##### https://github.com/cran/nacopula
Revision e24ab1e1bade02a8136bd488815825e92fa6acd7 authored by Martin Maechler on 18 August 2010, 00:00:00 UTC, committed by Gabor Csardi on 18 August 2010, 00:00:00 UTC
1 parent 57da57c
Tip revision: e24ab1e
opower.R
``````##' <description>
##'
##' @title Outer Power Transformation of an Archimedean Copula
##' @param copbase a "base" copula, i.e. of class "acopula";
##'    must be one of the 5 five predefined families
##' @param thetabase the (univariate) parameter 'theta' for the base copula
##' @return a new "acopula" object; the outer power copula
##' @author Marius Hofert
opower <- function(copbase, thetabase) {
new("acopula", name = paste("opower", copbase@name, sep=":"),
## generator
psi = function(t,theta) { copbase@psi(t^(1/theta), thetabase) },
psiInv = function(t,theta) { copbase@psiInv(t, thetabase)^theta },
## parameter interval
paraInterval = interval("[1,Inf)"),
## nesting constraint
nestConstr = function(theta0,theta1) {
copbase@paraConstr(theta0) &&
copbase@paraConstr(theta1) && theta1 >= theta0
},
## V0 and V01
V0 = function(n,theta) {
if(theta == 1) {
## Sample from S(1,1,0,1;1)
## with Laplace-Stieltjes transform exp(-t)
rep.int(1., n)
} else {
V0base <- copbase@V0(n,thetabase) # draw from the base generator
alpha <- 1/theta
## Sample from S(alpha,1,(cos(alpha*pi/2))^(1/alpha),0;1)
## with Laplace-Stieltjes transform exp(-t^alpha)
S <- rstable1(n, alpha, beta=1,
gamma = (cos(alpha*pi/2))^(1/alpha))
S*V0base^theta
}
},
V01 = function(V0,theta0,theta1) {
alpha <- theta0/theta1
if(alpha == 1) {
## Sample from S(1,1,0,V0;1)
## with Laplace-Stieltjes transform exp(-V0*t)
V0
} else {
rstable1(length(V0), alpha, beta=1,
gamma = (cos(alpha*pi/2)*V0)^(1/alpha))
## Sample from S(alpha,1,(cos(alpha*pi/2)V0)^(1/alpha),0;1)
## with Laplace-Stieltjes transform exp(-V0*t^alpha)
}
},
## Kendall's tau
tau = function(theta) {
1-(1-copbase@tau(thetabase))/theta
},
tauInv = function(tau) {
taubase <- copbase@tau(thetabase)
if(tau >= taubase) (1-taubase)/(1-tau)
else {
stop("The provided tau has to be >= taubase")
NA * tau
}
},
## lower tail dependence coefficient lambda_l
lambdaL = function(theta) {
if(copbase@name=="Clayton") 2^(-1/(thetabase*theta)) else 0*theta
},
lambdaLInv = function(lambda) {
if(copbase@name=="Clayton") {
if(lambda >= 2^(-1/thetabase)) -1/(thetabase*log2(lambda))
else {
stop("The provided lambda has to be >= 2^(-1/thetabase)")
NA * lambda
}
} else {
if(any(lambda != 0))
stop("Any parameter for this outer power Archimedean copula gives lambdaL = 0")
NA * lambda
}
},
## upper tail dependence coefficient lambda_u
lambdaU = function(theta) {
2 - 2^(1/if(copbase@name %in% c("Gumbel", "Joe")) thetabase*theta else theta)
},
lambdaUInv = function(lambda) {
if(copbase@name %in% c("Gumbel", "Joe")) {
if(lambda >= 2-2^(1/thetabase)) 1/(thetabase*log2(2-lambda))
else {
stop("The provided lambda has to be >= 2-2^(1/thetabase)")
NA * lambda
}
} else 1/log2(2-lambda)
})
}
``````

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