fgmCopula: Construction of a fgmCopula Class Object

In copula: Multivariate Dependence with Copulas

Construction of a fgmCopula Class Object

Description

Constructs a multivariate multiparameter Farlie-Gumbel-Morgenstern copula class object with its corresponding parameters and dimension.

Usage

fgmCopula(param, dim = 2)

Arguments

param	a numeric vector specifying the parameter values.
dim	the dimension of the copula.

Value

A Farlie-Gumbel-Morgenstern copula object of class "fgmCopula".

Note

Note that a d-dimensional fgmCopula must have npar= 2^d - d - 1 parameters. The verification of the validity of the parameter values is of high complexity and may not work for high dimensional copulas.

The random number generation needs to be properly tested, especially for dimensions higher than 2.

References

Nelsen, R. B. (2006), An introduction to Copulas, Springer, New York.

See Also

Copula, copula-class, fitCopula.

Examples

## length(param) = #{parameters}  for  d-dimensional  FGM copula:
d <- 2:10; rbind(d, npar = 2^d - d - 1)
## d       2    3    4    5    6    7    8    9   10
## npar    1    4   11   26   57  120  247  502 1013

## a bivariate example
fgm.cop <- fgmCopula(1)
x <- rCopula(1000, fgm.cop)
cor(x, method = "kendall")
tau(fgm.cop)
cor(x, method = "spearman")
rho(fgm.cop)
persp  (fgm.cop, dCopula)
contour(fgm.cop, dCopula)

## a trivariate example with wrong parameter values
try(
 fgm2.cop <- fgmCopula(c(1,1,1,1), dim = 3)
) # Error: "Bad vector of parameters"

## a trivariate example with satisfactory parameter values
fgm2.cop <- fgmCopula(c(.2,-.2,-.4,.6), dim = 3)
fgm2.cop

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