https://github.com/cran/RandomFields
Tip revision: fd4911aa390fd49ddab92bd139bbbf35422e32e5 authored by Martin Schlather on 06 February 2020, 05:20:37 UTC
version 3.3.8
version 3.3.8
Tip revision: fd4911a
RMaskey.Rd
\name{RMaskey}
\alias{RMaskey}
\alias{RMtent}
\alias{truncated power function}
\title{Askey model}
\description{
Askey's model
\deqn{C(x)= (1-x)^\alpha 1_{[0,1]}(x)}
}
\usage{
RMaskey(alpha, var, scale, Aniso, proj)
RMtent(var, scale, Aniso, proj)
}
\arguments{
\item{alpha}{a numerical value in the interval [0,1]}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above covariance
function remains unmodified.}
}
\details{
This covariance function is valid for dimension \eqn{d}{d} if
\eqn{\alpha \ge (d+1)/2}.
For \eqn{\alpha=1} we get the well-known triangle (or tent)
model, which is only valid on the real line.
}
\value{
\command{\link{RMaskey}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
Covariance function
\itemize{
\item Askey, R. (1973) \emph{Radial characteristic functions.}
Technical report, Research Center, University of Wisconsin-Madison.
\item
Golubov, B. I. (1981) On Abel-Poisson type and Riesz means,
\emph{Anal. Math.} 7, 161-184.
}
Applications as covariance function
\itemize{
\item Gneiting, T. (1999) Correlation functions for atmospheric data
analysis. \emph{Quart. J. Roy. Meteor. Soc.}, 125:2449-2464.
\item
Gneiting, T. (2002) Compactly supported correlation functions.
\emph{J. Multivar. Anal.}, 83:493-508.
\item
Wendland, H. (1994) \emph{Ein Beitrag zur Interpolation mit radialen
Basisfunktionen.} Diplomarbeit, Goettingen.
\item
Wendland, H.
Piecewise polynomial, positive definite and compactly supported radial
functions of minimal degree. Adv. Comput. Math., 4:389-396, 1995.
}
Tail correlation function (for \eqn{\alpha \ge [d / 2] + 1})
\itemize{
\item Strokorb, K., Ballani, F., and Schlather, M. (2014)
Tail correlation functions of max-stable processes: Construction
principles, recovery and diversity of some mixing max-stable
processes with identical TCF.
\emph{Extremes}, \bold{} Submitted.
}
}
\me
\seealso{
\command{\link{RMmodel}},
\command{\link{RMbigneiting}},
\command{\link{RMgengneiting}},
\command{\link{RMgneiting}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\keyword{spatial}
\keyword{models}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMtent()
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}}