RandomFields (version 3.1.16)

Extremal t: 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 $\alpha$-Frechet marginal distribution, see the original literature for details.

Details

The argument xi is always a number, i.e. $\xi$ is constant in space. In contrast, $\mu$ 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 $z\xi$, respectively.

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")