EMPIRcopdf: Dataframe of the Bivariate Emprical Copula

Description

Generate a data.frame representation of the bivariate empirical copula (Salvadori et al., 2007, p. 140) using the coordinates as preserved in the raw data in the parameter object of the bivariate empirical copula.

Usage

EMPIRcopdf(para=NULL, ...)

Arguments

para

A vector (single element) of parameters---the U-statistics of the data (see example) to pass to EMPIRcop; and

...

Additional arguments to pass to EMPIRcop.

Value

An Rdata.frame of $u$, $v$, and $\mathbf{C}_{n}(u,v)$ values of the bivariate empirical copula is returned.

References

Salvadori, G., De Michele, C., Kottegoda, N.T., and Rosso, R., 2007, Extremes in Nature---An approach using copulas: Springer, 289 p.

Examples

Run this code

psp <- simCOP(n=39, cop=PSP, ploton=FALSE, points=FALSE) * 150
# Pretend psp is real data, the * 150 is to clearly get into an arbitrary unit system.

# The sort=FALSE is critical in the following two calls to pp() from lmomco.
fakeU <- lmomco::pp(psp[,1], sort=FALSE) # Weibull plotting position i/(n+1)
fakeV <- lmomco::pp(psp[,2], sort=FALSE) # Weibull plotting position i/(n+1)
uv <- data.frame(U=fakeU, V=fakeV) # our U-statistics

empcop <- EMPIRcopdf(para=uv)
plot(empcop$u, empcop$v, cex=1.75*empcop$empcop, pch=16,
     xlab="U NONEXCEEDANCE PROBABILITY", ylab="V NONEXCEEDANCE PROBABILITY")
# Dot size increases with joint probability (height of the copulatic surface).
points(empcop$u, empcop$v, col=2)