https://github.com/cran/nacopula
Tip revision: e24ab1e1bade02a8136bd488815825e92fa6acd7 authored by Martin Maechler on 18 August 2010, 00:00:00 UTC
version 0.4-3
version 0.4-3
Tip revision: e24ab1e
acopula-class.Rd
\name{acopula-class}
\Rdversion{1.1}
\title{Class "acopula" of Archimedean Copula Families}
\docType{class}
\alias{acopula-class}
%
\alias{initialize,acopula-method}
\alias{show,acopula-method}
%
\description{
This class \code{"acopula"} of Archimedean Copula Families
is mainly used for providing objects of known Archimedean families
with all related functions.
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{new("acopula", ...)}.
For several well-known Archimedean copula families, the package \pkg{nacopula}
already provides such family objects.
}
\section{Slots}{
\describe{
\item{\code{name}:}{a string (class \code{"character"}) describing
the copula family, e.g., "AMH" (or simply "A"), "Clayton" ("C"),
"Frank" ("F"), "Gumbel" ("G"), or "Joe" ("J").}
\item{\code{psi}, \code{psiInv}:}{The Archimedean generator, a
\code{\link{function}}, and its inverse.}
\item{\code{theta}:}{parameter value, a \code{\link{numeric}}, where
\code{NA} means \dQuote{unspecified}.}
\item{\code{paraInterval}:}{Either \code{\link{NULL}} or object of class
\code{"\linkS4class{interval}"}, typically from a call such as
\code{\link{interval}("[a,b)")}.}
\item{\code{paraConstr}:}{A function of \code{theta} returning
\code{TRUE} if and only if \code{theta} is a valid parameter value. Note
that \code{paraConstr} is built automatically from the interval,
whenever the \code{paraInterval} slot is valid.
\code{"\linkS4class{interval}"}.}
\item{\code{nestConstr}:}{A \code{\link{function}}, which returns
\code{TRUE} if and only if the two provided parameters \code{theta0} and
\code{theta1} satisfy the sufficient nesting condition for this family.}
\item{\code{V0}:}{A \code{\link{function}} which samples \code{n} random
variates from the distribution \eqn{F} with Laplace-Stieltjes transform
\eqn{\psi}{psi} and parameter \code{theta}.}
\item{\code{V01}:}{A \code{\link{function}} which obtains a vector of
realizations of \code{V0} and two parameters \code{theta0}, \code{theta1}
which satisfy the sufficient nesting condition for this family, and which
returns a vector of the same length as \code{V0} with random variates from
the distribution function \eqn{F_{01}}{F01} with Laplace-Stieltjes
transform \eqn{\psi_{01}}{psi01} and parameters
\eqn{\vartheta_0=\,}{theta0=}\code{theta0},
\eqn{\vartheta_1=\,}{theta1=}\code{theta1}.}
\item{\code{tau}, \code{tauInv}:}{Compute Kendall's tau of the bivariate
Archimedean copula with generator \eqn{\psi}{psi} as a
\code{\link{function}} of \code{theta}, respectively, \code{theta} as a
functionof Kendall's tau.}
\item{\code{lambdaL}, \code{lambdaU}, \code{lambdaLInv}, \code{lambdaUInv}:}{
Compute the lower (upper) tail-dependence coefficient of the bivariate
Archimedean copula with generator \eqn{\psi}{psi} as a
\code{\link{function}} of \code{theta}, respectively, \code{theta} as a
function of the lower (upper) tail-dependence coefficient.}
}
For more details about Archimedean families, corresponding distributions and
properties, see the references.
}
\section{Methods}{
\describe{
\item{initialize}{\code{signature(.Object = "acopula")}: is used to
automatically construct the \code{paraConstr} function slot, when
the \code{paraInterval} is provided (typically via
\code{\link{interval}()}).}
\item{show}{\code{signature("acopula")}: compact overview of the copula.}
}
}
\author{Martin Maechler}
\seealso{
Specific provided copula family objects, e.g.,
\code{\link{copAMH}}, \code{\link{copClayton}}, \code{\link{copFrank}},
\code{\link{copGumbel}}, \code{\link{copJoe}}.
\cr To access these, \code{\link{getAcop}}.
A \emph{nested} Archimedean copula \emph{without}
child copulas, see class \code{"\linkS4class{nacopula}"},
is a proper Archimedean copula, and hence,
\code{\link{onacopula}()} can be used to construct a specific
parametrized Archimedean copula, see the example below.
}
\references{
Hofert, M. (2010a),
Efficiently sampling nested Archimedean copulas,
\emph{Computational Statistics & Data Analysis}, in press.
Hofert, M. (2010b),
\emph{Sampling Nested Archimedean Copulas with Applications to CDO Pricing},
Suedwestdeutscher Verlag fuer Hochschulschriften AG & Co. KG.
}
\examples{
## acopula class information
showClass("acopula")
## Information and structure of Clayton copulas
copClayton
str(copClayton)
## What are admissible parameters for Clayton copulas?
copClayton@paraInterval
## Can two Clayton copulas with parameters theta0 and theta1 be nested?
## Case 1: theta0 = 3, theta1 = 2
copClayton@nestConstr(theta0 = 3, theta1 = 2) # FALSE
## Case 2: theta0 = 2, theta1 = 3
copClayton@nestConstr(theta0 = 2, theta1 = 3) # TRUE
## For more examples, see help(acopula-families)
}
\keyword{classes}