RandomFields (version 3.0.5)

RMcubic: Cubic Covariance Model

Description

RMcubic is a stationary isotropic covariance model which is only valid for dimensions $d \le 3$. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = (1 -7 r^(2) + 8.75 r^3 - 3.5 r^5 + 0.75 r^7) 1_{[0,1]}(r).$$

Usage

RMcubic(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

• RMcubic returns an object of class RMmodel

Details

The model is only valid for dimensions $d \le 3$. It is a 2 times differentiable covariance function with compact support (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 84).

References

• Chiles, J.-P. and Delfiner, P. (1999)Geostatistics. Modeling Spatial Uncertainty.New York: Wiley.

See Also

RMmodel, RFsimulate, RFfit.

Examples

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