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RandomFields (version 3.1.36)

RMmodelsAdvanced: Advanced features of the mdoels

Description

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

Arguments

Details

Further stationary and isotropic models

RMaskey
Askey model (generalized test or triangle model)
RMbcw
bridging model between RMcauchy and RMgenfbm
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
RMlsfbm locally stationary fractal Brownian motion
RMpenta
penta model (see Chiles \& Delfiner)
RMpower
Golubov's model
RMwave
cardinal sine

Variogram models (stationary increments/intrinsically stationary)

RMbcw
bridging model between RMcauchy and RMgenfbm
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.

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

Stationary and isotropic composed models (operators)

RMcutoff
Gneiting's modification towards finite range
RMintrinsic
Stein's modification towards finite range
RMnatsc
practical range
RMstein
Stein's modification towards finite range

Stationary space-time models

See RMmodelsSpaceTime

Non-stationary models

See RMmodelsNonstationary

Negative definite models that are not variograms

RMsum
a non-stationary variogram model

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

See RMmodelsTailCorrelation.

Other covariance models

RMuser
User defined model
RMfixcov
User defined covariance structure

Trend models

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.
  • 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.
  • Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. Journal of Statistical Software, 63 (8), 1-25, url = ‘http://www.jstatsoft.org/v63/i08/’

    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

Run this code
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

## 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)



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