RandomFields (version 3.1.12)

RMmodelsAdvanced: Advanced features of the mdoels

Description

Here, further models and advanced comments for RMmodel are given. See also RFgetModelNames.

Details

Further stationary and isotropic models

ll{ RMaskey Askey model (generalized test or triangle model) RMbessel Bessel family RMcircular circular model RMconstant spatially constant model RMcubic cubic model (see Chiles & Delfiner) RMdagum Dagum model RMdampedcos exponentially damped cosine RMqexp Variant of the exponential model RMfractdiff fractionally differenced process RMfractgauss fractional Gaussian noise RMgengneiting generalized Gneiting model RMgneitingdiff Gneiting model for tapering RMhyperbolic generalised hyperbolic model RMlgd Gneiting's local-global distinguisher RMma one of Ma's model RMpenta penta model (see Chiles & Delfiner) RMpower Golubov's model RMwave cardinal sine }

Variogram models (stationary increments/intrinsically stationary)

ll{ RMdewijsian generalised version of the DeWijsian model RMgenfbm generalized fractal Brownian motion RMflatpower similar to fractal Brownian motion but always smooth at the origin }

General composed models (operators)

Here, composed models are given that can be of any kind (stationary/non-stationary), depending on the submodel.

ll{RMbernoulli Correlation function of a binary field based on a Gaussian field RMexponential exponential of a covariance model RMintexp integrated exponential of a covariance model (INCLUDES ma2) RMpower powered variograms RMqam Porcu's quasi-arithmetric-mean model RMS details on the optional transformation arguments (var, scale, Aniso, proj). }

Stationary and isotropic composed models (operators)

ll{ RMcutoff Gneiting's modification towards finite range RMintrinsic Stein's modification towards finite range RMnatsc practical range RMstein Stein's modification towards finite range RMtbm Turning bands operator }

Stationary space-time models See RMmodelsSpaceTime

Non-stationary models See RMmodelsNonstationary

Negative definite models that are not variograms ll{ RMsum a non-stationary variogram model }

Models related to max-stable random fields (tail correlation functions) See RMmodelsTailCorrelation.

Other covariance models ll{ RMuser User defined model RMfixcov User defined covariance structure }

Trend models ll{ Aniso for space transformation (not really trend, but similiar) RMcovariate spatial covariates RMprod to model variability of the variance RMpolynome easy modelling of polynomial trends RMtrend for explicite trend modelling R.models for implicite trend modelling R.c for multivariate trend modelling }

Auxiliary models See Auxiliary RMmodels.

References

• Chiles, J.-P. and Delfiner, P. (1999)Geostatistics. Modeling Spatial Uncertainty.New York: Wiley. % \item Gneiting, T. and Schlather, M. (2004) % Statistical modeling with covariance functions. % \emph{In preparation.}
• Schlather, M. (1999)An introduction to positive definite functions and to unconditional simulation of random fields.Technical report ST 99-10, Dept. of Maths and Statistics, Lancaster University.
• Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M.,Space-Time Processes and Challenges Related to Environmental Problems.New York: Springer. % \item Schlather, M. (2002) Models for stationary max-stable % random fields. \emph{Extremes} \bold{5}, 33-44.
• Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with packageRandomFields.Journal of Statistical Software,63(8), 1-25, url =http://www.jstatsoft.org/v63/i08/../doc/multivariate_jss.pdf{multivariate}, the corresponding vignette.
• Yaglom, A.M. (1987)Correlation Theory of Stationary and Related Random Functions I, Basic Results.New York: Springer.
• Wackernagel, H. (2003)Multivariate Geostatistics.Berlin: Springer, 3nd edition.

See Also

RFformula, RM, RMmodels, RMmodelsAuxiliary

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
StartExample()
## a non-stationary field with a sharp boundary of
## of the differentiabilities
x <- seq(-0.6, 0.6, len=50)
model <- RMwhittle(nu=0.8 + 1.5 * R.is(R.p(new="isotropic"), "<=", 0.5))
z <- RFsimulate(model=model, x, x, n=4)
plot(z)


FinalizeExample()