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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
# Copyrights (C)
# for this R-port:
# 1999 - 2006, Diethelm Wuertz, GPL
# Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
# info@rmetrics.org
# www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
# see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
# see Rmetrics's copyright file
################################################################################
# FUNCTION: SYMMETRIC STABLE DISTRIBUTION:
# dsymstb Returns density for symmetric stable DF
# psymstb Returns probabilities for symmetric stable DF
# qsymstb Returns quantiles for symmetric stable DF
# rsymstb Returns random variates for symmetric stable DF
# FUNCTIONS: STABLE DISTRIBUTION:
# stableMode Computes stable mode
# dstable Returns density for stable DF
# pstable Returns probabilities for stable DF
# qstable Returns quantiles for stable DF
# rstable Returns random variates for stable DF
# FUNCTION: STABLE SLIDERS:
# symstbSlider Displays symmetric stable distribution function
# stableSlider Displays stable distribution function
################################################################################
################################################################################
# dsymstb Returns density for symmetric stable DF
# psymstb Returns probabilities for symmetric stable DF
# qsymstb Returns quantiles for symmetric stable DF
# rsymstb Returns random variates for symmetric stable DF
dsymstb =
function (x, alpha)
{ # # A function implemented by Diethelm Wuertz
# Description:
# Return symmetric alpha-stable pdf
# Note:
# symstb - returns symmetric alpha-stable pdf/cdf. The function
# implements J.H. McCulloch's Fortran program for symmetric
# distributions. Mc Cullochs approach has a density precision of
# 0.000066 and a distribution precision of 0.000022 for alpha in
# the range [0.84, 2.00]. We have added only first order tail
# approximation to calculate the tail density and probability.
# This has still to be improved!
# Changes:
#
# FUNCTION:
# Density:
ans = .Fortran("symstb",
as.double(x),
as.double(1:length(x)),
as.double(1:length(x)),
as.integer(length(x)),
as.double(alpha),
PACKAGE = "fBasics")[[3]]
# Return Value:
ans
}
# ------------------------------------------------------------------------------
psymstb =
function (q, alpha)
{ # A function implemented by Diethelm Wuertz
# Description:
# Return symmetric alpha-stable cdf
# Notes:
# symstb:
# Return symmetric alpha-stable pdf/cdf. The function
# implements J.H. McCulloch's Fortran program for symmetric
# distributions.
# Mc Cullochs approach has a density precision of 0.000066
# and a distribution precision of 0.000022 for alpha in the
# range [0.84, 2.00]. We have added only first order tail
# approximation to calculate the tail density and probability.
# This has still to be improved!
# Changes:
#
# FUNCTION:
# Return Value:
ans = .Fortran("symstb",
as.double(q),
as.double(1:length(q)),
as.double(1:length(q)),
as.integer(length(q)),
as.double(alpha),
PACKAGE = "fBasics")[[2]]
# Return Value:
ans
}
# ------------------------------------------------------------------------------
qsymstb =
function(p, alpha)
{ # A function implemented by Diethelm Wuertz
# Changes:
#
# FUNCTION:
# Parameter Check:
if (alpha > +2) stop("Error: alpha greater than 2")
if (alpha <= 0) stop("Error: alpha less or equal 0")
# Special Cases:
if (alpha == 2) result = qnorm(p = p, mean = 0, sd = sqrt(2))
if (alpha == 1) result = qcauchy(p = p)
# Continue:
if (alpha != 1 && alpha != 2) {
.froot <<- function(x, alpha, p) {
psymstb(q = x, alpha = alpha) - p
}
# Calculate:
result = rep(NA, times = length(p))
for (i in 1:length(p)) {
pp = p[i]
# xmin = -(1-pp)/pp
if (pp < 0.5) {
xmin = qcauchy(pp)
} else {
xmin = qnorm(pp, mean = 0, sd = sqrt(2))
}
# xmax = pp/(1-pp)
if (pp < 0.5) {
xmax = qnorm(pp, mean = 0, sd = sqrt(2))
} else {
xmax = qcauchy(pp)
}
iteration = NA
counter = 0
while (is.na(iteration)) {
iteration = .unirootNA(f = .froot, interval = c(xmin, xmax),
alpha = alpha, p = pp)
counter = counter + 1
xmin = xmin - 2^counter
xmax = xmax + 2^counter
}
result[i] = iteration
}
}
# Return Value:
result
}
# ------------------------------------------------------------------------------
rsymstb =
function(n, alpha)
