copula (version 0.999-15)

matrix_tools: Tools to Work with Matrices

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".

extremePairs() identifies pairs with the largest (or smallest or both) entries in a symmetric matrix.

Usage

p2P(param, d = floor(1 + sqrt(2*length(param))))
P2p(P)
getSigma(copula)
extremePairs(x, n = 6, method = c("largest", "smallest", "both"), use.names = FALSE)

Arguments

param

a parameter vector.

d

dimension of the resulting matrix. The default is correct under the assumption (of p2P() in general!) that param is the lower-triangular part of a correlation matrix P and hence corresponds to ellipCopula(.., dispstr = "un").

P

a 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().

x

a symmetric matrix.

n

the number of pairs with smallest (or largest) values to be displayed.

method

a character string indicating the method to be used (with "largest" to comute the n pairs with largest entries in x (sorted in decreasing order); with "smallest" to compute the n pairs with smallest entries in x (sorted in increasing order); and with "both" to comute the 2n pairs with n largest entries and n smallest entries (sorted in decreasing order)).

use.names

A logical indicating whether colnames(x) are used as labels (if !is.null(colnames(x))).

Value

Details

These auxiliary functions are often used when working with elliptical copulas.

See Also

ellipCopula, tCopula, normalCopula.

Examples

## display the definitions
p2P
P2p
extremePairs

param <- (2:7)/10
tC <- tCopula(param, dim = 4, dispstr = "un", df = 3)
## consistency of the three functions :
P <- p2P(param) # (using the default 'd')
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))))