RandomFields (version 3.0.32)

RMpenta: Penta Covariance Model

Description

RMpenta is a stationary isotropic covariance model, which is valid only for dimensions $d \le 3$. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = (1 - \frac{22}{3}r^{2} + 33 r^{4} - \frac{77}{2} r^{5} + \frac{33}{2} r^{7} - \frac{11}{2} r^{9} + \frac{5}{6}r^{11}) 1_{[0,1]}(r) .$$

Usage

RMpenta(var, scale, Aniso, proj)

Arguments

var,scale,Aniso,proj

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

Value

• RMpenta returns an object of class RMmodel

Details

The model is only valid for dimension $d \le 3$.

It has a 4 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

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
model <- RMpenta()
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
FinalizeExample()