R: Exponentially Damped Cosine

RMdampedcos {RandomFields} | R Documentation

## Exponentially Damped Cosine

### Description

`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).

### Usage

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

### Arguments

`lambda` | numeric. The range depends on the dimension of the random field (see details)
`var, scale, Aniso, proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

The model is valid for any dimension d. However, depending on the dimension of the random field the following bound for the arguments 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.

### Value

`RMdampedcos` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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

    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))

[Package RandomFields version 3.1.50 Index]