convexCOP {copBasic} | R Documentation |
Convex Combination of an Arbitrary Number of Copulas
Description
The convex composition of number of copulas (Salvadori et al., p. 132, 2007) provides for complexity extension between coupla families. Let
be a copula with respective vector of parameters
, then the convex combination of these copulas is
where for
number of copulas. The weights
are silently treated as
if the
weights
element is absent in the R list
argument para
.
Usage
convexCOP(u,v, para, ...)
Arguments
u |
Nonexceedance probability |
v |
Nonexceedance probability |
para |
A special parameter |
... |
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
th copula;
parai
— Vector of parameters
; and
weights
— Optional vector of weights whose sum will be rescaled to unity; default is
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)