{ # A function implemented by Diethelm Wuertz
# Description:
# Return random deviates from the stable family
# of probability distributions. The results of
# Chambers, Mallows, and Stuck is used.
# Changes:
#
# FUNCTION:
# Calculate uniform and exponential distributed random numbers:
theta = pi * (runif(n)-1/2)
w = -log(runif(n))
# Calculate Random Deviates:
if (alpha == 1) {
result = rcauchy(n)
} else {
result = (sin(alpha*theta) / ((cos(theta))^(1/alpha))) *
(cos((1-alpha)*theta)/w)^((1-alpha)/alpha)
}
# Add Attribute:
attr(result, "control") = c(dist = "symstb", alpha = as.character(alpha))
# Return Value:
result
}
################################################################################
# dstable Returns density for stable DF
# pstable Returns probabilities for stable DF
# qstable Returns quantiles for stable DF
# rstable Returns random variates for stable DF
# stableMode Computes stable mode
# .integrateStable Integrates internal functions for *stable
dstable =
function(x, alpha, beta, gamma = 1, delta = 0, pm = c(0, 1, 2))
{ # A function implemented by Diethelm Wuertz
# Description:
# Return alpha-stable density function (pdf) in form
# of parmeterization 1.
# The function uses the approach of J.P. Nolan for general
# stable distributions. Nolan derived expressions in form
# of integrals based on the charcteristic function for
# standardized stable random variables. These integrals
# can be numerically evaluated.
# Arguments:
# alpha = index of stability, in the range (0,2]
# beta = skewness, in the range [-1, 1]
# gamma = scale, in the range (0, infinity)
# delta = location, in the range (-infinity, +infinity)
# param = type of parmeterization
# Notes:
# The function doesn't apply for x[i] == 1, this has to be fixed!
# For R and SPlus compatibility use integrate()[[1]] instead of
# integrate()$value and integrate()$integral.
# optimize() works in both R and SPlus.
# Changes:
#
# FUNCTION:
# Settings:
subdivisions = 1000
tol = .Machine$double.eps
if (class(version) == "Sversion") {
subdivisions = 100
tol = sqrt(tol)
}
# Parameter Check:
if (alpha > +2) stop("Error: alpha greater than 2")
if (alpha <= 0) stop("Error: alpha less or equal 0")
if (beta < -1) stop("Error: beta less than -1")
if (beta > +1) stop("Error: beta greater than 1")
# Parameterizations:
pm = pm[1]
if (pm == 1) {
if (alpha == 1) {
delta = delta + beta*(2/pi)*gamma*log(gamma)
} else {
delta = delta + beta*gamma*tan(pi*alpha/2)
}
}
if (pm == 2) {
delta = delta - alpha^(-1/alpha)*gamma*stableMode(alpha, beta)
gamma = alpha^(-1/alpha) * gamma
}
# Special Cases:
if (alpha == 2) {
result = dnorm(x, mean = 0, sd = sqrt(2))
}
if (alpha == 1 & beta == 0) {
result = dcauchy(x)
}
# Shift and Scale:
x = (x - delta) / gamma
# General Case 0 < alpha < 2 and -1 <= beta <= 1 :
if (abs(alpha-1) < 1 & alpha != 1 & abs(beta) <= 1) {
# Function to Integrate:
g1 <<-
function(x, xarg, alpha, beta) {
varzeta = -beta * tan(pi*alpha/2)
theta0 = (1/alpha) * atan( beta * tan(pi*alpha/2))
v = (cos(alpha*theta0))^(1/(alpha-1)) *
(cos(x)/sin(alpha*(theta0+x)))^(alpha/(alpha-1)) *
(cos(alpha*theta0+(alpha-1)*x)/cos(x))
g = (xarg-varzeta)^(alpha/(alpha-1)) * v
gval = g * exp(-g)
gval
}
# Integration:
fct1 <<-
function(xarg, alpha, beta, tol, subdivisions) {
varzeta = -beta * tan(pi*alpha/2)
theta0 = (1/alpha) * atan( beta * tan(pi*alpha/2))
theta2 = optimize(f = g1, lower = -theta0, upper = pi/2,
maximum = TRUE, tol = tol, xarg = xarg,
alpha = alpha, beta = beta)$maximum
c2 = ( alpha / (pi*abs(alpha-1)*(xarg-varzeta)) )
result1 = .integrateStable(f = g1, lower = -theta0,
upper = theta2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
result2 = .integrateStable(f = g1, lower = theta2,
upper = pi/2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
c2*(result1+result2)
}
# Loop over all x values:
result = NULL
varzeta = -beta * tan(pi*alpha/2)
