# 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: GENERALIZED DISTRIBUTION:
# nigFit Fits parameters of a normal inverse Gaussian density
# .nigFit.mle max Log-likelihood Estimation
# .nigFit.gmm gemeralized method of moments estimation
# .nigFit.mps maximum product spacings estimation
# .nigFit.vmps minimum variance product spacings estimation
################################################################################
nigFit <-
function(x, alpha = 1, beta = 0, delta = 1, mu = 0,
method = c("mle", "gmm", "mps", "vmps"),
scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
{
# A function implemented by Diethelm Wuertz
# FUNCTION:
# Settings:
method = match.arg(method)
# Select:
if (method == "mle") {
# MLE:
fit = .nigFit.mle(x = x, alpha = alpha, beta = beta, delta = delta,
mu = mu , scale = scale, doplot = doplot, span = span,
trace = trace, title = title, description = description, ...)
} else if (method == "gmm") {
# GMM:
fit = .nigFit.gmm(x = x, alpha = alpha, beta = beta, delta = delta,
mu = mu , scale = scale, doplot = doplot, span = span,
trace = trace, title = title, description = description, ...)
} else if (method == "mps") {
# MPS:
fit = .nigFit.mps(x = x, alpha = alpha, beta = beta, delta = delta,
mu = mu , scale = scale, doplot = doplot, span = span,
trace = trace, title = title, description = description, ...)
} else if (method == "vmps") {
# MPS:
fit = .nigFit.vmps(x = x, alpha = alpha, beta = beta, delta = delta,
mu = mu , scale = scale, doplot = doplot, span = span,
trace = trace, title = title, description = description, ...)
}
# Return Value:
fit
}
# ------------------------------------------------------------------------------
.nigFit.mle <-
function(x, alpha = 1, beta = 0, delta = 1, mu = 0,
scale = TRUE, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits parameters of a NIG using maximum log-likelihood
# Example:
# set.seed(4711); x = rnig(500); mle = .nigFit.mle(x); mle@fit$estimate
# FUNCTION:
# Transform:
x.orig = x
x = as.vector(x)
if (scale) {
SD = sd(x)
x = x / SD }
# Objective Function:
obj = function(x, y = x, trace) {
if (abs(x[2]) >= x[1]) return(1e9)
f = -sum(dnig(y, x[1], x[2], x[3], x[4], log = TRUE))
# Print Iteration Path:
if (trace) {
cat("\n Objective Function Value: ", -f)
cat("\n Parameter Estimates: ", x, "\n")
}
f }
# Parameter Estimation:
eps = 1e-10
BIG = 1000
fit = nlminb(
start = c(alpha, beta, delta, mu),
objective = obj,
lower = c(eps, -BIG, eps, -BIG),
upper = BIG,
y = x,
trace = trace)
names(fit$par) <- c("alpha", "beta", "delta", "mu")
# Rescale Result:
if (scale) {
fit$scaleParams = c(SD, SD, 1/SD, 1/SD)
fit$par = fit$par / fit$scaleParams
fit$objective = obj(fit$par, y = as.vector(x.orig), trace = trace)
} else {
fit$scaleParams = rep(1, time = length(fit$par))
}
fit$scale = scale
fit$estimate = fit$par
fit$minimum = -fit$objective
fit$code = fit$convergence
# Standard Errors and t-Values:
fit = .distStandardErrors(fit, obj, x)
# Add Title and Description:
if (is.null(title)) title = "Normal Inverse Gaussian Parameter Estimation"
if (is.null(description)) description = description()
# Optional Plot:
if (doplot) .distFitPlot(
fit,
x = x.orig,
FUN = "dnig",
main = "NIG Parameter Estimation",
span = span, add = add, ...)
