fgac (version 0.6-1)

fitCBB: 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 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

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.

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.

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

#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))