RandomFields (version 3.0.32)

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 RMcauchy modified Cauchy family RMcubic cubic model (see Chiles & Delfiner) RMdagum Dagum model RMdampedcos exponentially damped cosine RMqexp Variant of the exponential model RMid identity 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, 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 for 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 natural pratical range operator RMstein Stein's modification towards finite range RMtbm Turning bands operator in three (spatial) dimensions }

Stationary space-time models

Here, most of the models are composed models (operators). ll{ RMave space-time moving average model RMcoxisham Cox-Isham model RMcurlfree curlfree (spatial) field (stationary and anisotropic) RMdivfree divergence free (spatial) vector valued field, (stationary and anisotropic) RMiaco non-separabel space-time model RMmastein Ma-Stein model RMnsst Gneiting's non-separable space-time model RMstein Stein's non-separabel space-time model RMstp Single temporal process RMtbm Turning bands operator}

Multivariate/Multivariable and vector valued models ll{ RMbiwm full bivariate Whittle-Matern model (stationary and isotropic) RMbigneiting bivariate Gneiting model (stationary and isotropic) RMcurlfree curlfree (spatial) vector-valued field (stationary and anisotropic) RMdelay bivariate delay effect model (stationary) RMdivfree divergence free (spatial) vector valued field, (stationary and anisotropic) RMkolmogorov Kolmogorov's model of turbulence RMmatrix trivial multivariate model RMmqam multivariate quasi-arithmetic mean (stationary) RMparswm multivariate Whittle-Matern model (stationary and isotropic) RMschur element-wise product with a positive definite matrix RMvector vector-valued field (combining RMcurlfree and RMdivfree) }

Non-stationary models ll{ RMnonstwm one of Stein's non-stationary Wittle-Matern model }

Models related to max-stable random fields (tail correlation functions) ll{ RMaskey Askey model (generalized test or triangle model) with $\alpha \ge [dim / 2] +1$ RMbessel Bessel family RMbernoulli Correlation function of a binary field based on a Gaussian field RMbr2bg Operator relating a Brown-Resnick process to a Bernoulli process RMbr2eg Operator relating a Brown-Resnick process to an extremal Gaussian process RMbrownresnick tail correlation function of Brown-Resnick process RMgencauchy generalized Cauchy family with $\alpha\le 1/2$ RMm2r shapes functions related max-stable processes RMm3b shapes functions related max-stable processes RMmatern Whittle-Matern model with $\nu\le 1$ RMmps shapes functions related max-stable processes RMschlather tail correlation function of the extremal Gaussian field RMstable symmetric stable family or powered exponential model with $\alpha\le 1$ RMwhittle Whittle-Matern model, alternative parametrization with $\nu\le 1/2$ }

Other covariance models ll{ RMuser User defined model }

Auxiliary models There are models or better function that are not covariance functions, but can be part of a model definition. 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.
• 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, RMmodels, RMmodelsAuxiliary

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
RFgetModelNames(type="positive", group.by=c("domain", "isotropy"))
FinalizeExample()