dist-ghFit.R
# 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:
# ghFit Fits parameters of a generalized hyperbolic DF
################################################################################
ghFit <-
function(x, alpha = 1, beta = 0, delta = 1, mu = 0, lambda = -1/2,
scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits parameters of a generalized hyperbolic density
# FUNCTION:
# Transform:
x.orig = x
x = as.vector(x)
if (scale) {
SD = sd(x)
x = x / SD
}
# Settings:
CALL = match.call()
# Log-likelihood Function:
obj = function(x, y = x, trace){
if (NA %in% x) return(1e99)
if (abs(x[2]) >= x[1]) return(1e99)
f = -sum(dgh(y, x[1], x[2], x[3], x[4], x[5], log = TRUE))
# Print Iteration Path:
if (trace) {
cat("\n Objective Function Value: ", -f)
cat("\n Parameter Estimates: ", x, "\n")
}
f
}
# Minimization:
r = # Variable Transformation and Minimization:
eps = 1e-10
BIG = 1000
f = obj(x = c(alpha, beta, delta, mu, lambda), y = x, trace = FALSE)
r = nlminb(start = c(alpha, beta, delta, mu, lambda), objective = obj,
lower = c(eps, -BIG, eps, -BIG, -BIG), upper = BIG, y = x,
trace = trace)
names(r$par) <- c("alpha", "beta", "delta", "mu", "lambda")
# Result:
if (scale) {
r$par = r$par / c(SD, SD, 1/SD, 1/SD, 1)
r$objective = obj(r$par, y = as.vector(x.orig), trace = trace)
}
# Optional Plot:
if (doplot) {
x = as.vector(x.orig)
if (span == "auto") span = seq(min(x), max(x), length = 51)
z = density(x, n = 100, ...)
x = z$x[z$y > 0]
y = z$y[z$y > 0]
y.points = dnig(span, r$par[1], r$par[2], r$par[3], r$par[4])
ylim = log(c(min(y.points), max(y.points)))
plot(x, log(y), xlim = c(span[1], span[length(span)]),
ylim = ylim, type = "p", xlab = "x", ylab = "log f(x)", ...)
title("GH Parameter Estimation")
lines(x = span, y = log(y.points), col = "steelblue")
}
# Add Title and Description:
if (is.null(title)) title = "Generalized Hyperbolic Parameter Estimation"
if (is.null(description)) description = description()
# Fit:
fit = list(estimate = r$par, minimum = -r$objective, code = r$convergence)
# Return Value:
new("fDISTFIT",
call = as.call(CALL),
model = "Generalized Hyperbolic Distribution",
data = as.data.frame(x.orig),
fit = fit,
title = as.character(title),
description = description() )
}
################################################################################