copBasic (version 2.1.5)

convexCOP: Convex Combination of an Arbitrary Number of Copulas

Description

The convex composition of \(N\) number of copulas (Salvadori et al., p. 132, 2007) provides for complexity extension between coupla families. Let \(\mathbf{C}_{i}\) be a copula with respective vector of parameters \(\Theta_i\), then the convex combination of these copulas is

$$\mathbf{C}^{\times}_{\omega}(u,v) = \sum_{i=1}^N \omega_i \mathbf{C}_{i}(u, v; \Theta_i)\mbox{,}$$

where \(\sum_{i=1}^N \omega_i = 1\) for \(N\) number of copulas. The weights \(\omega\) are silently treated as \(1/N\) if the weights element is absent in the R list argument para.

Usage

convexCOP(u,v, para, ...)

Arguments

u

Nonexceedance probability \(u\) in the \(X\) direction;

v

Nonexceedance probability \(v\) in the \(Y\) direction;

para

A special parameter list (see Note); and

...

Additional arguments to pass to the copula.

Value

Value(s) for the convex combination 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

convex2COP

Examples

# NOT RUN {
# The copulas and parameters are named by sequence number appended to cop and para.
para1 <- list(cop1=GHcop, cop2=PLcop, para1=8, para2=.03, weights=c(.8,.2))
para2 <- list(cop1=GHcop, cop2=PLcop, para1=8, para2=.03, alpha=0.8)
H <- convexCOP( 0.6,0.4, para=para1)
G <- convex2COP(0.6,0.4, para=para2)
if( abs(H-G) <= 1e-6 )  message("They are equal.")

# }
# NOT RUN {
# A convex combination of three copulas. A GHcop with strong positive association and
# a Plackett with strong negative association, and independence. The weights favor the
# GHcop but a little outlier and expansive spread is superimposed on the core trend.
para <- list(cop1=GHcop, cop2=PLcop, cop3=P,
             para1=8, para2=.03, para3=NA, weights=c(40,7,10))
UV <- simCOP(1000, cop=convexCOP, para=para, lwd=0.8) #
# }