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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: PARAMETER ESTIMATION:
# sgedFit Fit the parameters for a skew GED distribution
################################################################################
.sgedFit <-
function(x, mean = 0, sd = 1, nu = 2, xi = 1.5,
scale = NA, doplot = TRUE, add = FALSE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits parameters of skewed GED using maximum log-likelihood
# Example:
# set.seed(4711); x = rsged(500); .sgedFit(x)@fit$estimate
# FUNCTION:
# Settings:
dist = dsged
model = "SGED Parameter Estimation"
scale = "not used"
x = x.orig = as.vector(x)
# Parameter Estimation:
obj = function(x, y = x, trace) {
f <- tryCatch(-sum(log(dist(y, x[1], x[2], x[3], x[4]))), error=identity)
if (is.na(f) || inherits(f, "error")) return(1e9)
# Print Iteration Path:
if (trace) {
cat("\n Objective Function Value: ", -f)
cat("\n Parameter Estimates: ", x, "\n")
}
f }
r = nlminb(
start = c(mean = 0, sd = 1, nu = 2, xi = 1.5),
objective = obj,
lower = c(-Inf, 0, 0, 0),
upper = c( Inf, Inf, Inf, Inf),
y = x,
trace = trace)
names(r$par) <- c("mean", "sd", "nu", "xi")
# Add Title and Description:
if (is.null(title)) title = model
if (is.null(description)) description = description()
# Result:
fit = list(estimate = r$par, minimum = -r$objective, 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$y > 0]
y.points = dist(span, r$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(main = model)
lines(x = span, y = log(y.points), col = "steelblue")
}
}
# Return Value:
new("fDISTFIT",
call = match.call(),
model = model,
data = as.data.frame(x.orig),
fit = fit,
title = title,
description = description() )
}
# ------------------------------------------------------------------------------
sgedFit <-
function(x, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fit the parameters for a skew Normal distribution
# FUNCTION:
# Start Value:
start = c(mean = mean(x), sd = sqrt(var(x)), nu = 2, xi = 1)
# Log-likelihood Function:
loglik = function(x, y = x){
f = -sum(log(dsged(y, x[1], x[2], x[3], x[4])))
f }
# Minimization:
fit = nlminb(
start = start,
objective = loglik,
lower = c(-Inf, 0, 0, 0),
upper = c( Inf, Inf, Inf, Inf), y = x, ...)
# Add Names to $par
names(fit$par) = c("mean", "sd", "nu", "xi")
# Return Value:
fit
}
################################################################################
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