RandomFields (version 3.1.16)

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

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)

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

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)