RandomFields (version 3.0.5)

RMdelay: Bivariate Delay Effect

Description

RMdelay is a $(m+1)$-variate stationary covariance model. which depends on a univariate stationary covariance model $C_0$. The corresponding covariance function only depends on the difference $h \in {\bf R}^d$ between two points in $d$-dimensional space and is given by $$C(h)=(C_0(h - s_i +s_j))_{i,j=0,\ldots,m}$$ where $s \in {\bf R}^{d\times m}$ and $s_0=0$

Usage

RMdelay(phi,s,var, scale, Aniso, proj)

Arguments

phi

a univariate stationary covariance model, that means an RMmodel whose vdim equals 1.

s

a $d\times m$-dimensional shift matrix, where $d$ is the dimension of the space, giving the components $s=(s_1,\ldots, s_m)$ where the $s_i$ are vectors.

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• RMdelay returns an object of class RMmodel

Details

Here, a multivariate random field is obtained from single univariate random field, by shifting it by fixed value.

References

• Schlather, M., Malinowski, A., Menck, P.J., Oesting, M., Strokorb, K. (2013).Submitted to J. Statist. Software
• Wackernagel, H. (2003)Multivariate Geostatistics.Berlin: Springer, 3nd edition.

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

x <- y <- seq(-10,10,0.2)
model <- RMdelay(RMstable(alpha=1.9, scale=2), s=c(4,4))
plot(model, dim=2, xlim=c(-6, 6), ylim=c(-6,6))

simu <- RFsimulate(model, x, y)
plot(simu, zlim="joint")

FinalizeExample()