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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: ARCHIMEDEAN COPULAE PARAMETER FITTING:
# archmCopulaSim Simulates bivariate elliptical copula
# archmCopulaFit Fits the paramter of an elliptical copula
################################################################################
################################################################################
# FUNCTION: ARCHIMEDEAN COPULAE PARAMETER FITTING:
# archmCopulaSim Simulates bivariate elliptical copula
# archmCopulaFit Fits the paramter of an elliptical copula
archmCopulaSim <-
function (n, alpha = NULL, type = archmList())
{
# A function implemented by Diethelm Wuertz
# Description:
# Simulates bivariate elliptical Copula
# Match Arguments:
type <- match.arg(type)
Type <- as.integer(type)
# Settings:
if (is.null(alpha)) alpha = archmParam(type)$param
# Random Variates:
ans <- rarchmCopula(n = n, alpha = alpha, type = type)
# Control:
control = list(alpha = alpha[[1]], copula = "archm", type = type)
attr(ans, "control")<-unlist(control)
# Return Value:
ans
}
# ------------------------------------------------------------------------------
archmCopulaFit <-
function(u, v = NULL, type = archmList(), ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits the paramter of an elliptical copula
# Note:
# The upper limit for nu is 100
# FUNCTION:
# Match Arguments:
type = match.arg(type)
Type = as.integer(type)
# Settings:
U = u
V = v
if (is.list(u)) {
U = u[[1]]
V = u[[2]]
}
if (is.matrix(u)) {
U = u[, 1]
V = u[, 2]
}
# Estimate Rho from Kendall's tau for all types of Copula:
alpha = archmParam(type)$param
# Estimate Copula:
fun = function(x, type, U, V) {
-mean( log(darchmCopula(u = U, v = V, alpha = x, type = type)) )
}
range = archmRange(type)
fit = nlminb(start = alpha, objective = fun,
lower = range[1], upper = range[2], type = type, U = U, V = V, ...)
# Return Value:
fit
}
################################################################################
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