EMPIRsim: Simulate a Bivariate Empirical Copula

Description

Perform a simulation on a bivariate empirical copula to produce the random variates $U$ and $V$ and return an Rdata.frame of them. This function is an empirical parallel to simCOP that is used for parametric copulas. If circumstances require conditional simulation of $V|U$, then function EMPIRsimv, which produces a vector of $V$ from a fixed $u$, should be used.

For the usual situation in which an individual $u$ during the simulation loops is not a value aligned on the grid, then the bounding conditional quantile functions are solved for each of the $n$ simulations and the following interpolation is made by $v = \frac{v_{1} / w_{1} + v_{2} / w_{2}}{1 / w_{1} + 1 / w_{2}},$ which states that that the weighted mean is computed. The values $v_1$ and $v_2$ are ordinates of the conditional quantile function for the respective grid lines to the left and right of the $u$ value. The values $w_1$ $=$ $u - u^\mathrm{left}_\mathrm{grid}$ and $w_2$ $=$ $u^\mathrm{right}_\mathrm{grid} - u$.

Usage

EMPIRsim(n=100, empgrid=NULL, kumaraswamy=FALSE, ploton=TRUE, points=TRUE, ...)

Arguments

A sample size, default is 100;

empgrid

Gridded empirical copula from EMPIRgrid;

kumaraswamy

A logical to trigger Kumaraswamy smoothing of the conditional quantile function that is passed to EMPIRgridderinv. The Kumaraswamy distribution is a distribution having support $[0,1]$ with an expl

ploton

A logical to toggle on the plot;

points

A logical to actually draw the simulations by the points() function in R; and

...

Additional arguments to pass to the points() function or to EMPIRgridderinv.

Value

An Rdata.frame of the simulated values is returned.

Examples

Run this code

pdf("EMPIRsim_experiment.pdf")
  nsim <- 5000
  para <- list(alpha=0.15, beta=0.65,
               cop1=PLACKETTcop, cop2=PLACKETTcop, para1=0.005, para2=1000)
  set.seed(1)
  uv <- simCOP(n=nsim, cop=composite2COP, para=para, pch=16, col=rgb(0,0,0,.2))
  mtext("A highly complex simulated bivariate relation")
  # set.seed(1) # try not resetting the seed
  uv.grid <- EMPIRgrid(para=uv, deluv=0.025)

  tmp <- EMPIRsim(n=nsim, empgrid=uv.grid, kumaraswamy=FALSE, col=rgb(1,0,0,0.1),pch=16)
  mtext("Resimulation without Kumaraswamy smoothing")

  tmp <- EMPIRsim(n=nsim, empgrid=uv.grid, kumaraswamy=TRUE,  col=rgb(1,0,0,0.1),pch=16)
  mtext("Resimulation but using the Kumaraswamy Distribution for smoothing")
dev.off()
# See other examples under EMPIRsimv

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