for (z in x) {
# if (z == varzeta) Modified D.W.
if (abs(z - varzeta) < 2 * .Machine$double.eps) {
theta0 = (1/alpha) * atan( beta * tan(pi*alpha/2))
result = c(result, gamma(1+1/alpha)*cos(theta0) /
(pi*(1+varzeta^2)^(1/(2*alpha))))
} else {
if (z > varzeta) {
result = c(result, fct1(xarg = z, alpha = alpha,
beta = beta, tol = tol, subdivisions = subdivisions))
}
if (z < varzeta) {
result = c(result, fct1(xarg = -z, alpha = alpha,
beta = -beta, tol = tol, subdivisions = subdivisions))
}
}
}
}
# General Case 0 < alpha < 2 and -1 <= beta <= 1 :
if (alpha == 1 & abs(beta) <= 1 & beta != 0) {
# Function to Integrate:
g2 <<-
function(x, xarg, alpha, beta) {
# x is a non-sorted vector!
v = (2/pi) * ((pi/2+beta*x) / cos(x)) *
exp((1/beta)*(pi/2+beta*x)*tan(x))
g = exp( -pi*xarg/(2*beta) ) * v
gval = g * exp(-g)
# replace NA at pi/2
for (i in 1:length(gval)) if(is.na(gval[i])) gval[i] = 0
gval
}
# Integration:
fct2 <<-
function(xarg, alpha, beta, tol, subdivisions) {
theta2 = optimize(f = g2, lower = -pi/2, upper = pi/2,
maximum = TRUE, tol = tol, xarg = xarg,
alpha = alpha, beta = beta)$maximum
c2 = 1 / (2*abs(beta))
result1 = .integrateStable(f = g2, lower = -pi/2,
upper = theta2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
result2 = .integrateStable(f = g2, lower = theta2,
upper = pi/2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
c2*(result1+result2)
}
# Loop over all x values:
result = NULL
for (z in x) {
if (z >= 0) {
result = c(result, fct2(xarg = z, alpha = alpha,
beta = beta, tol = tol, subdivisions = subdivisions))
} else {
result = c(result, fct2(xarg = -z, alpha = alpha,
beta = -beta, tol = tol, subdivisions = subdivisions))
}
}
}
# Result:
ans = result/gamma
# Return Value:
ans
}
# ------------------------------------------------------------------------------
pstable =
function(q, alpha, beta, gamma = 1, delta = 0, pm = c(0, 1, 2))
{ # A function implemented by Diethelm Wuertz
# Changes:
#
# FUNCTION:
# Settings:
subdivisions = 1000
tol = .Machine$double.eps
if (class(version) == "Sversion") {
subdivisions = 100
tol = sqrt(tol)
}
x = q
# Parameter Check:
if (alpha > +2) stop("Error: alpha greater than 2")
if (alpha <= 0) stop("Error: alpha less or equal 0")
if (beta < -1) stop("Error: beta less than -1")
if (beta > +1) stop("Error: beta greater than 1")
# Parameterizations:
pm = pm[1]
if (pm == 1) {
if (alpha== 1) {
delta = delta + beta*(2/pi)*gamma*log(gamma)
} else {
delta = delta + beta*gamma*tan(pi*alpha/2)
}
}
if (pm == 2) {
delta = delta - alpha^(-1/alpha)*gamma*stableMode(alpha, beta)
gamma = alpha^(-1/alpha) * gamma
}
