoP <- tCt@getRho(tCt))
stopifnot(identical(getSigma (tCt),
toeplitz (c(1, rhoP))))
providing 
.