copBasic (version 1.7.1)

EMPIRgridder: Derivatives of the Grid of the Bivariate Emprical Copula for V with respect to U

Description

Generate derivatives of $V$ with respect to $U$ of a gridded representation of the bivariate empirical copula (see EMPIRcop).

Usage

EMPIRgridder(empgrid=NULL, ...)

Arguments

empgrid

The grid from EMPIRgrid; and

...

Additional arguments to pass.

Value

• The gridded values of the derivatives of the bivariate empirical copula.

See Also

EMPIRcop, EMPIRcopdf, EMPIRgrid, EMPIRgridder2

Examples

para   <- list(alpha=0.15,  beta=0.65, cop1=PLACKETTcop, cop2=PLACKETTcop,
               para1=0.005, para2=1000)
uv <- simCOP(n=1000, cop=composite2COP, para=para)
fakeU <- pp(uv[,1], sort=FALSE); fakeV <- pp(uv[,2], sort=FALSE)
uv <- data.frame(U=fakeU, V=fakeV)

"trans3d" <- function(x,y,z, pmat) {
   tmat <- cbind(x,y,z,1) %*% pmat; return(tmat[,1:2] / tmat[,4])
}

the.grid <- EMPIRgrid(para=uv, deluv=0.1)
the.diag <- diagCOP(cop=EMPIRcop, para=uv, ploton=FALSE, lines=FALSE)
empcop <- EMPIRcopdf(para=uv) # data.frame of all points

the.persp <- persp(the.grid$empcop, theta=-25, phi=20,
                   xlab="U VARIABLE", ylab="V VARIABLE", zlab="COPULA C(u,v)")
points(trans3d(empcop$u, empcop$v, empcop$empcop, the.persp),
       col=rgb(0,1-sqrt(empcop$empcop),1,sqrt(empcop$empcop)), pch=16, cex=0.75)

# Now extract the copula sections
some.lines <- trans3d(rep(0.2, length(the.grid$v)),
                      the.grid$v, the.grid$empcop[3,], the.persp)
lines(some.lines, lwd=2, col=2)
some.lines <- trans3d(the.grid$u, rep(0.6, length(the.grid$u)),
                      the.grid$empcop[,7], the.persp)
lines(some.lines, lwd=2, col=3)
some.lines <- trans3d(rep(0.7, length(the.grid$v)), the.grid$v,
                      the.grid$empcop[8,], the.persp)
lines(some.lines, lwd=2, col=6)

# Now compute some derivatives or conditional cumulative
# distribution functions
empder <- EMPIRgridder(empgrid=the.grid)
some.lines <- trans3d(rep(0.2, length(the.grid$v)), the.grid$v, empder[3,], the.persp)
lines(some.lines, lwd=4, col=2)

empder <- EMPIRgridder2(empgrid=the.grid)
some.lines <- trans3d(the.grid$u, rep(0.6, length(the.grid$u)), empder[,7], the.persp)
lines(some.lines, lwd=4, col=3)

empder <- EMPIRgridder(empgrid=the.grid)
some.lines <- trans3d(rep(0.7, length(the.grid$v)), the.grid$v, empder[8,], the.persp)
lines(some.lines, lwd=4, col=6)

# Demonstrate conditional quantile function extraction for
# the 70th percentile of U and see how it plots on top of
# the thick purple line
empinv <- EMPIRgridderinv(empgrid=the.grid)
some.lines <- trans3d(rep(0.7, length(the.grid$v)), empinv[8,],
                      attributes(empinv)$colnames, the.persp)
lines(some.lines, lwd=4, col=5, lty=2)