asymcoptests/asymgal-test.r

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

# test of functions for asymmetric Galambos (or negative bilogistic)

library(CopulaModel)
#source("../R/asymgal.R")
ze=-.365; eta=-.716
ww=seq(.05,.95,.05)
out=Basymgal(ww,c(ze,eta))
cat("B function for ", ze, eta,"\n")
print(cbind(ww,out$Bfn,out$Bder,out$Bder2))

# check of  first and second order derivatives of B
cat("\nchecking derivatives of B\n")
w=.1
heps=1.e-5
weps=w+heps
out1=Basymgal(w,c(ze,eta))
out2=Basymgal(w+heps,c(ze,eta))
out3=Basymgal(w+2*heps,c(ze,eta))
der=(out2$Bfn-out1$Bfn)/heps
der2=(out3$Bfn-2*out2$Bfn+out1$Bfn)/heps^2
cat("analytic and numerical:\n")
print(out1)
cat(der,der2,"\n")

# check pcond
cat("\nchecking pcond of asymmetric Gumbel\n")
u=.1
v=.3
#v=.8
cdf=pasymgal(u,v,c(ze,eta))
ccdf21=pcondasymgal21(v,u,c(ze,eta))
ccdf12=pcondasymgal12(u,v,c(ze,eta))
cdfu=pasymgal(u+heps,v,c(ze,eta))
cdfv=pasymgal(u,v+heps,c(ze,eta))
cat("two different conditional cdfs\n")
cat((cdfu-cdf)/heps,ccdf21,"\n")
cat((cdfv-cdf)/heps,ccdf12,"\n")
param=c(ze,eta)
chkcopderiv(u,v,param,bcdf=pasymgal,pcond=pcondasymgal21,bpdf=dasymgal,
  str="asymgal",eps=heps)

# compare Galambos in special case
cat("\nsymmetric case Galambos\n")
param=c(-.5,-.5)
cdf1=pasymgal(u,v,param)
cdf2=pgal(u,v,-1/param[1])  # OK
cat(cdf1,cdf2,"\n")

v=seq(.1,.9,.2)
cdf1=pasymgal(u,v,param)
cdf2=pgal(u,v,-1/param[1]) 
print(cbind(cdf1,cdf2))

cat("\ntau and rhoS, symmetric case\n")
param=c(-.5,-.5)
tau=asymgal.cpar2tau(param)
rho=asymgal.cpar2rhoS(param)
cat(tau,rho,"\n")
cat("\ntau and rhoS, compare Galambos\n")
tau=gal.cpar2tau(-1/param[1])
rho=gal.cpar2rhoS(-1/param[1])
cat(tau,rho,"\n")

cat("\ntau and rhoS, asymmetric case\n")
#param=c(-.6,-.7)
param=c(-.2,-.4)
tau=asymgal.cpar2tau(param)
rho=asymgal.cpar2rhoS(param)
cat(tau,rho,"\n")