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
,
y
, and z
should be
interpreted as a grid definition, see Details.()
to get all options;
interpretation depends on the value of 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 NULL
or string; method used for simulating,
see ()
to get all optiogridtriple=FALSE
ascending
sequences for the parameters
x
, y
, and z
are
expected; if gridtriple=TRUE
triples of form
c(start,end,step)
expecteInitMaxStableRF
returns 0 if no error has occurred, and
a positive value if failed.
MaxStableRF
and 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.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 vectorparam
, themodel
,
and themethod
are interpreted
in the same way as for Gaussian random fields, seemaxstable="BooleanFunction"
Deterministic or random, upper semi-continuous$L_1$-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()
for a complete list of suitable covariance models.
The only value allowed formethod
is 'max.MPP' (andNULL
),
seeparam
the first two entries, namelymean
andvariance
, are ignored. If the nugget is positive,
for each point an additional independent unit Frechet variable
with scale parameternugget
is involved when building the maximum
over all functions. The model may be defined alternatively in one of the two extended
ways as introduced inCovarianceFct
andGaussRF
.
However only a single model may be given! The model may be
anisotropic.
RandomFields
,
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)
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