MaxStableRF {RandomFields}R Documentation

Max-Stable Random Fields

Description

These functions simulate stationary and isotropic max-stable random fields with unit Frechet margins.

Usage

MaxStableRF(x, y=NULL, z=NULL, grid, model, param, maxstable,
            method=NULL, n=1, register=0, gridtriple=FALSE)

InitMaxStableRF(x, y=NULL, z=NULL, grid, model, param, maxstable,
               method=NULL, register=0, gridtriple=FALSE)

Arguments

x matrix of coordinates, or vector of x coordinates
y vector of y coordinates
z vector of z coordinates
grid logical; determines whether the vectors x, y, and z should be interpreted as a grid definition, see Details.
model string; see CovarianceFct, or type PrintModelList() to get all options; interpretation depends on the value of maxstable, see Details.
param parameter vector: param=c(mean, variance, nugget, scale,...); the parameters must be given in this order; further parameters are to be added in case of a parametrised class of covariance functions, see CovarianceFct, or be given in one of the extended forms, see Details
maxstable string. Either 'extremalGauss' or 'BooleanFunction'; see Details.
method NULL or string; method used for simulating, see RFMethods, or type PrintMethodList() to get all options; interpretation depends on the value of maxstable.
n number of realisations to generate
register 0:9; place where intermediate calculations are stored; the numbers are aliases for 10 internal registers
gridtriple logical; if gridtriple==FALSE ascending sequences for the parameters x, y, and z are expected; if gridtriple==TRUE triples of form c(start,end,step) expected; this parameter is used only if grid==TRUE

Details

There are two different kinds of models for max-stable processes implemented:

Value

InitMaxStableRF returns 0 if no error has occurred, and a positive value if failed.

MaxStableRF and DoSimulateRF return NULL if an error has occurred; otherwise the returned object depends on the parameters:
n==1:
* grid==FALSE. A vector of simulated values is returned (independent of the dimension of the random field)
* grid==TRUE. An array of the dimension of the random field is returned.

n>1:
* grid==FALSE. A matrix is returned. The columns contain the repetitions.
* grid==TRUE. An array of dimension d+1, where d is the dimension of the random field, is returned. The last dimension contains the repetitions.

Author(s)

Martin Schlather, martin.schlather@cu.lu http://www.cu.lu/~schlathe

References

Schlather, M. (2002) Models for stationary max-stable random fields. Extremes 5, 33-44.

See Also

CovarianceFct, GaussRF, RandomFields, RFMethods, RFparameters, DoSimulateRF, .

Examples

 n <- 30 ## nicer, but time consuming if n <- 100
 x <- y <- 1:n
 ms <- MaxStableRF(x, y, grid=TRUE, model="exponen",
                 param=c(0,1,0,40), maxstable="extr")
 image(x,y,ms)

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