RMstein {RandomFields}

R Documentation

Stein's non-separable space-time model

Description

RMstein is a univariate stationary covariance model whose corresponding covariance function only depends on the difference h between two points and is given by

C(h, t) = W_{\nu}(y) - ( < h, z > t)/((\nu - 1)(2\nu + d)) * W_{\nu-1}(y)

Here, W_\nu is the covariance of the RMwhittle model with smoothness parameter \nu; y=\|(h,t)\| is the norm of the vector (h,t), d is the dimension of the space on which the random field is considered.

Usage

RMstein(nu, z, var, scale, Aniso, proj)

Arguments

nu	numerical value; greater than 1; smoothness parameter of the RMwhittle model
z	a vector; the norm of z must be less or equal to 1.
var, scale, Aniso, proj	optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Details

See Stein (2005).

Value

RMstein returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

• Stein, M.L. (2005) Space-time covariance functions. J. Amer. Statist. Assoc. 100, 310-321. Equation (8).

See Also

RMmodel, RFsimulate, RFfit.

Examples

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

model <- RMstein(nu=1.5, z=0.9)
x <- seq(0, 10, 0.05)
plot(RFsimulate(model, x=x, y=x))

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