fitCBB {fgac}R Documentation

fitCBB

Description

Fitting an specific generalized archimedean copula

Usage

fitCBB(x, y, theta0, delta0, copulamodel = c("pCBB1", "pCBB2", "pCBB3", "pCBB4", 
"pCBB5", "pCBB6", "pCBB7", "pCMax", "pCMin"), m, step, deltamin, thetamin,
 test = c("wilcox.test", "t.test"), empcumulative = TRUE, cumulative1, 
cumulative2, parameters1, parameters2)

Arguments

x real vector
y real vector
theta0 parameter in the model pCBBi (in variable copulamodel). For default, theta0 is obtained from fitlambdas
delta0 parameter in the model pCBBi (in variable copulamodel). For default, delta0 is obtained from fitlambdas
copulamodel specific model that we need to fit, it need to be one option like {pCBB1 (default), pCBB2, pCBB3, pCBB4, pCBB5, pCBB6, pCBB7, pCMax, pCMin}
m integer positive number (default=15)
step real positive number (default=0.01)
deltamin minimum value admited for delta's domain (default=epsilon-see details)
thetamin minimum value admited for theta's domain (default=epsilon-see details)
test test used for fitting selection, it need to be wilcox.test(default) or t.test
empcumulative logical value, can be TRUE (default) or FALSE (see details)
cumulative1 marginal cumulative associated with x. Can be used pnorm, pbeta, pempirical,...(only used when empcumulative=FALSE)
cumulative2 marginal cumulative associated with y. Can be used pnorm, pbeta, pempirical,...(only used when empcumulative=FALSE)
parameters1 specifics parameters for cumulative1's definition
parameters2 specifics parameters for cumulative2's definition

Details

The function constructs a neighbourhood around (theta0,delta0) for family specified in ‘copulamodel’ , and using the test specified in ‘test’ the function search the best (theta*,delta*) in the neighbourhood such that copulamodel(theta*,delta*,u,v) is close to the bivariate empirical copula from (x,y). Where (u,v)=(cumulative1(x),cumulative2(y)). m and step control the neighbourhood' definition. deltamin and thetamin depend on the model worked. For default, we have, pCBB1: deltamin=1, thetamin=0.05; pCBB2: deltamin=0.05, thetamin = 0.05; pCBB3: deltamin=1, thetamin=0.05; pCBB4: deltamin=0.05, thetamin=0.05; pCBB5: deltamin=0.05, thetamin=1; pCBB6: deltamin=1, thetamin=1; pCBB7: deltamin = 0.05, thetamin = 1. If empcumulative=TRUE like default, the algorithm uses for uniformization, empirical cumulative from x for x and empirical cumulative from y for y. If empcumulative=FALSE, we need to put an specific cumulative1 and an specific cumulative2. If necessary, parameters1 contains the special parameter(s) for cumulative1 and parameters2 contains the special parameter(s) for cumulative2.

Value

Empirical empirical copula from (x,y)
Copula best copulamodel evaluated in (u,v)=(cumulative1(x),cumulative2(y))
fit performance from the best copulamodel in the neighbourhood. Result: p.value in fit[1], delta in fit[2], theta in fit[3]
thetai theta's vector constructed in the neighbourhood
deltaj delta's vector constructed in the neighbourhood
pthetaideltaj p value matrix from each combination. The position (i,j) represents the p value from ‘test’ in thetai(i),deltaj(j) for copulamodel.

Author(s)

Veronica Andrea Gonzalez-Lopez

References

Veronica A. Gonzalez-Lopez and Nelson I. Tanaka. ‘Bi-variate Data Modeling Through Generalized Archimedean Copula’ RT-MAE 2003-03. Harry Joe. ‘Multivariate Models and Dependence Concepts’ Monogra. Stat. & Appl. Probab. 73. Chapman and Hall (1997)

See Also

fitlambdas, OptimCBB ~~~

Examples

#x<-rnorm(100)
#y<-x/10+rnorm(100)
#M<-fitCBB(x,y) # default fitting 
#default: thetas0 and delta0 from fitlambdas function,  m=15, step=0.01,
#copulamodel="pCBB1", test="wilcox.test", empcumulative=TRUE.
#
#M<-fitCBB(x,y,theta0=1.1,delta0=0.8,copulamodel="pCBB5",m=20,step=0.5,deltamin=0.1,thetamin=1.1, 
#test="w",empcumulative=FALSE,cumulative1=pnorm,cumulative2=pnorm)
#
#x<-rnorm(100)
#y<-x/100+rnorm(100,5,2)
#M<-fitCBB(x,y,theta0=1.1,delta0=0.8,copulamodel="pCBB7",m=20,step=0.5,deltamin=0.1,thetamin=1.1,
#test="t",empcumulative=FALSE,cumulative1=pnorm,cumulative2=pnorm,parameters2=c(5,2))


[Package fgac version 0.6-0 Index]