RandomFields (version 3.0.5)

RMdampedcos: Exponentially Damped Cosine

Description

RMdampedcos is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = exp(-\lambda r) \cos(r).$$

Usage

RMdampedcos(lambda, var, scale, Aniso, proj)

Arguments

lambda

parameter whose allowed range depends on the dimension of the random field (see details)

var, scale, Aniso, proj

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

Value

• RMdampedcos returns an object of class RMmodel

Details

The model is valid for any dimension $d$. However, depending on the dimension of the random field the following bound for the parameter $\lambda$ has to be respected:

$$\lambda \ge 1/{\tan(\pi/(2d))}.$$

This covariance models a hole effect (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 92).

For $\lambda = 0$ we obtain the covariance function $$C(r)=\cos(r)$$ which is only valid for $d=1$ and corresponds to RMbessel for $\nu=-0.5$, there.

References

• Chiles, J.-P. and Delfiner, P. (1999)Geostatistics. Modeling Spatial Uncertainty.New York: Wiley.
• Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010)Handbook of Spatial Statistics.Boca Raton: Chapman & Hall/CRL.

See Also

RMbessel, RMmodel, RFsimulate, RFfit.

Examples

set.seed(0)
model <- RMdampedcos(lambda=0.3, scale=0.1)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(-1, 1))
plot(RFsimulate(model, x=x))