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# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
################################################################################
# FUNCTION: DESCRIPTION:
# dsght Standardized generalized hyperbolic Student-t
# psght Probability of the Standardized GHT
# qsght Quantiles of the Standardized GHT
# rsght Random variates of the Standardized GHT
################################################################################
dsght <-
function(x, beta = 0.1, delta = 1, mu = 0, nu = 10, log = FALSE)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns density of the generalized hyperbolic Student-t
# Arguments:
# Example:
# x = (-5):5; dght(x)
# FUNCTION:
# Parameters:
if (length(beta) == 4) {
nu = beta[4]
mu = beta[3]
delta = beta[2]
beta = beta[1]
}
# Density:
ans = dgh(x, alpha = abs(beta) + 1e-6, beta, delta, mu, lambda = -nu/2,
log = log)
# Return Value:
ans
}
# ------------------------------------------------------------------------------
psght <-
function(q, beta = 0.1, delta = 1, mu = 0, nu = 10)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns probabilities of the generalized hyperbolic Student-t
# Arguments:
# Example:
# q = (-5):5; pght(q)
# FUNCTION:
# Cumulative Probability:
ans = NULL
for (Q in q) {
Integral = integrate(dght, -Inf, Q, stop.on.error = FALSE,
beta = beta, delta = delta, mu = mu, nu = nu)
ans = c(ans, as.numeric(unlist(Integral)[1]) )
}
# Return Value:
ans
}
# ------------------------------------------------------------------------------
qsght <-
function(p, beta = 0.1, delta = 1, mu = 0, nu = 10)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns quantiles of the generalized hyperbolic Student-t
# Arguments:
# Example:
# p = (1:9)/10; qght(p); round(pght(qght(p)), digits = 4)
# FUNCTION:
# Internal Functions:
.froot <- function(x, beta = beta, delta = delta, mu = mu, nu = nu, p)
{
pght(q = x, beta = beta, delta = delta, mu = mu, nu = nu) - p
}
# Loop over all p's:
result = NULL
for (pp in p) {
lower = -1
upper = +1
counter = 0
iteration = NA
while (is.na(iteration)) {
iteration = .unirootNA(f = .froot, interval = c(lower,
upper), beta = beta, delta = delta, mu = mu,
nu = nu, p = pp)
counter = counter + 1
lower = lower - 2^counter
upper = upper + 2^counter
}
result = c(result, iteration)
}
# Return Value:
ans = result + mu
ans
}
# ------------------------------------------------------------------------------
rsght <-
function(n, beta = 0.1, delta = 1, mu = 0, nu = 10)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns random Variates of generalized hyperbolic Student-t
# Arguments:
# Example:
# r = rght(10)
# FUNCTION:
# Random Variates:
x = rgh(n, alpha = abs(beta) + 1e-6, beta = beta, delta = delta, mu = mu,
lambda = -nu/2)
# Return Value:
x
}
################################################################################
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