#' Function from CDVine
#' https://github.com/cran/CDVine
#' @noRd
Frank.itau.JJ <- function(tau) {
a <- 1
if (tau < 0) {
a <- -1
tau <- -tau
}
f <- function(x) {
x/(exp(x) - 1)
}
tauF <- function(x) 1 - 4/x + 4/x^2 * integrate(f, lower = 0 + .Machine$double.eps^0.5, upper = x)$value
v <- uniroot(function(x) tau - tauF(x), lower = 0, upper = 500, tol = .Machine$double.eps^0.5)$root
return(a * v)
}
Joe.itau.JJ <- function(tau) {
if (tau < 0) {
return(1.000001)
} else {
tauF <- function(a) {
# euler=0.5772156649015328606 1+((-2+2*euler+2*log(2)+digamma(1/a)+digamma(1/2*(2+a)/a)+a)/(-2+a))
1 + 4/a^2 * integrate(function(x) log(x) * x * (1 - x)^(2 * (1 - a)/a), 0, 1)$value
}
v <- uniroot(function(x) tau - tauF(x), lower = 1, upper = 500, tol = .Machine$double.eps^0.5)$root
return(v)
}
}
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