fitCBB: fitCBB
In fgac: Generalized Archimedean Copula

Description Usage Arguments Details Value Author(s) References See Also Examples

Fitting an specific generalized archimedean copula

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)

`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 from: 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

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.

`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.

Veronica Andrea Gonzalez-Lopez

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)

fitlambdas, OptimCBB ~~~

#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))