# Return Value:
new("fDISTFIT",
call = match.call(),
model = "Normal Inverse Gaussian Distribution",
data = as.data.frame(x.orig),
fit = fit,
title = as.character(title),
description = description() )
}
# ------------------------------------------------------------------------------
.nigFit.gmm <-
function(x,
scale = TRUE, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits parameters of a NIG using GMM estimator
# Example:
# set.seed(4711); x = rnig(500); gmm = .nigFit.gmm(x)@fit$estimate; gmm
# FUNCTION:
# Transform:
x.orig = x
x = as.vector(x)
if (scale) {
SD = sd(x)
x = x / SD }
# Settings:
CALL = match.call()
# Parameter Estimation:
obj <- function(Theta, x) {
# Parameters:
alpha = Theta[1]
beta = Theta[2]
delta = Theta[3]
mu = Theta[4]
names(Theta) <- c("alpha", "beta", "delta", "mu")
# Trace:
if (TRUE) print(Theta)
# Moments:
m1 <- x - .ghMuMoments(1, alpha, beta, delta, mu, lambda = -0.5)
m2 <- x^2 - .ghMuMoments(2, alpha, beta, delta, mu, lambda = -0.5)
m3 <- x^3 - .ghMuMoments(3, alpha, beta, delta, mu, lambda = -0.5)
m4 <- x^4 - .ghMuMoments(4, alpha, beta, delta, mu, lambda = -0.5)
# Result:
f <- cbind(m1, m2, m3, m4)
return(f)
}
r <- .gmm(g = obj, x = x, t0 = c(1, 0, 1, 0))
names(r$par) <- c("alpha", "beta", "delta", "mu")
# Add Title and Description:
if (is.null(title)) title = "Normal Inverse Gaussian Parameter Estimation"
if (is.null(description)) description = description()
# Rescale Result:
if (scale) {
r$par = r$par / c(SD, SD, 1/SD, 1/SD)
r$objective = NA
}
fit = list(estimate = r$par)
# Optional Plot:
if (doplot) {
x = as.vector(x.orig)
if (span == "auto") span = seq(min(x), max(x), length = 51)
z = density(x, n = 100, ...)
x = z$x[z$y > 0]
y = z$y[z$y > 0]
y.points = dnig(span, r$par[1], r$par[2], r$par[3], r$par[4])
ylim = log(c(min(y.points), max(y.points)))
if (add) {
lines(x = span, y = log(y.points), col = "steelblue")
} else {
plot(x, log(y), xlim = c(span[1], span[length(span)]),
ylim = ylim, type = "p", xlab = "x", ylab = "log f(x)", ...)
title("NIG GMM Parameter Estimation")
lines(x = span, y = log(y.points), col = "steelblue")
}
}
# Return Value:
new("fDISTFIT",
call = as.call(CALL),
model = "Normal Inverse Gaussian Distribution",
data = as.data.frame(x.orig),
fit = fit,
title = as.character(title),
description = description() )
}
# ------------------------------------------------------------------------------
.nigFit.mps <-
function(x, alpha = 1, beta = 0, delta = 1, mu = 0,
scale = TRUE, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits parameters of a NIG using maximum product spacings
# Example:
# set.seed(4711); x = rnig(500); mps = .nigFit.mps(x)@fit$estimate; mps
# FUNCTION:
# Transform:
x.orig = x
x = as.vector(x)
if (scale) {
SD = sd(x)
x = x / SD }
# Settings:
CALL = match.call()
# Parameter Estimation:
obj <- function(x, y = x, trace) {
if (abs(x[2]) >= x[1]) return(1e9)
DH = diff(c(0, na.omit(.pnigC(sort(y), x[1], x[2], x[3], x[4])), 1))
f = -mean(log(DH[DH > 0]))*length(y)
# Print Iteration Path:
if (trace) {
cat("\n Objective Function Value: ", -f)
cat("\n Parameter Estimates: ", x[1], x[2], x[3], x[4], "\n")
}
f }
eps = 1e-10
BIG = 1000
r = nlminb(start = c(alpha, beta, delta, mu), objective = obj,
lower = c(eps, -BIG, eps, -BIG), upper = BIG, y = x, trace = trace)
names(r$par) <- c("alpha", "beta", "delta", "mu")
# Standard Errors:
hessian = tsHessian(x = r$par, fun = obj, y = x, trace = FALSE)
colnames(hessian) = rownames(hessian) = names(r$par)
varcov = solve(hessian)
par.ses = sqrt(diag(varcov))
if (scale) par.ses = par.ses / c(SD, SD, 1/SD, 1/SD)
# Add Title and Description:
if (is.null(title)) title = "NIG mps Parameter Estimation"
if (is.null(description)) description = description()
# Result:
if (scale) {
r$par = r$par / c(SD, SD, 1/SD, 1/SD)
r$objective = obj(r$par, y = as.vector(x.orig), trace = trace)
}
fit = list(
estimate = r$par,
minimum = -r$objective,
error = par.ses,
code = r$convergence)
# Optional Plot:
if (doplot) {
x = as.vector(x.orig)
if (span == "auto") span = seq(min(x), max(x), length = 501)
z = density(x, n = 100, ...)
