R: Construction of Fréchet-Hoeffding Bound Copula Objects

fhCopula {copula} | R Documentation

## Construction of Fréchet-Hoeffding Bound Copula Objects

### Description

Constructs the Fréchet-Hoeffding lower and upper bound copulas aka W and M.

### Usage

    fhCopula(family = c("upper", "lower"), dim = 2L)

    lowfhCopula(dim = 2L)
     upfhCopula(dim = 2L)

### Arguments

`family` | a character string specifying the Fréchet-Hoeffding bound copula.
`dim` | the dimension of the copula; note that the lower Fréchet-Hoeffding bound is only available in the bivariate case.

### Value

A copula object of class `"lowfhCopula"` or `"upfhCopula"`.

### Note

`fhCopula()` is a wrapper for `lowfhCopula()` and `upfhCopula()`.

The `dCopula()` method will simply return an error for these copulas (as their density does not exist). Also, since the Fréchet-Hoeffding bound copulas are not parametric, certain methods available for parametric copulas are not available.

### Examples

    ## Lower bound  W : -------------------------

    try(W <- lowfhCopula(dim = 3)) # lower bound is *not* a copula for dim > 2
    W <- lowfhCopula()
    wireframe2(W, FUN = pCopula)
    plot(W, n=100) # perfect anti-correlation ( rho = tau = -1 )

    ## Upper bound  M : -------------------------

    wireframe2(upfhCopula(dim = 2), pCopula)
    M <- upfhCopula(dim = 3)
    set.seed(271)
    splom2(M, n = 100) # "random" data: all perfectly correlated

[Package copula version 1.0-1 Index]