R: Simulation methods for Brown-Resnick processes

Brown-Resnick-Specific {RandomFields} | R Documentation

## Simulation methods for Brown-Resnick processes

### Description

These models define the particular way to simulate Brown-Resnick processes

### Usage

    RPbrmixed(phi, tcf, xi, mu, s, meshsize, vertnumber, optim_mixed,
              optim_mixed_tol,lambda, areamat, variobound)

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

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

### Arguments

`phi` | object of class `RMmodel`; specifies the covariance model to be simulated.
`tcf` | the extremal correlation function; either `phi` or `tcf` must be given.
`xi, mu, s` | the shape parameter, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details.
`lambda` | positive constant factor in the intensity of the Poisson point processused in the M3 representation, cf. Thm. 6 and Remark 7 in Oesting et. al (2012); can be estimated by setting `optim_mixed` if unknown. Default value is 1.
`areamat` | vector or matrix of values in [0,1] with odd length (odd number of rows and columns, respectively). Each value represents the portion of processes whose maximum is located at a specific location on a grid taken into account for the simulation of the shape function in the M3 representation. The center of `areamat` represents the value for the origin, the other entries belong to the corresponding locations on a 1D or 2D grid. `areamat` can be used for dimensions 1 and 2 only; can be optimized by setting `optim_mixed` if unknown. Default value is 1.
`meshsize, vertnumber, optim_mixed, optim_mixed_tol, variobound` | further arguments for simulation via the mixed moving maxima (M3) representation; see `RFoptions`

### 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 functions `RPbrorig`, `RPbrshifted` and `RPbrmixed` simulate a Brown-Resnick process, which is defined by

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

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`. The functions correspond to the following ways of simulation:

`RPbrorig`

  simulation via using the original definition (method 0 in Oesting et al., 2012)

`RPbrshifted`

  simulation using a random shift (similar to method 1 and 2)

`RPbrmixed`

  simulation using M3 representation (method 4)

### Value

The functions return an object of class `RMmodel`

### Note

Advanced options for `RPbroriginal` and `RPbrshifted` are `maxpoints` and `max_gauss`, see `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

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

### See Also

`RPbrownresnick`, `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

    ## currently does not work

[Package RandomFields version 3.1.50 Index]