R: Brown-Resnick process

BrownResnick {RandomFields} | R Documentation

## Brown-Resnick process

### Description

`RPbrownresnick` defines a Brown-Resnick process.

### Usage

      RPbrownresnick(phi, tcf, xi, mu, s)

### Arguments

`phi` | specifies the covariance model or variogram, see RMmodel and RMmodelsAdvanced.
`tcf` | the extremal correlation function; either `phi` or `tcf` must be given.
`xi, mu, s` | the extreme value index, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details.

### Details

The extreme value index `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.

The functions `RPbrorig`, `RPbrshifted` and `RPbrmixed` perform the simulation of a Brown-Resnick process, which is defined by

Z(x) = max_{i=1, 2, ...} X_i * exp(W_i(x) - gamma^2),

where the X_i are the points of a Poisson point process on the positive real half-axis with intensity 1/x^2 dx, W_i ~ Y are iid centered Gaussian processes with stationary increments and variogram gamma given by `model`.

For simulation, internally, one of the methods `RPbrorig`, `RPbrshifted` and `RPbrmixed` is chosen automatically.

### Note

Advanced options are `maxpoints` and `max_gauss`, see `RFoptions`.

Further advanced options related to the simulation methods `RPbrorig`, `RPbrshifted` and `RPbrmixed` can be found in the paragraph ‘Specific method options for Brown-Resnick Fields’ in `RFoptions`.

### Author(s)

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

### References

- Brown, B.M. and Resnick, S.I. (1977). Extreme values of independent stochastic processes. J. Appl. Probab. 14, 732-739.

- Buishand, T., de Haan , L. and Zhou, C. (2008). On spatial extremes: With application to a rainfall problem. Ann. Appl. Stat. 2, 624-642.

- Kabluchko, Z., Schlather, M. and de Haan, L (2009) Stationary max-stable random fields associated to negative definite functions Ann. Probab. 37, 2042-2065.

- Oesting, M., Kabluchko, Z. and Schlather M. (2012) Simulation of Brown-Resnick Processes, Extremes, 15, 89-107.

### See Also

`RPbrorig`, `RPbrshifted`, `RPbrmixed`, `RMmodel`, `RPgauss`, `maxstable`, `maxstableAdvanced`

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    ## for some more sophisticated models see 'maxstamableAdvanced'

[Package RandomFields version 3.1.50 Index]