# Special Cases:
if (alpha == 2) result = pnorm(x, mean = 0, sd = sqrt(2))
if (alpha == 1 & beta == 0) result = pcauchy(x)
# Shift and Scale:
x = (x - delta) / gamma
# General Case 0 < alpha < 2 and -1 <= beta <= 1 :
if (abs(alpha-1) < 1 & alpha !=1 & abs(beta) <= 1) {
# Function to Integrate:
G1 <<-
function(x, xarg, alpha, beta) {
varzeta = -beta * tan(pi*alpha/2)
theta0 = (1/alpha) * atan( beta * tan(pi*alpha/2))
v = (cos(alpha*theta0))^(1/(alpha-1)) *
(cos(x)/sin(alpha*(theta0+x)))^(alpha/(alpha-1)) *
cos(alpha*theta0+(alpha-1)*x)/cos(x)
g = (xarg-varzeta)^(alpha/(alpha-1)) * v
gval = exp(-g)
gval
}
# Integration:
FCT1 <<-
function(xarg, alpha, beta, tol, subdivisions) {
varzeta = -beta * tan(pi*alpha/2)
theta0 = (1/alpha) * atan( beta * tan(pi*alpha/2))
theta2 = optimize(f = G1, lower = -theta0, upper = pi/2,
maximum = TRUE, tol = tol, xarg = xarg,
alpha = alpha, beta = beta)$maximum
if (alpha < 1) c1 = (1/pi)*(pi/2-theta0)
if (alpha > 1) c1 = 1
c3 = sign(1-alpha)/pi
result1 = .integrateStable(f = G1, lower = -theta0,
upper = theta2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
result2 = .integrateStable(f = G1, lower = theta2,
upper = pi/2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
c1 + c3*(result1+result2)
}
# Loop over all x values:
result = rep(0, times = length(x))
for ( i in 1:length(result) ) {
varzeta = -beta * tan(pi*alpha/2)
if (abs(x[i] - varzeta) < 2 * .Machine$double.eps) {
theta0 = (1/alpha) * atan( beta * tan(pi*alpha/2))
result[i] = (1/pi)*(pi/2-theta0)
} else {
if (x[i] > varzeta) result[i] =
FCT1(xarg = x[i], alpha = alpha, beta = beta,
tol = tol, subdivisions = subdivisions)
if (x[i] < varzeta) result[i] =
1 - FCT1(xarg = -x[i], alpha = alpha, beta = -beta,
tol = tol, subdivisions = subdivisions)
}
}
}
# General alpha == 1 and 0 < |beta| <= 1 :
if (alpha == 1 & abs(beta) <= 1 & beta != 0) {
# Function to Integrate:
G2 <<-
function(x, xarg, alpha, beta) {
# x is a non-sorted vector!
v = (2/pi) * ((pi/2+beta*x) / cos(x)) *
exp((1/beta)*(pi/2+beta*x)*tan(x))
g = exp( -pi*xarg/(2*beta) ) * v
gval = exp(-g)
# replace NA at pi/2
for (i in 1:length(gval)) if(is.na(gval[i])) gval[i] = 0
gval
}
# Integration:
FCT2 <<-
function(xarg, alpha, beta, tol, subdivisions) {
theta2 = optimize(f = G2, lower = -pi/2, upper = pi/2,
maximum = TRUE, tol = tol, xarg = xarg,
alpha=alpha, beta = beta)$maximum
c3 = 1/pi
result1 = .integrateStable(f = G2, lower = -pi/2,
upper = theta2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
result2 = .integrateStable(f = G2, lower = theta2,
upper = pi/2, subdivisions = subdivisions,
rel.tol = tol, abs.tol = tol, xarg = xarg,
alpha = alpha, beta = beta)[[1]]
