# pnacopula: Evaluation of (Nested) Archimedean Copulas In copula: Multivariate Dependence with Copulas

## Description

For a (nested) Archimedean copula (object of class nacopula) x, pCopula(u, x) (or also currently still pnacopula(x, u)) evaluates the copula x at the given vector or matrix u.

## Usage

 1 2 3 4 5 ## S4 method for signature 'matrix,nacopula' pCopula(u, copula, ...) ## *Deprecated*: pnacopula(x, u)

## Arguments

 copula, x (nested) Archimedean copula of dimension d, that is, an object of class nacopula, typically from onacopula(..). u a numeric vector of length d or matrix with d columns. ... unused: potential optional arguments passed from and to methods.

## Details

The value of an Archimedean copula C with generator psi at u is given by

C(u) = psi(psi^{-1}(u_1)+...+psi^{-1}(u_d)), u in [0,1]^d.

The value of a nested Archimedean copula is defined similarly. Note that a d-dimensional copula is called nested Archimedean if it is an Archimedean copula with arguments possibly replaced by other nested Archimedean copulas.

## Value

A numeric in [0,1] which is the copula evaluated at u. (Currently not parallelized.)

## Note

pCopula(u, copula) is a generic function with methods for all our copula classes, see pCopula.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ## Construct a three-dimensional nested Joe copula with parameters ## chosen such that the Kendall's tau of the respective bivariate margins ## are 0.2 and 0.5. theta0 <- copJoe@iTau(.2) theta1 <- copJoe@iTau(.5) C3 <- onacopula("J", C(theta0, 1, C(theta1, c(2,3)))) ## Evaluate this copula at the vector u u <- c(.7,.8,.6) pCopula(u, C3) ## Evaluate this copula at the matrix v v <- matrix(runif(300), ncol=3) pCopula(v, C3) ## Back-compatibility check stopifnot(identical( pCopula (u, C3), suppressWarnings( pnacopula(C3, u))), identical( pCopula (v, C3), suppressWarnings( pnacopula(C3, v))))

copula documentation built on Nov. 17, 2017, 2:25 p.m.