copBasic (version 1.7.1)

EMPIRgridderinv: Derivative Inverses of the Grid of the Bivariate Emprical Copula for V with respect to U

Description

Generate a gridded representation of the inverse of the derivatives of the bivariate empirical copula of $V$ with respect to $U$.

Usage

EMPIRgridderinv(empgrid=NULL, kumaraswamy=FALSE, ...)

Arguments

empgrid

The grid from EMPIRgrid;

kumaraswamy

A logical to trigger Kumaraswamy smoothing of the conditional quantile function; and

...

Additional arguments to pass.

Value

• The gridded values of the inverse of the derivative of $V$ with respect $U$.

See Also

EMPIRcop, EMPIRcopdf, EMPIRgrid, EMPIRgridder2

Examples

uv <- simCOP(n=10000, cop=PSP, ploton=FALSE, points=FALSE)
fakeU <- pp(uv[,1], sort=FALSE); fakeV <- pp(uv[,2], sort=FALSE)
uv <- data.frame(U=fakeU, V=fakeV)

uv.grid <- EMPIRgrid(para=uv, deluv=.1) # CPU hungry
uv.inv1 <- EMPIRgridderinv(empgrid=uv.grid)
uv.inv2 <- EMPIRgridderinv2(empgrid=uv.grid)
plot(uv, pch=16, col=rgb(0,0,0,.1), xlim=c(0,1), ylim=c(0,1),
     xlab="U, NONEXCEEDANCE PROBABILITY", ylab="V, NONEXCEEDANCE PROBABILITY")
lines(qua.regressCOP(f=0.5, cop=PSP), col=2)
lines(qua.regressCOP(f=0.2, cop=PSP), col=2)
lines(qua.regressCOP(f=0.7, cop=PSP), col=2)
lines(qua.regressCOP(f=0.1, cop=PSP), col=2)
lines(qua.regressCOP(f=0.9, cop=PSP), col=2)

med.wrtu <- EMPIRqua.regress(f=0.5, empinv=uv.inv1)
lines(med.wrtu, col=2, lwd=4)
qua.wrtu <- EMPIRqua.regress(f=0.2, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=2)
qua.wrtu <- EMPIRqua.regress(f=0.7, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=2)
qua.wrtu <- EMPIRqua.regress(f=0.1, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=4)
qua.wrtu <- EMPIRqua.regress(f=0.9, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=4)

lines(qua.regressCOP2(f=0.5, cop=PSP), col=4)
lines(qua.regressCOP2(f=0.2, cop=PSP), col=4)
lines(qua.regressCOP2(f=0.7, cop=PSP), col=4)
lines(qua.regressCOP2(f=0.1, cop=PSP), col=4)
lines(qua.regressCOP2(f=0.9, cop=PSP), col=4)

med.wrtv <- EMPIRqua.regress2(f=0.5, empinv=uv.inv2)
lines(med.wrtv, col=4, lwd=4)
qua.wrtv <- EMPIRqua.regress2(f=0.2, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=2)
qua.wrtv <- EMPIRqua.regress2(f=0.7, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=2)
qua.wrtv <- EMPIRqua.regress2(f=0.1, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=4)
qua.wrtv <- EMPIRqua.regress2(f=0.9, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=4)
# Now try a much more complex shape
para   <- list(alpha=0.15,  beta=0.65, cop1=PLACKETTcop, cop2=PLACKETTcop,
               para1=0.005, para2=1000)
uv <- simCOP(n=30000, cop=composite2COP, para=para)
fakeU <- pp(uv[,1], sort=FALSE); fakeV <- pp(uv[,2], sort=FALSE)
uv <- data.frame(U=fakeU, V=fakeV)

uv.grid <- EMPIRgrid(para=uv, deluv=0.05) # CPU hungry
uv.inv1 <- EMPIRgridderinv(empgrid=uv.grid)
uv.inv2 <- EMPIRgridderinv2(empgrid=uv.grid)
plot(uv, pch=16, col=rgb(0,0,0,0.1), xlim=c(0,1), ylim=c(0,1),
     xlab="U, NONEXCEEDANCE PROBABILITY", ylab="V, NONEXCEEDANCE PROBABILITY")
lines(qua.regressCOP(f=0.5, cop=composite2COP, para=para), col=2)
lines(qua.regressCOP(f=0.2, cop=composite2COP, para=para), col=2)
lines(qua.regressCOP(f=0.7, cop=composite2COP, para=para), col=2)
lines(qua.regressCOP(f=0.1, cop=composite2COP, para=para), col=2)
lines(qua.regressCOP(f=0.9, cop=composite2COP, para=para), col=2)

med.wrtu <- EMPIRqua.regress(f=0.5, empinv=uv.inv1)
lines(med.wrtu, col=2, lwd=4)
qua.wrtu <- EMPIRqua.regress(f=0.2, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=2)
qua.wrtu <- EMPIRqua.regress(f=0.7, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=2)
qua.wrtu <- EMPIRqua.regress(f=0.1, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=4)
qua.wrtu <- EMPIRqua.regress(f=0.9, empinv=uv.inv1)
lines(qua.wrtu, col=2, lwd=2, lty=4)

lines(qua.regressCOP2(f=0.5, cop=composite2COP, para=para), col=4)
lines(qua.regressCOP2(f=0.2, cop=composite2COP, para=para), col=4)
lines(qua.regressCOP2(f=0.7, cop=composite2COP, para=para), col=4)
lines(qua.regressCOP2(f=0.1, cop=composite2COP, para=para), col=4)
lines(qua.regressCOP2(f=0.9, cop=composite2COP, para=para), col=4)

med.wrtv <- EMPIRqua.regress2(f=0.5, empinv=uv.inv2)
lines(med.wrtv, col=4, lwd=4)
qua.wrtv <- EMPIRqua.regress2(f=0.2, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=2)
qua.wrtv <- EMPIRqua.regress2(f=0.7, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=2)
qua.wrtv <- EMPIRqua.regress2(f=0.1, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=4)
qua.wrtv <- EMPIRqua.regress2(f=0.9, empinv=uv.inv2)
lines(qua.wrtv, col=4, lwd=2, lty=4)