fhCopula: Construction of Fréchet-Hoeffding Bound Copula Objects

In copula: Multivariate Dependence with Copulas

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

copula documentation built on Sept. 11, 2024, 7:48 p.m.