FactorCopulaModel (version 0.1.1)

tailDep: Tail dependence parameter estimation

Description

Tail dependence parameter estimate based on extrapolating zeta(alpha)

Usage

tailDep(u1,u2, lowertail=FALSE, eps=0.1, semictol=0.1, rank=TRUE,
  iprint=FALSE)

Value

upper tail dependence parameter based on extrapolation of zeta(alpha) for large alpha

Arguments

u1

nx1 vector with values (in (0,1) if rank=FALSE)

u2

nx1 vector with values (in (0,1) if rank=FALSE)

lowertail

TRUE if lower tail-weighted dependence measure, default is FALSE

eps

tolerance (default 0.1) for rate parameter in method 2; non-linear (use method 2) if rate < 1-eps

semictol

tolerance (default 0.1) for exceedance of normal semicorrelation to treat as tail dependent; use something like semicol=-0.5 if normal scores plot suggest tail dependence

rank

TRUE (default) if data matrix needs to be converted to uniform scores in (0,1)

iprint

TRUE for intermediate prints

References

Lee D, Joe H, Krupskii P (2018). J Nonparametric Statistics, 30(2), 262-290

Examples

mytest = function(qcond,cpar,n=500,seed=123)
{ set.seed(seed)
  u1 = runif(n)
  u2 = qcond(runif(n),u1,cpar)
  #convert to uniform scores (marginals are usually not known)
  u1 = (rank(u1)-0.5)/n
  u2 = (rank(u2)-0.5)/n
  alp = c(1,5,10:20)
  zetaL = zetaDep(cbind(u1,u2),alp,rank=FALSE,lowertail=FALSE)
  zetaU = zetaDep(cbind(u1,u2),alp,rank=FALSE,lowertail=TRUE)
  print(cbind(alp,zetaL,zetaU))
  utd = tailDep(u1,u2, lowertail=FALSE, eps=0.1, semictol=0.1, rank=FALSE, iprint=TRUE)
  ltd = tailDep(u1,u2, lowertail=TRUE, eps=0.1, semictol=0.1, rank=FALSE, iprint=TRUE)
  cat(ltd,utd,"\n")
  utd = tailDep(u1,u2, lowertail=FALSE, eps=0.1, semictol=0.1, rank=FALSE, iprint=FALSE)
  ltd = tailDep(u1,u2, lowertail=TRUE, eps=0.1, semictol=0.1, rank=FALSE, iprint=FALSE)
  cat(ltd,utd,"\n")
  #par(mfrow=c(2,1))
  #zetaPlot(cbind(u1,u2),alp,ylim=c(0,1),inverse=FALSE)
  #zetaPlot(cbind(u1,u2),alp,ylim=c(0,1),inverse=TRUE)
  0
}
mytest(qcondFrank,3)
mytest(qcondbvtcop,c(0.6,5))