x = z$x[z$y > 0]
y = z$y[z$y > 0]
y.points = dnig(span, r$par[1], r$par[2], r$par[3], r$par[4])
ylim = log(c(min(y.points), max(y.points)))
if (add) {
lines(x = span, y = log(y.points), col = "steelblue")
} else {
plot(x, log(y), xlim = c(span[1], span[length(span)]),
ylim = ylim, type = "p", xlab = "x", ylab = "log f(x)", ...)
title("NIG MPS Parameter Estimation")
lines(x = span, y = log(y.points), col = "steelblue")
}
}
# Return Value:
new("fDISTFIT",
call = as.call(CALL),
model = "Normal Inverse Gaussian Distribution",
data = as.data.frame(x.orig),
fit = fit,
title = as.character(title),
description = description() )
}
# ------------------------------------------------------------------------------
.nigFit.vmps <-
function (x, alpha = 1, beta = 0, delta = 1, mu = 0,
scale = TRUE, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
title = NULL,description = NULL, ...)
{
# A function implemented by Yohan Chalabi
# Description:
# Fits parameters of a NIG using maximum product spacings
# Example:
# set.seed(4711); x = rnig(500); vmps = .nigFit.vmps(x)@fit$estimate; vmps
# FUNCTION:
# Transform:
x.orig = x
x = as.vector(x)
if (scale) {
SD = sd(x)
x = x/SD
}
# Settings:
CALL = match.call()
# Parameter Estimation:
obj <- function(x, y = x, trace) {
if (abs(x[2]) >= x[1]) return(1e+9)
DH = diff(c(0, na.omit(.pnigC(sort(y), x[1], x[2], x[3], x[4])), 1))
f = log(var(DH[DH > 0]))
if (trace) {
cat("\n Objective Function Value: ", -f)
cat("\n Parameter Estimates: ", x[1], x[2], x[3], x[4], "\n")
}
f
}
eps = 1e-10
BIG = 1000
r = nlminb(
start = c(alpha, beta, delta, mu),
objective = obj,
lower = c(eps, -BIG, eps, -BIG),
upper = BIG, y = x,
trace = trace)
names(r$par) <- c("alpha", "beta", "delta", "mu")
# Standard Errors:
hessian = tsHessian(x = r$par, fun = obj, y = x, trace = FALSE)
colnames(hessian) = rownames(hessian) = names(r$par)
varcov = solve(hessian)
par.ses = sqrt(diag(varcov))
if (scale) par.ses = par.ses / c(SD, SD, 1/SD, 1/SD)
# Add Title and Description:
if (is.null(title)) title = "NIG varMPS Parameter Estimation"
if (is.null(description)) description = description()
# Result:
if (scale) {
r$par = r$par/c(SD, SD, 1/SD, 1/SD)
r$objective = obj(r$par, y = as.vector(x.orig), trace = trace)
}
fit = list(
estimate = r$par,
minimum = -r$objective,
error = par.ses,
code = r$convergence)
# Optional Plot:
if (doplot) {
x = as.vector(x.orig)
if (span == "auto") span = seq(min(x), max(x), length = 501)
z = density(x, n = 100, ...)
x = z$x[z$y > 0]
y = z$y[z$y > 0]
y.points = dnig(span, r$par[1], r$par[2], r$par[3], r$par[4])
ylim = log(c(min(y.points), max(y.points)))
if (add) {
lines(x = span, y = log(y.points), col = "steelblue")
} else {
plot(x, log(y), xlim = c(span[1], span[length(span)]),
ylim = ylim, type = "p", xlab = "x", ylab = "log f(x)", ...)
title("NIG varMPS Parameter Estimation")
lines(x = span, y = log(y.points), col = "steelblue")
}
}
# Return Value:
new("fDISTFIT",
call = as.call(CALL),
model = "Normal Inverse Gaussian Distribution",
data = as.data.frame(x.orig),
fit = fit,
title = as.character(title),
description = description() )
}
################################################################################