c3*(result1+result2)
}
# Loop over all x values:
result = rep(0, times = length(x))
for ( i in 1:length(result) ) {
if (beta >= 0) {
result[i] = FCT2(xarg = x[i], alpha = alpha,
beta = beta, tol = tol, subdivisions = subdivisions)
} else {
result[i] = 1 - FCT2(xarg = -x[i], alpha = alpha,
beta = -beta, tol = tol, subdivisions = subdivisions)
}
}
}
# Return Value:
result
}
# ------------------------------------------------------------------------------
qstable =
function(p, alpha, beta, gamma = 1, delta = 0, pm = c(0, 1, 2))
{ # A function implemented by Diethelm Wuertz
# Changes:
#
# FUNCTION:
# Settings:
subdivisions = 1000
tol = .Machine$double.eps
if (class(version) == "Sversion") {
subdivisions = 100
tol = sqrt(tol)
}
# Parameter Check:
if (alpha > +2) stop("Error: alpha greater than 2")
if (alpha <= 0) stop("Error: alpha less or equal 0")
if (beta < -1) stop("Error: beta less than -1")
if (beta > +1) stop("Error: beta greater than 1")
# Parameterizations:
pm = pm[1]
if (pm == 1) {
if (alpha== 1) {
delta = delta + beta*(2/pi)*gamma*log(gamma)
} else {
delta = delta + beta*gamma*tan(pi*alpha/2)
}
}
if (pm == 2) {
delta = delta - alpha^(-1/alpha)*gamma*stableMode(alpha, beta)
gamma = alpha^(-1/alpha) * gamma
}
# Special Cases:
if (alpha == 2) result = qnorm(p, mean = 0, sd = sqrt(2))
if (alpha == 1 & beta == 0) result = qcauchy(p)
# Range 0 < alpha < 2:
if (abs(alpha-1) < 1) {
.froot <<- function(x, alpha, beta, subdivisions, p) {
pstable(q = x, alpha = alpha, beta = beta, pm = 0) - p
}
# Calculate:
result = rep(NA, times = length(p))
for (i in 1:length(p)) {
pp = p[i]
if (beta < 0) {
xmin = -(1-pp)/pp
# xmax = pp/(1-pp)
if (pp < 0.5) {
xmax = qnorm(pp, mean = 0, sd = sqrt(2))
} else {
xmax = qcauchy(pp)
}
}
if (beta > 0 ) {
# xmin = -(1-pp)/pp
if (pp < 0.5) {
xmin = qcauchy(pp)
} else {
xmin = qnorm(pp, mean = 0, sd = sqrt(2))
}
xmax = pp/(1-pp)
}
if (beta == 0 ) {
# xmin = -(1-pp)/pp
if (pp < 0.5) {
xmin = qcauchy(pp)
} else {
xmin = qnorm(pp, mean = 0, sd = sqrt(2))
}
# xmax = pp/(1-pp)
if (pp < 0.5) {
xmax = qnorm(pp, mean = 0, sd = sqrt(2))
} else {
xmax = qcauchy(pp)
}
}
iteration = NA
counter = 0
while (is.na(iteration)) {
iteration = .unirootNA(f = .froot, interval = c(xmin, xmax),
alpha = alpha, beta = beta, p = pp, subdivisions =
subdivisions)
counter = counter + 1
xmin = xmin-2^counter
xmax = xmax+2^counter
}
result[i] = iteration
}
}
# Result:
ans = result * gamma + delta
# Return Value:
ans
}
# ------------------------------------------------------------------------------
rstable =
function(n, alpha, beta, gamma = 1, delta = 0, pm = c(0, 1, 2))
