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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:
# nigMean Returns true NIG mean
# nigVar Returns true NIG variance
# nigSkew Returns true NIG skewness
# nigKurt Returns true NIG kurtosis
# FUNCTION: DESCRIPTION:
# nigMoments Returns true NIG moments
# FUNCTION: DESCRIPTION:
# nigShapeTriangle Plots NIG Shape Triangle
################################################################################
nigMean <-
function(alpha = 1, beta = 0, delta = 1, mu = 0)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns true NIG mean
# FUNCTION:
# Mean:
gamma = sqrt(alpha^2 - beta^2)
ans = c(mean = (mu + delta * beta / gamma)[[1]])
# Return Value:
ans
}
# ------------------------------------------------------------------------------
nigVar <-
function(alpha = 1, beta = 0, delta = 1, mu = 0)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns true NIG variance
# FUNCTION:
# Variance:
gamma = sqrt(alpha^2 - beta^2)
ans = c(var = (delta * alpha^2 / gamma^3)[[1]])
# Return Value:
ans
}
# ------------------------------------------------------------------------------
nigSkew <-
function(alpha = 1, beta = 0, delta = 1, mu = 0)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns true NIG skewness
# FUNCTION:
# Skewness:
gamma = sqrt(alpha^2 - beta^2)
ans = c(skew = (3*beta / ( alpha * sqrt(delta*gamma) ))[[1]] )
# Return Value:
ans
}
# ------------------------------------------------------------------------------
nigKurt <-
function(alpha = 1, beta = 0, delta = 1, mu = 0)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns true NIG kurtosis
# FUNCTION:
# Skewness:
gamma = sqrt(alpha^2 - beta^2)
ans = c(kurt = (3 * ( 1 + 4 * beta^2 / alpha^2) / (delta * gamma))[[1]])
# Return Value:
ans
}
###############################################################################
nigMoments <-
function(order, type = c("raw", "central", "mu"),
alpha=1, beta=0, delta=1, mu=0)
{
# A function implemented by Diethelm Wuertz
# Descriptions:
# Returns true moments of the NIG distribution
# FUNCTION:
# Settings:
type = match.arg(type)
# Moments:
lambda = -1/2
if (type == "raw") {
ans = .ghRawMoments(order, alpha, beta, delta, mu, lambda)
} else if (type == "central") {
ans = .ghCentralMoments(order, alpha, beta, delta, mu, lambda)
} else if (type == "central") {
ans = .ghMuMoments(order, alpha, beta, delta, mu, lambda)
}
# Return Value:
ans
}
################################################################################
nigShapeTriangle <-
function(object, add = FALSE, labels = TRUE, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Plots NIG Shape Triangle
# Arguments:
# object - an object of class 'fDISTFIT' as returned by the
# function nigFit()
# Example:
# nigShapeTriangle(nigFit(rnig(100), doplot = FALSE))
# FUNCTION:
# Settings:
stopifnot(class(object) == "fDISTFIT")
# Plot Frame:
if (labels) {
xlab = "Asymmetry: chi"
ylab = "Steepness: zeta"
main = "NIG Shape Traingle"
} else {
xlab = ylab = main = ""
}
if (!add) {
x = c(-1, 0, 1, -1)
y = c( 1, 0, 1, 1)
plot(x, y, type = "l", xlab = xlab, ylab = ylab, main = main, ...)
for (s in c(0.8, 0.6, 0.4, 0.2))
lines(c(-s, s), c(s, s), lty = 3, col = "grey")
lines(c(0, 0), c(0, 1), lty = 3, col = "grey")
}
# Transform:
par = object@fit$estimate
names(par) = c("alpha", "beta", "delta", "mu")
alpha = par[1]
beta = par[2]
delta = par[3]
mu = par[4]
# Add Points:
zeta = 1/sqrt(1+delta*sqrt(alpha^2-beta^2))
chi = zeta*(beta/alpha)
if (labels) {
points(chi, zeta, pch = 19, ...)
} else {
points(chi, zeta, ...)
}
# Result:
ans = list(chi = chi[[1]], zeta = zeta[[1]])
attr(ans, "control")<-par
# Return Value:
ans
}
################################################################################
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