# OptimCBB: OptimCBB In fgac: Generalized Archimedean Copula

## Description

The best fitting into the generalized archimedean copula class is selected

## Usage

 ```1 2``` ```OptimCBB(x, y, m, step, test = c("wilcox.test", "t.test"), empcumulative = TRUE, cumulative1, cumulative2, parameters1, parameters2) ```

## Arguments

 `x` real vector `y` real vector `m` integer positive number (default=15) `step` real positive number (default=0.01) `test` test used for fitting selection, it have 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 cheks the compatibility of each family using ‘fitlambdas’ then, the function ‘fitCBB’ is applied for each possible family . Partial and global good fit are showed.

## Value

 `Empirical` empirical copula for (x,y) `Copula` best copulamodel evaluated in (u,v)=cumulative1(x),cumulative2(y) `OptimumFit` performance from the best copulamodel in the neighbourhood and between all copula's families pCBB1,..., pCBB7, pCMax, pCMin. Family in OptimumFit[1]; p.value in OptimumFit[2], delta in OptimumFit[3], theta in OptimumFit[4], MSE in OptimumFit[5] `Initial.BBi` For i in 1,...,7. Initial values for BBi family provided by the fitlambdas function. If Initial.BBi[1]=FALSE BBi, the BBi family is excluded (because empirical evidence from the data shows that this family is not appropriated). If Initial.BBi[1]=TRUE BBi, theta e delta suggested from fitlambdas function is showed in Initial.BBi[2] and Initial.BBi[3] respectively. `Final.BBi` For i in 1,...,7, we have the characteristics from the best fit in BBi family. If Final.BBi[1]=FALSE BBi, the BBi family is excluded (only when the family was excluded in Initial. BBi). In other case ,Final.BBi[1]=p.value (from test); the best theta e delta are showed in Final.BBi[2] and Final.BBi[3] respectively. `Initial.CMax (Initial.CMin)` like Initial.BBi (in this kind of component theta and delta do not have sense) `Final.CMax (Final.CMin)` like Final.BBi

## Author(s)

Veronica A. Gonzalez-Lopez

## References

Veronica A. Gonzalez-Lopez and Nelson I. Tanaka. ‘Bi-variate Data Modeling Through Generalized Archimedean Copula’ RT-MAE 2003-03

`fitCBB`, `fitlambdas`
 ```1 2 3 4 5 6 7 8 9``` ```#x<-rnorm(100) #y<-x/100+rnorm(100,5,2) #M<-OptimCBB(x=x,y=y) # #x<-rbeta(50,2,3) #y<-0.5*x+rgamma(50,1,2) #M<-OptimCBB(x,y,m=30,step=0.5,test="t",empcumulative=TRUE) #M<-OptimCBB(x,y,m=30,step=0.5,test="w",empcumulative=FALSE,cumulative1=pbeta, #cumulative2=pempirical,parameters1=c(2,3)) ```