Exponentially Damped Cosine
RMdampedcos is a stationary isotropic covariance model.
The corresponding covariance function only depends on the distance r ≥ 0 between
two points and is given by
C(r) = exp(-λ r) cos(r).
RMdampedcos(lambda, var, scale, Aniso, proj)
lambda |
numeric. The range depends on the dimension of the random field (see details). |
var, scale, Aniso, proj |
optional arguments; same meaning for any
|
The model is valid for any dimension d. However, depending on the dimension of the random field the following bound for the argument λ has to be respected:
λ ≥ 1/{tan(π/(2d))}.
This covariance models a hole effect (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 92).
For λ = 0 we obtain the covariance function
C(r)=cos(r)
which is only valid for d=1
and corresponds to RMbessel for
ν=-0.5, there.
RMdampedcos returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMdampedcos(lambda=0.3, scale=0.1) x <- seq(0, 10, 0.02) plot(model) plot(RFsimulate(model, x=x))
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.