CDVine (version 1.4)

BiCopLambda: Lambda-function (plot) for bivariate copula data

Description

This function plots the lambda-function of given bivariate copula data.

Usage

BiCopLambda(u1=NULL, u2=NULL, family="emp", par=0, par2=0, 
            PLOT=TRUE, ...)

Arguments

u1,u2

Data vectors of equal length with values in [0,1] (default: u1 and u2 = NULL).

family

An integer defining the bivariate copula family or indicating the empirical lambda-function: "emp" = empirical lambda-function (default) 1 = Gaussian copula; the theoretical lambda-function is simulated (no closed formula avail

par

Copula parameter; if the empirical lambda-function is chosen, par = NULL or 0 (default).

par2

Second copula parameter for t-, BB1, BB6, BB7 and BB8 copulas (default: par2 = 0).

PLOT

Logical; whether the results are plotted. If PLOT = FALSE, the values empLambda and/or theoLambda are returned (see below; default: PLOT = TRUE).

...

Additional plot arguments.

Value

• empLambda
  If the empirical lambda-function is chosen and PLOT=FALSE, a vector of the empirical lambda's is returned.
• theoLambda
  If the theoretical lambda-function is chosen and PLOT=FALSE, a vector of the theoretical lambda's is returned.

References

Genest, C. and L.-P. Rivest (1993). Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association, 88 (423), 1034-1043. Schepsmeier, U. (2010). Maximum likelihood estimation of C-vine pair-copula constructions based on bivariate copulas from different families. Diploma thesis, Technische Universitaet Muenchen. http://mediatum.ub.tum.de/doc/1079296/1079296.pdf.

See Also

BiCopMetaContour, BiCopKPlot, BiCopChiPlot

Examples

# Clayton and rotated Clayton copulas
n = 1000
tau = 0.5

# simulate from Clayton copula
fam = 3	
theta = BiCopTau2Par(fam,tau)
dat = BiCopSim(n,fam,theta)

# create lambda-function plots
dev.new(width=16,height=5)
par(mfrow=c(1,3))
BiCopLambda(dat[,1],dat[,2])	# empirical lambda-function	
BiCopLambda(family=fam,par=theta)	# theoretical lambda-function
BiCopLambda(dat[,1],dat[,2],family=fam,par=theta)	# both

# simulate from rotated Clayton copula (90 degrees)
fam = 23  
theta = BiCopTau2Par(fam,-tau)
dat = BiCopSim(n,fam,theta)

# rotate the data to standard Clayton copula data
rot_dat = 1-dat[,1]

dev.new(width=16,height=5)
par(mfrow=c(1,3))
BiCopLambda(rot_dat,dat[,2])  # empirical lambda-function	
BiCopLambda(family=3,par=-theta)	# theoretical lambda-function
BiCopLambda(rot_dat,dat[,2],family=3,par=-theta)	# both