R: Extremal t process

Extremal t {RandomFields} | R Documentation

## Extremal t process

### Description

`RPopitz` defines an extremal t process.

### Usage

    RPopitz(phi, xi, mu, s, alpha)

### Arguments

`phi` | an `RMmodel`; covariance model for a standardized Gaussian random fields, or the field itself.
`xi,mu,s` | the extreme value index, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details.
`alpha` | originally referred to the α-Frechet marginal distribution, see the original literature for details.

### Details

The argument `xi` is always a number, i.e. ξ is constant in space. In contrast, μ and s might be constant numerical value or given a `RMmodel`, in particular by a `RMtrend` model. The default values of mu and s are 1 and zξ, respectively.

### Author(s)

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

### References

- Davison, A.C., Padoan, S., Ribatet, M. (2012). Statistical modelling of spatial extremes. Stat. Science 27, 161-186.

- Opitz, T. (2012) A spectral construction of the extremal t process. arxiv 1207.2296.

### See Also

`RMmodel`, `RPgauss`, `maxstable`, `maxstableAdvanced`

### Examples

    RFoptions(seed=0, xi=0)
    ## seed=0: *ANY* simulation will have the random seed 0; set
    ##         RFoptions(seed=NA) to make them all random again
    ## xi=0: any simulated max-staable random field has extreme value index 0

    x <- seq(0, 2, 0.01)
    model <- RPopitz(RMgauss(), alpha=2)
    z1 <- RFsimulate(model, x)
    plot(z1, type="l")

[Package RandomFields version 3.1.50 Index]