copBasic (version 1.5.1)

composite1COP: Composition of a Single Symmetric Copula

Description

The composition of a single copula is created by the following result related to composition of copulas in the reference. Let $\mathbf{C}(u,v)$ by a symmetric copula, $\mathbf{C} \ne \Pi$ (for $\Pi$ see P). A family of asymmetric copulas $\mathbf{C}_{\alpha,\beta}$, with parameters $0 < \alpha,\beta < 1, \alpha \ne \beta$, that includes $\mathbf{C}(u,v)$ as a limiting case, is given by

$$\mathbf{C}_{\alpha,\beta}(u,v) = u^\alpha v^\beta \cdot \mathbf{C}(u^{1-\alpha},v^{1-\beta})\mbox{.}$$

The composite2COP function is based on a more general result (see composite2COP for full details of compositing copulas.

Usage

composite1COP(u,v,para,...)

Arguments

u

A nonexceedance probability in X direction,

v

A nonexceedance probability in Y direction,

para

A special parameter list() (see Note), and

...

Additional arguments to pass.

Value

• A value for the composited copula is returned.

References

Salvadori, G., De Michele, C., Kottegoda, N.T., and Rosso, R., 2007, Extremes in Nature---An approach using copulas: Springer, 289 p.

See Also

COP, composite2COP

Examples

alpha <- 0.24; beta <- 0.23
Theta1 <- NA;

# The W() and PSP() copulas do not take parameters, but show how
# the parameters (ThetaX) would be set should either or both of the
# copulas require parameters.
para   <- list(alpha=alpha,      beta=beta,
                cop1=W,          para1=c(Theta1))
t <- composite1COP(0.4,0.6,para)
print(t)
print(W(0.4,0.6))