simcomposite3COP: Compute the L-comoments of a Four-Value Composited Copula by Simulation

Description

Simulate copula parameters and compute L-comoments and provision for plotting features for a composited copula using four compositing parameters (see composite3COP). The compositing parameters are each independent and uniformly distributed: $$\alpha \sim \mathrm{U}[0,1];\ \beta \sim \mathrm{U}[0,1];\ \kappa \sim \mathrm{U}[0,1];\ \gamma \sim \mathrm{U}[0,1]\mbox{.}$$ L-comoment estimation is provided by the lcomCOP.

Usage

simcomposite3COP(nsim=100, compositor=composite3COP,
                 parents=NULL, ploton=FALSE, points=FALSE,
                 showpar=FALSE, showresults=FALSE, digits=6, ...)

Arguments

nsim

Number of simulations to perform;

compositor

The compositing function that could be either composite1COP, composite2COP, and composite3COP;

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 the 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 in R);

digits

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

...

Additional arguments to pass.

Value

An R matrix of results is returned. Each row represents a single simulation run. The first four columns are the $\alpha$, $\beta$, $\kappa$, and $\gamma$ 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.

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8.

Examples

Run this code

# NOT RUN {
# EXAMPLE 1: Make a single simulation result.
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(nsim=1, parent=mainpara, showresults=TRUE)
print(v)

# EXAMPLE 2: Make 1000 "results" and plot two columns.
mainpara <- list(cop1=PLACKETTcop, cop2=N4212cop,
                 para1gen=function() { return(c(10^runif(1,min=-5,max=5))) },
                 para2gen=function() { return(c(10^runif(1,min= 0,max=2))) })
v <- simcomposite3COP(nsim=100, parent=mainpara); labs <- colnames(v)
plot(v[,5],v[,7], # open circles are 1 with respect to 2
     xlab=paste(c(labs[5], "and", labs[6]), collapse=" "),
     ylab=paste(c(labs[6], "and", labs[8]), collapse=" "))
points(v[,6],v[,8], pch=16) # black dots are 2 with respect to 1
# }