RandomFields (version 3.0.5)

RMexp: Exponential Covariance Model

Description

RMexp is a stationary isotropic covariance model whose corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = e^(-r).$$

Usage

RMexp(var, scale, Aniso, proj)

Arguments

var,scale,Aniso,proj

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

Value

• RMexp returns an object of class RMmodel.

Details

This model is a special case of the Whittle covariance model (see RMwhittle) if $\nu=\frac{1}{2}$ and of the symmetric stable family (see RMstable) if $\nu = 1$. Moreover, it is the continuous-time analog of the first order autoregressive time series covariance structure.

The exponential covariance function is a normal scale mixture.

References

Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

See Also

RMwhittle, RMstable, RMmodel, RFsimulate, RFfit.

Examples

set.seed(0)
model <- RMexp()
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))