copula (version 0.9-5)

Copula: Copula distribution functions

Description

Density, distribution function, and random generation for a copula object.

Usage

dcopula(copula, u)
pcopula(copula, u)
rcopula(copula, n)

Arguments

copula

a "copula" object.

u

a vector of the copula dimension or a matrix with number of rows being the copula dimension, giving the coordinates of the points where the density or distribution function needs to be evaluated.

n

number of observations to be generated.

Value

• "dcopula" gives the density, "pcopula" gives the distribution function, and "rcopula" generates random variates.

Details

The density function of an Archimedean copula was obtained by differentiating the distribution function symbolically using Mathematica and then processed by deriv to give algorithmic expressions. The maximum dimension implemented is 10 for Clayton and Gumbel, and 6 for Frank. The distribution function of a t copula uses pmvt from package mvtnorm. The density function of a t copula uses the dmst from package sn. The random number generator for an Archimedean copula uses the conditional approach for the bivariate case and the Marshal-Olkin (1988) approach for dimension greater than 2.

References

E.W. Frees and E.A. Valdez (1998). Understanding relationships using copulas. North American Actuarial Journal, 2:1--25. C. Genest and A.-C. Favre (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering, 12:347--368. H. Joe (1997). Multivariate Models and Dependence Concepts. Chapman and Hall, London.

A.W. Marshal and I. Olkin (1988). Families of multivariate distributions. Journal of the American Statistical Association, 83:834--841. R.B. Nelsen (2006). An introduction to Copulas. Springer, New York.

See Also

copula-class, ellipCopula, archmCopula, fgmCopula.

Examples

norm.cop <- normalCopula(0.5)
norm.cop
x <- rcopula(norm.cop, 100)
plot(x)
dcopula(norm.cop, x)
pcopula(norm.cop, x)
persp(norm.cop, dcopula)
contour(norm.cop, pcopula)
## a 3-dimensional normal copula
u <- rcopula(normalCopula(0.5, dim = 3), 1000)
## scatterplot3d(u)
## a 3-dimensional clayton copula
v <- rcopula(claytonCopula(2, dim = 3), 1000)
## scatterplot3d(v)