R: Exponential Covariance Model

RMexp {RandomFields} | R Documentation

## Exponential Covariance Model

### Description

`RMexp` is a stationary isotropic covariance model whose corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r) = exp(-r).

### Usage

    RMexp(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.

### Details

This model is a special case of the Whittle covariance model (see `RMwhittle`) if ν=0.5 and of the symmetric stable family (see `RMstable`) if ν=1. Moreover, it is the continuous-time analog of the first order autoregressive time series covariance structure.

The exponential covariance function is a normal scale mixture.

### Value

`RMexp` returns an object of class `RMmodel`.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### References

Covariance model

- Gelfand, A. E., Diggle, P., Fuentes, M. and Guttorp, P. (eds.) (2010) Handbook of Spatial Statistics. Boca Raton: Chapman & Hall/CRL.

Tail correlation function

- Strokorb, K., Ballani, F., and Schlather, M. (2014) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, Submitted.

### See Also

`RMwhittle`, `RMstable`, `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 <- RMexp()
    x <- seq(0, 10, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]