fgac (version 0.6-1)

OptimCBB: OptimCBB

Description

The best fitting into the generalized archimedean copula class is selected

Usage

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

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

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.

References

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

See Also

fitCBB, fitlambdas

Examples

#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))