{ # A function implemented by Diethelm Wuertz
# Description:
# Return random deviates from the stable family
# of probability distributions.
# Changes:
#
# FUNCTION:
# Parameter Check:
if (alpha > +2) stop("Error: alpha greater than 2")
if (alpha <= 0) stop("Error: alpha less or equal 0")
if (beta < -1) stop("Error: beta less than -1")
if (beta > +1) stop("Error: beta greater than 1")
# Parameterizations:
pm = pm[1]
if (pm == 1) {
if (alpha== 1) {
delta = delta + beta*(2/pi)*gamma*log(gamma)
} else {
delta = delta + beta*gamma*tan(pi*alpha/2)
}
}
if (pm == 2) {
delta = delta - alpha^(-1/alpha)*gamma*stableMode(alpha, beta)
gamma = alpha^(-1/alpha) * gamma
}
# Calculate uniform and exponential distributed random numbers:
theta = pi * (runif(n)-1/2)
w = -log(runif(n))
# If alpha is equal 1 then:
if (alpha == 1 & beta == 0) {
result = rcauchy(n)
# Otherwise, if alpha is different from 1:
} else {
c = (1+(beta*tan(pi*alpha/2))^2)^(1/(2*alpha))
theta0 = (1/alpha)*atan(beta*tan(pi*alpha/2))
result = ( c*sin(alpha*(theta+theta0))/
(cos(theta))^(1/alpha) ) *
(cos(theta-alpha*(theta+theta0))/w)^((1-alpha)/alpha)
# Use Parametrization 0:
result = result - beta * tan(alpha*pi/2)
}
# Result:
ans = result * gamma + delta
# Add Attribute:
attr(ans, "control") = c(dist = "stable", alpha = as.character(alpha),
beta = as.character(beta), gamma = as.character(gamma),
delta = as.character(delta), pm = as.character(pm))
# Return Value:
ans
}
# ------------------------------------------------------------------------------
stableMode =
function(alpha, beta)
{ # A function implemented by Diethelm Wuertz
# Description:
# Compute the mode of the stable distribution function
# Notes:
# # Test for values close to beta = 1
# alpha = seq(0, 2, by = 0.1)
# ans = NULL
# for ( i in 1:length(alpha) ) {
# ans = rbind(ans, c(alpha[i],
# stableMode(alpha = alpha[i], beta = 0.99 ),
# stableMode(alpha = alpha[i], beta = 0.99999 ),
# stableMode(alpha = alpha[i], beta = 0.99999999 ),
# stableMode(alpha = alpha[i], beta = 0.99999999999 ) ) ) }
# ans
#
# alpha 0.99 0.99999 0.99999999 0.99999999999
# 0.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
# 0.2 -3.214142e-01 -3.246759e-01 -3.246787e-01 -3.246788e-01
# 0.4 -6.105318e-01 -6.158562e-01 -6.158616e-01 -6.158616e-01
# 0.6 -6.550106e-01 -6.594746e-01 -6.594790e-01 -6.594790e-01
# 0.8 -5.558811e-01 -5.590032e-01 -5.590063e-01 -5.590063e-01
# 1.0 -4.271033e-01 -4.293078e-01 -4.293099e-01 -4.293099e-01
# 1.2 -3.074015e-01 -3.090820e-01 -3.090804e-01 -3.090804e-01
# 1.4 -2.050956e-01 -2.063979e-01 -2.063951e-01 -2.063951e-01
# 1.6 -1.199623e-01 -1.208875e-01 -1.208853e-01 -1.208853e-01
# 1.8 -5.098617e-02 -5.145758e-02 -5.145639e-02 -5.145639e-02
# 2.0 -7.487432e-05 -7.487432e-05 -7.487432e-05 -7.487432e-05
# Changes:
#
# FUNCTION:
# Stable Mode:
if (beta > 0.99999999999) beta = 0.99999999999
if (beta == 0) {
ans = 0
} else {
if (alpha == 0) {
ans = 0
} else {
ans = optimize(f = dstable, interval = c(-0.7, 0),
maximum = TRUE, alpha = alpha, beta = beta)$maximum
}
}
# Return Value:
ans
}
# ------------------------------------------------------------------------------
.integrateStable =
function (f, lower, upper, subdivisions, rel.tol, abs.tol, ...)
{ # A function implemented by Diethelm Wuertz
# Changes:
#
# FUNCTION:
# Integrate:
if (class(version) != "Sversion") {
# R:
f = match.fun(f)
ff = function(x) f(x, ...)
wk = .External("call_dqags", ff,
rho = environment(), as.double(lower),
as.double(upper), as.double(abs.tol),
as.double(rel.tol), limit = as.integer(subdivisions),
PACKAGE = "base")
ans = wk[c("value", "abs.error", "subdivisions")]
} else {
# SPlus:
ans = integrate(f, lower, upper, subdivisions, rel.tol, abs.tol, ...)
