EMPIRgridderinv {copBasic}

Derivative Inverses of the Grid of the Bivariate Empirical 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. This function is the empirical analog to derCOPinv.

Usage

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

Arguments

empgrid

The grid from EMPIRgrid;

kumaraswamy

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

dergrid

The results of EMPIRgridder and if left NULL then that function is called internally. There is some fragility at times in the quality of the numerical derivative and the author has provided this argument so that the derivative can be computed externally and then fed to this inversion function; and

...

Additional arguments to pass.

Value

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

Author(s)

W.H. Asquith

See Also

EMPIRcop, EMPIRcopdf, EMPIRgrid, EMPIRgridder2

Examples

## Not run: 
uv <- simCOP(n=10000, cop=PSP, ploton=FALSE, points=FALSE)
fakeU <- lmomco::pp(uv[,1], sort=FALSE)
fakeV <- lmomco::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)#
## End(Not run)

## Not run: 
# 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 <- lmomco::pp(uv[,1], sort=FALSE)
fakeV <- lmomco::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)#
## End(Not run)