copula (version 0.999-14)

p2P: 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 $\Sigma$ 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().

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.

Details

These auxiliary functions are often used when working with 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))))