tailweightedDepmeas: Tail-weighted dependence measures
In vincenzocoia/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description Usage Arguments Value References See Also Examples

Tail-weighted dependence measures: (a) bivariate copulas and (b) empirical data

twdm(pcop,param,power,nq,tscore=F)
twdm.emp(data,power)
twdm.emp.vec(data,power)  # vectorized, faster version
twdmnestcop(dcop,pcondcop,param1,param2,power,nq) # bivariate margin of
#                       nested-factor copula, 2 different groups
twdm1factcop(pcondcop,param,power,nq) # bivariate margin of 1-factor copula
twdm2factcop(pcondcop1,pcondcop2,param1,param2,power,nq) # bivariate margin of 2-factor copula

`pcop`	function for bivariate copula cdf
`param`	dependence parameter of pcop, or pcondcop in the two variables
`power`	power to use for tail-weighted dependence measure, good choice is 6 for twdm
`nq`	number of quadrature points for Gauss-Legendre quadrature
`tscore`	if T, Student t transform or normal transform of Gauss-Legendre quadrature points are used; this is faster is pcop is pbvncop or pbvtcop
`data`	data matrix with dimensions nxd
`dcop`	function for bivariate copula density for global with group1 and group2 latent
`pcondcop`	function for copula conditional cdf given latent
`pcondcop1`	function for copula conditional cdf for first latent
`pcondcop2`	function for copula conditional cdf for second latent
`param1`	dependence parameter of pcondcop1 in the two variables for twdm2factcop; dependence parameter of dcop for two group variables for twdmnestcop
`param2`	dependence parameter of pcondcop2 in the two variables; dependence parameter of pcondcop for two observed variables in twdmnestcop

`twdm`	for twdm, twdmnestcop, twdm1factcop, twdm2factcop: vector of length 2 lower and upper tail-weighted dependence measure values
`ltwdm`	for twdm.emp and twdm.emp.vec: dxd matrix of empirical lower tail-weighted dependence measure values; for upper tail-weighted values, input with negation of the data set.

Krupskii P (2014). Structured Factor Copulas and Tail Inference. PhD thesis, University of British Columbia.

Krupskii P and Joe H (2015). Tail-weighted measures of dependence. J Applied Statistics, 42, 614-629.

factorcopcdf factorcopsim pcond structcop

th1=gum.b2cpar(.7)
th2=gum.b2cpar(.6)
gum0.tw=twdm(pgum,th1,power=6,nq=15)
# 1-factor and 2-factor
gum1.tw=twdm(pfact1gum,c(th1,th1),power=6,nq=15)
gum2.tw=twdm(pfact2gum,matrix(c(th1,th1,th2,th2),2,2),power=6,nq=15)
gum1b=twdm1factcop(pcondgum,c(th1,th1),6,35)
gum2b=twdm2factcop(pcondgum,pcondgum,c(th1,th1),c(th2,th2),6,35)
# theoretical
cat(gum0.tw,"\n")
cat(gum1.tw,gum1b,"\n") # same from the two methods
cat(gum2.tw,gum2b,"\n") # same from the two methods
#
n=1000
set.seed(123)
gumdat1=sim1fact(n,c(th1,th1),qcondgum,"gumbel",ivect=TRUE)
set.seed(124)
gumdat2=sim2fact(n,c(th1,th1),c(th2,th2),qcondgum,qcondgum,"gumbel","gumbel",ivect=TRUE)
# empirical
gum1.ltw=twdm.emp(gumdat1,power=6)
gum1.utw=twdm.emp(1-gumdat1,power=6)
print(c(gum1.ltw[1,2],gum1.utw[1,2]))
gum2.ltw=twdm.emp.vec(gumdat2,power=6)
gum2.utw=twdm.emp.vec(1-gumdat2,power=6)
print(c(gum2.ltw[1,2],gum2.utw[1,2]))
# nested-factor
gumn=twdmnestcop(dgum,pcondgum,c(th1,th1),c(th2,th2),6,55) 
cat(gumn,"\n")
n=1000
set.seed(123)
grsize=c(2,2)
gumdatn=simnestfact(n,grsize, cop=3, c(th1,th1,th2,th2,th2,th2))
gumn.ltw=twdm.emp.vec(gumdatn,power=6)
gumn.utw=twdm.emp.vec(1-gumdatn,power=6)
print(c(gumn.ltw[1,2],gumn.utw[1,2]))