R: Bivariate Delay Effect

RMdelay {RandomFields} | R Documentation

## 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 between two points in d-dimensional space and is given by

C(h)=(C_0(h - s_i +s_j))_{i,j=0,…,m}

where h \in R^{d x 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 x m-dimensional shift matrix, where d is the dimension of the space, giving the components s=(s_1,..., 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.

### Details

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

### Value

`RMdelay` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

- Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. Journal of Statistical Software, 63 (8), 1-25, url = ‘http://www.jstatsoft.org/v63/i08/’

- 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")

[Package RandomFields version 3.1.50 Index]