R: Simulation of Max-Stable Random Fields

rmaxstab {SpatialExtremes} | R Documentation

## Simulation of Max-Stable Random Fields

### Description

This function generates realisation from a max-stable random field.

### Usage

    rmaxstab(n, coord, cov.mod = "gauss", grid = FALSE, control =
    list(), ...)

### Arguments

`n` | Integer. The number of observations.
`coord` | A vector or matrix that gives the coordinates of each location. Each row corresponds to one location - if any.
`cov.mod` | A character string that gives the max-stable model. This must be one of "gauss" for the Smith model, "brown" for the Brown–Resnick model, or "whitmat", "cauchy", "powexp" and "bessel" for the Schlather model with the given correlation family. If the latters are prefix by a "t", e.g., "twhitmat", this would corresponds to the extremal-t model.
`grid` | Logical. Does the coordinates represent grid points?
`control` | A named list with arguments 'nlines' (number of lines of the TBM simulation), 'method' the name of the simulation method - must be one of 'exact', 'tbm' or 'circ', and 'uBound' the uniform upper bound. See details.
`...` | The parameters of the max-stable model. See details.

### Details

Users must supply the parameters for the max-stable model. For the Schlather model, users should supply the "nugget", "range" and "smooth" parameter values. For the Smith model, if `coord` is univariate you must specify `var`, otherwise users should supply the covariance parameters i.e. parameters with names such as `cov11`, `cov12`, ... For the extremal-t model, users should supply the "DoF", "nugget", "range" and "smooth" parameters. Finally for the Brown–Resnick model, users should supply the "range" and the "smooth" parameters.

Here are the details for each allowed components of 'control'. If 'method' is `NULL` (default), the function tries to find the most appropriate simulation technique. Current simulation techniques are a direct approach, i.e. Cholesky decomposition of the covariance matrix, the turning bands and the circular embedding methods. If 'nlines' is `NULL`, it is set to 1000. If 'uBound' is `NULL`, it is set to reasonable values - for example 3.5 for the Schlather model.

### Value

A matrix containing observations from the required max-stable model. Each column represents one stations. If `grid = TRUE`, the function returns an array of dimension nrow(coord) x nrow(coord) x n.

### Author(s)

Mathieu Ribatet

### References

Schlather, M. (2002) Models for Stationary Max-Stable Random Fields. Extremes 5:1, 33–44.

Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.

### See Also

`fitmaxstab`

### Examples

    ## 1. Smith's model
    set.seed(8)
    x <- y <- seq(0, 10, length = 100)
    coord <- cbind(x, y)
    data <- rmaxstab(1, coord, "gauss", cov11 = 9/8, cov12 = 0, cov22 = 9/8,
      grid = TRUE)
    ##We change to unit Gumbel margins for visibility
    filled.contour(x, y, log(data), color.palette = terrain.colors)

    ## 2. Schlather's model
    data <- rmaxstab(1, coord, cov.mod = "powexp", nugget = 0, range = 3,
    smooth = 1, grid = TRUE)
    filled.contour(x, y, log(data), color.palette = terrain.colors)

    ## 3. Brown--Resnick's model **** Only available for non gridded points currently ****
    data <- rmaxstab(1, x, cov.mod = "brown", range = 3, smooth = 0.5)
    plot(x, log(data), type = "l")

    ## 4. Extremal-t model *** Very time consuming for 2d grids ***
    data <- rmaxstab(1, x, "twhitmat", DoF = 4, nugget = 0, range = 3,
    smooth = 0.7)
    plot(x, log(data), type = "l")

[Package SpatialExtremes version 2.0-5 Index]