copBasic (version 1.7.1)

simcompositeCOP: Simulation of a Composited Copula

Description

This function simulates, computes L-comoments, and provides plotting features for a composited copula using using two compositing parameters (see composite1COP and composite2COP). The compositing parameters are each independent and uniformly distributed: $$\alpha \sim \mathrm{U}[0,1];\ \beta \sim \mathrm{U}[0,1]\mbox{.}$$ L-comoment estimation is provided by the lcomoms2 function of the lmomco package. The intention of this function is to provide an interface connecting highly complex copula composition to the L-comoments---that is why the compositing parameters are randomly drawn with each simulation (nsim). This function also provides a mechanism for random parameter generation for the composited copulas. This function is partially misnamed. For example if simulation of nonexceedance probabilities $u$ and $v$ for a known composite copula (the compositing parameters are specified and constant), then the more familiar simCOP function is to be used instead.

Usage

simcompositeCOP(n=1000, nsim=100, compositor=composite2COP,
                parents=NULL, ploton=FALSE, points=FALSE,
                showpar=FALSE, showresults=FALSE, digits=6, ...)

Arguments

n

Sample size $n$ per simulation;

nsim

Number of simulations to perform;

compositor

The compositing function, could be either composite1COP or composite2COP. Each of these is acceptable because two compositing parameters are used

parents

A special parameter list (see Note);

ploton

A logical to toggle on intermediate plotting;

points

A logical to actually draw the simulations on the ploton by points function in R;

showpar

Print the simulated parameter set with each iteration;

showresults

Print the results (useful if harvest results from a batch operation of R);

digits

The number digits to pass to round if showresults is true; and

...

Additional arguments to pass.

Value

• A matrix of results is returned. Each row represents a single simulation run. The first two columns are the $\alpha$ and $\beta$ compositing parameters and are labeled as such. The next two columns are the opposing diagonals, by first row and then second, of the L-comoment correlation. The following two columns are the opposing diagnonals, by row and then second, of the L-coskew. The following two columns are the opposing diagnonals, by row and then second, of the L-cokurtosis. The L-comoment columns are labeled to reflect the L-comoment matrix: T2.21 means the L-comoment correlation row 2 column 1 and T3.12 mean the L-coskew row 1 column 2. The remaining columns represent the $\Theta_n$ parameters for copula 1, the $\Theta_m$ parameters for copula 2. The columns are labeled Cop1Thetas or Cop2Thetas.

See Also

composite1COP, composite2COP, simCOP

Examples

# EXAMPLE 1: A single simulation "result" sample size 10---for accuracy n >>> 10.
mainpara <- list(cop1=PLACKETTcop, cop2=PLACKETTcop,
                 para1gen=function() { return(c(10^runif(1,min=-5,max=0))) },
                 para2gen=function() { return(c(10^runif(1,min= 0,max=5))) })
v <- simcompositeCOP(n=10, nsim=1, parent=mainpara, showresults=TRUE)
print(v)