RandomFields (version 3.0.5)

RMnugget: Nugget Effect Covariance Model

Description

RMnugget is a multivariate stationary isotropic covariance model called nugget effect. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given for $i,j$ in $1,...,$vdim by $$C_{ij}(r) = \delta_ij 1_{0}(r),$$ where $\delta_{ij}=1$ if $i=j$ and $\delta_{ij}=0$ otherwise.

Usage

RMnugget(tol, vdim, var, scale, Aniso, proj)

Arguments

tol

Only for advanced users. See RPnugget.

vdim

Only for advanced users. See RPnugget.

var,scale,Aniso,proj

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

Value

• RMnugget returns an object of class RMmodel

Details

Note that the argument scale does not affect the covariance model; Aniso has an effect in case of zonal anisotropy.

The nugget effect belongs to Gaussian white noise and is often used for modeling measurement errors.

The locations at a distance less than or equal to nugget.tol are considered as being identical. This strategy applies to the simulation method and the covariance function itself. Hence, the covariance function is only positive definite if nugget.tol=0.0. However, if the anisotropy matrix does not have full rank and nugget.tol=0.0 then, the simulations are likely to be odd. The value of nugget.tol should be of order $10^{-15}$.

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 <- RMnugget(Aniso=matrix(1, nr=2, nc=2))
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(RFsimulate(model, x=x, y=x, tol=1e-10))
FinalizeExample()