MaxStableRF {RandomFields} | R Documentation |
These functions simulate stationary and isotropic max-stable random fields with unit Frechet margins.
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)
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 |
model |
string; see |
param |
parameter vector:
|
maxstable |
string. Either 'extremalGauss' or 'BooleanFunction'; see Details. |
method |
|
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 |
... |
|
There are two different kinds of models for max-stable processes implemented:
maxstable="extremalGauss"
Gaussian random fields are multiplied by independent
random factors,
and the maximum is taken. The random factors are such that
the resulting random field has unit
Frechet margins; the specification of the random factor
is uniquely given by the specification of the random
field. The parameter vector param
, the model
,
and the method
are interpreted
in the same way as for Gaussian random fields, see
GaussRF
.
maxstable="BooleanFunction"
Deterministic or random, upper semi-continuous
L1-functions are randomly centred and multiplied by
suitable, independent random factors; the pointwise maximum over all
these functions yields a max-stable random field.
The simulation technique is related to the random coin
method for Gaussian random field simulation,
see RFMethods
. Hence, only
models that are suitable for the random coin method
are suitable for this technique, see PrintModelList
()
for a complete list of suitable covariance models.
The only value allowed for method
is 'max.MPP' (and
NULL
),
see PrintMethodList()
. In the parameter list
param
the first two entries, namely mean
and
variance
, are ignored. If the nugget is positive,
for each point an additional independent unit Frechet variable
with scale parameter
nugget
is involved when building the maximum
over all functions.
The model may be defined alternatively in one of the two extended
ways as introduced in CovarianceFct
and GaussRF
.
However only a single model may be given! The model may be
anisotropic.
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 realisations.
* grid=TRUE
. An array of dimension
d+1, where d is the dimension of
the random field, is returned. The last
dimension contains the realisations.
Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/~schlather
Schlather, M. (2002) Models for stationary max-stable random fields. Extremes 5, 33-44.
CovarianceFct
,
sophisticated,
GaussRF
,
RandomFields
,
RFMethods
,
RFparameters
,
DoSimulateRF
,
.
n <- 30 ## nicer, but time consuming if n <- 100 x <- y <- 1:n ms0 <- MaxStableRF(x, y, grid=TRUE, model="exponen", param=c(0,1,0,40), maxstable="extr", CE.force = TRUE) image(x,y,ms0)