RandomFields (version 3.1.36)

RMstein: Stein nonseparable 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.

Value

RMstein returns an object of class RMmodel

Details

See Stein (2005).

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))