}
# Return Value:
ans
}
################################################################################
# symstbSlider Displays symmetric stable distribution function
# stableSlider Displays stable distribution function
symstbSlider =
function()
{ # A function implemented by Diethelm Wuertz
# Description
# Displays the symmetric stable distribution
# Changes:
#
# FUNCTION:
# Internal Function:
refresh.code = function(...)
{
# Sliders:
N = .sliderMenu(no = 1)
alpha = .sliderMenu(no = 2)
# Compute Data:
xmin = round(qsymstb(0.01, alpha), digits = 2)
xmax = round(qsymstb(0.99, alpha), digits = 2)
s = seq(xmin, xmax, length = N)
y1 = dsymstb(s, alpha)
y2 = psymstb(s, alpha)
main1 = paste("Symmetric Stable Density\n",
"alpha = ", as.character(alpha))
main2 = paste("Symmetric Stable Probability\n",
"xmin [0.01%] = ", as.character(xmin), " | ",
"xmax [0.99%] = ", as.character(xmax))
# Frame:
par(mfrow = c(2, 1), cex = 0.7)
# Density:
plot(s, y1, type = "l", xlim = c(xmin, xmax), col = "steelblue")
abline (h = 0, lty = 3)
title(main = main1)
# Probability:
plot(s, y2, type = "l", xlim = c(xmin, xmax), ylim = c(0, 1),
col = "steelblue" )
abline (h = 0, lty = 3)
title(main = main2)
# Reset Frame:
par(mfrow = c(1, 1), cex = 0.7)
}
# Open Slider Menu:
.sliderMenu(refresh.code,
names = c( "N", "alpha"),
minima = c( 50, 0.10),
maxima = c( 1000, 2.00),
resolutions = c( 50, 0.10),
starts = c( 50, 1.75))
}
# ------------------------------------------------------------------------------
stableSlider =
function()
{ # A function implemented by Diethelm Wuertz
# Description:
# Displays the stable distribution
# Changes:
#
# FUNCTION:
# Internal Function:
refresh.code = function(...)
{
# Sliders:
N = .sliderMenu(no = 1)
alpha = .sliderMenu(no = 2)
beta = .sliderMenu(no = 3)
gamma = .sliderMenu(no = 4)
delta = .sliderMenu(no = 5)
pm = .sliderMenu(no = 6)
# Compute Data:
xmin = round(qstable(0.01, alpha, beta, gamma, delta, pm), digits = 2)
xmax = round(qstable(0.99, alpha, beta, gamma, delta, pm), digits = 2)
s = seq(xmin, xmax, length = N)
y1 = dstable(s, alpha, beta, gamma, delta, pm)
y2 = pstable(s, alpha, beta, gamma, delta, pm)
main1 = paste("Stable Density\n",
"alpha = ", as.character(alpha), " | ",
"beta = ", as.character(beta), " | ",
"gamma = ", as.character(gamma), " | ",
"delta = ", as.character(delta))
main2 = paste("Stable Probability\n",
"xmin 0.01% = ", as.character(xmin), " | ",
"xmax 0.99% = ", as.character(xmax), " | ",
"pm = ", as.character(pm))
# Frame:
par(mfrow = c(2, 1), cex = 0.7)
# Density:
plot(s, y1, type = "l", xlim = c(xmin, xmax), col = "steelblue")
abline (h = 0, lty = 3)
title(main = main1)
# Probability:
plot(s, y2, type = "l", xlim = c(xmin, xmax), ylim = c(0, 1),
col = "steelblue" )
abline(h = 0.0, lty = 3)
abline(h = 1.0, lty = 3)
abline(h = 0.5, lty = 3)
abline(v = delta, lty = 3, col = "red")
title(main = main2)
# Reset Frame:
par(mfrow = c(1, 1), cex = 0.7)
}
# Open Slider Menu:
.sliderMenu(refresh.code,
names = c( "N", "alpha", "beta", "gamma", "delta", "pm"),
minima = c( 10, 0.00, -1.00, 0.00, -5.0, 0),
maxima = c( 1000, 2.00, +1.00, 5.00, +5.0, 2),
resolutions = c( 50, 0.20, 0.20, 1.00, 1.0, 1),
starts = c( 50, 1.80, 0.00, 1.00, 0.0, 0))
}
################################################################################
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