EMPIRgridder {copBasic}

Derivatives of the Grid of the Bivariate Empirical 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). This function is the empirical analog to derCOP.

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.

Author(s)

W.H. Asquith

See Also

EMPIRcop, EMPIRcopdf, EMPIRgrid, EMPIRgridder2

Examples

## Not run: 
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 <- lmomco::pp(uv[,1], sort=FALSE)
fakeV <- lmomco::pp(uv[,2], sort=FALSE)
uv <- data.frame(U=fakeU, V=fakeV)

"trans3d" <-                         # blackslashes seem needed for the package
function(x,y,z, pmat) {              # for user manual building but bad syntax
  tmat <- cbind(x,y,z,1) %*% pmat    # because remember the percent sign is a
  return(tmat[,1:2] / tmat[,4])      # a comment character in LaTeX.
}

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)#
## End(Not run)