convexCOP {copBasic}R Documentation

Convex Combination of an Arbitrary Number of Copulas

Description

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

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

where i=1Nωi=1\sum_{i=1}^N \omega_i = 1 for NN number of copulas. The weights ω\omega are silently treated as 1/N1/N if the weights element is absent in the R list argument para.

Usage

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

Arguments

u

Nonexceedance probability uu in the XX direction;

v

Nonexceedance probability vv in the YY 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 iith copula;

parai

— Vector of parameters Θi\Theta_i; and

weights

— Optional vector of weights whose sum will be rescaled to unity; default is 1/N1/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)

[Package copBasic version 2.2.4 Index]