convexCOP {copBasic}

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.

Note

The following descriptions list in detail the structure and content of the para argument but please reference the Examples to see the i notation:

copi

— The ith copula;

parai

— Vector of parameters \Theta_i; and

weights

— Optional vector of weights whose sum will be rescaled to unity; default is 1/N for each weight.

Author(s)

W.H. Asquith

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, breveCOP, convex2COP, composite1COP, composite2COP, composite3COP, glueCOP

Examples

# 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) #
## End(Not run)