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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:
# dgh Returns density for generalized hyperbolic DF
# pgh Returns probability for generalized hyperbolic DF
# qgh Returns quantiles for generalized hyperbolic DF
# rgh Returns random variates for generalized hyperbolic DF
################################################################################
dgh <-
function(x, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2, log = FALSE)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns density for the generalized hyperbolic distribution
# FUNCTION:
# Parameters:
if (length(alpha) == 4) {
mu = alpha[4]
delta = alpha[3]
beta = alpha[2]
alpha = alpha[1]
}
# Checks:
if (alpha <= 0) stop("alpha must be greater than zero")
if (delta <= 0) stop("delta must be greater than zero")
if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
# Density:
arg = delta*sqrt(alpha^2-beta^2)
a = (lambda/2)*log(alpha^2-beta^2) - (
log(sqrt(2*pi)) + (lambda-0.5)*log(alpha) + lambda*log(delta) +
log(besselK(arg, lambda, expon.scaled = TRUE)) - arg )
f = ((lambda-0.5)/2)*log(delta^2+(x - mu)^2)
# Use exponential scaled form to prevent from overflows:
arg = alpha * sqrt(delta^2+(x-mu)^2)
k = log(besselK(arg, lambda-0.5, expon.scaled = TRUE)) - arg
e = beta*(x-mu)
# Put all together:
ans = a + f + k + e
if(!log) ans = exp(ans)
# Return Value:
ans
}
# ------------------------------------------------------------------------------
pgh <-
function(q, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns probability for the generalized hyperbolic distribution
# FUNCTION:
# Checks:
if (alpha <= 0) stop("alpha must be greater than zero")
if (delta <= 0) stop("delta must be greater than zero")
if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
# Probability:
ans = NULL
for (Q in q) {
Integral = integrate(dgh, -Inf, Q, stop.on.error = FALSE,
alpha = alpha, beta = beta, delta = delta, mu = mu,
lambda = lambda)
ans = c(ans, as.numeric(unlist(Integral)[1]))
}
# Return Value:
ans
}
# ------------------------------------------------------------------------------
qgh <-
function(p, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns quantiles for the generalized hyperbolic distribution
# FUNCTION:
# Checks:
if (alpha <= 0) stop("alpha must be greater than zero")
if (delta <= 0) stop("delta must be greater than zero")
if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
# Internal Function:
.froot <- function(x, alpha, beta, delta, mu, lambda, p)
{
pgh(q = x, alpha = alpha, beta = beta, delta = delta,
mu = mu, lambda = lambda) - p
}
# Quantiles:
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), alpha = alpha, beta = beta, delta = delta,
mu = mu, lambda = lambda, p = pp)
counter = counter + 1
lower = lower - 2^counter
upper = upper + 2^counter
}
result = c(result, iteration)
}
# Return Value:
result
}
# ------------------------------------------------------------------------------
rgh <-
function(n, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns random variates for the generalized hyperbolic distribution
# FUNCTION:
# Checks:
if (alpha <= 0) stop("alpha must be greater than zero")
if (delta <= 0) stop("delta must be greater than zero")
if (abs(beta) >= alpha) stop("abs value of beta must be less than alpha")
# Settings:
theta = c(lambda, alpha, beta, delta, mu)
# Random Numbers:
ans = .rghyp(n, theta)
# Return Value:
ans
}
################################################################################
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