genbeta2: Copula based on generalized beta of order 2

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Copula based on generalized beta of order 2

Usage

dbgb2(y1,y2,param) # bivariate density
pbgb2(y1,y2,param)  # bivariate cdf
dbgb2cop(u,v,param) # bivariate copula density
pbgb2cop(u,v,param)  # bivariate copula cdf
pcondbgb2cop(v,u,param)  # bivariate copula conditional cdf
dmgb2(yvec,param)    # multivariate density
dmgb2cop(uvec,param)    # multivariate copula density
logdmgb2cop(uvec,param) # log of multivariate copula density
rmgb2cop(n,param)  # simulation
bgb2.cpar2lm(param) # upper tail dependence 
mgb2.cpar2cor(param) # correlation matrix if zeta>2

Arguments

y1	positive value; could be a vector
y2	positive value; could be a vector
yvec	positive vector of length d
u	value in interval (0,1); could be a vector
v	value in interval (0,1); could be a vector
uvec	vector of length d; values in (0,1)
param	parameter vector of dimension d+1; (eta1,eta2,zeta) for bivariate and (etavec,zeta) for d-variate; all parameters are positive
n	simulation sample size

Value

pdf for dbgb2, dmgb2, dbgb2cop, dmgb2cop;

cdf for pbgb2, pbgb2cop;

conditional cdf for pcondbgb2cop;

log density for logdmgb2cop (use for maximum likelihood);

random d-vectors for rmgb2cop;

upper tail dependence parameter for bgb2.cpar2lm;

correlation matrix for mgb2.cpar2cor

References

Yang X, Frees EW, Zhang Z (2011). A generalized beta copula with applications in modeling multivariate long-tailed data. Insurance: Mathematics and Economics 49, 265-284.

Examples

y1=2; y2=3;
param=c(1.5,1.8,2.3)
dbgb2(y1,y2,param)
dmgb2(c(y1,y2),param) # same as above
u1=.2; u2=.3;
dbgb2cop(u1,u2,param)
dmgb2cop(c(u1,u2),param) # same as above
n=1000
param=c(4.5,4.8,2.3)
set.seed(124)
udat=rmgb2cop(n,param)
print(cor(udat))
cat("compare theoretical\n")
print(mgb2.cpar2cor(param))
dmgb2copnllk= function(param,udat)
{ n=nrow(udat)
  if(any(param<=0)) return(1.e10)
  nllk=0
  for(i in 1:n) nllk=nllk-logdmgb2cop(udat[i,],param)
  nllk
}
out=nlm(dmgb2copnllk,p=param,udat=udat,hessian=TRUE,print.level=1,iterlim=20)
print(sqrt(diag(solve(out$hess))))
## Not run: 
# contour of density with N(0,1) margins
zvec=seq(-3,3,.2)
contourBivCop(param,zvec,dcop=dbgb2cop) 
## End(Not run)

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.