R: Evaluation of (Nested) Archimedean Copulas

pnacopula {copula} | R Documentation

## Evaluation of (Nested) Archimedean 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

    ## 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

    ## 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))))

[Package copula version 1.0-1 Index]