RMstable: Stable Family / Powered Exponential Model
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

RMstable is a stationary isotropic covariance model belonging to the so called stable family. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r)=e^{-r^α}

where 0 < α ≤ 2.

1 2	RMstable(alpha, var, scale, Aniso, proj) RMpoweredexp(alpha, var, scale, Aniso, proj)

`alpha`	a numerical value; should be in the interval (0,2] to provide a valid covariance function for a random field of any dimension.
`var,scale,Aniso,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

The parameter α determines the fractal dimension D of the Gaussian sample paths:

D = d + 1 - α/2

where d is the dimension of the random field. For α < 2 the Gaussian sample paths are not differentiable (cf. Gelfand et al., 2010, p. 25).

Each covariance function of the stable family is a normal scale mixture.

The stable family includes the exponential model (see RMexp) for α = 1 and the Gaussian model (see RMgauss) for α = 2.

The model is called stable, because in the 1-dimensional case the covariance is the characteristic function of a stable random variable (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 90).

RMstable returns an object of class RMmodel.

Covariance function

Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.
Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998) Model-based geostatistics (with discussion). Applied Statistics 47, 299–350.
Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

Tail correlation function (for 0 < α ≤ 1)

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. Extremes, Submitted.

RMbistable, RMexp, RMgauss, RMmodel, RFsimulate, RFfit.

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

model <- RMstable(alpha=1.9, scale=0.4)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: ‘RandomFields’

The following object is masked from ‘package:RandomFieldsUtils’:

    RFoptions

NULL
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.