rExtDepSpat | R Documentation |
Generates realizations from a max-stable process.
rExtDepSpat(n, coord, model = "SCH", cov.mod = "whitmat", grid = FALSE,
control = list(), cholsky = TRUE, ...)
n |
An integer indicating the number of observations. |
coord |
A vector or matrix corresponding to the coordinates of locations where the process is simulated. Each row corresponds to a location. |
model |
A character string indicating the max-stable model. See |
cov.mod |
A character string indicating the correlation function. See |
grid |
Logical; |
control |
A named list with arguments:
See |
cholsky |
Logical; if |
... |
Additional parameters of the max-stable model. See |
This function extends the rmaxstab
function from the SpatialExtremes
package in two ways:
The extremal skew-t model is included.
The function returns the hitting scenarios, i.e., the index of which 'storm' (or process) led to the maximum value for each location and observation.
Available max-stable models:
(model = 'SMI'
) does not require cov.mod
. If
coord
is univariate, var
needs to be specified. For higher dimensions,
covariance parameters such as cov11
, cov12
, cov22
, etc. should be provided.
(model = 'SCH'
) requires cov.mod
as one of
'whitmat'
, 'cauchy'
, 'powexp'
or 'bessel'
.
Parameters nugget
, range
and smooth
must be specified.
(model = 'ET'
) requires cov.mod
as above.
Parameters nugget
, range
, smooth
and DoF
must be specified.
(model = 'EST'
) requires cov.mod
as above.
Parameters nugget
, range
, smooth
, DoF
, alpha
(vector of length 3)
and acov1
, acov2
(vectors of length equal to number of locations) must be specified.
The skewness vector is \alpha = \alpha_0 + \alpha_1 \textrm{acov1} + \alpha_2 \textrm{acov2}
.
(model = 'GG'
) requires cov.mod
as above.
Parameters sig2
, nugget
, range
and smooth
must be specified.
(model = 'BR'
) does not require cov.mod
.
Parameters range
and smooth
must be specified.
In control
: NULL by default, meaning the function selects the most appropriate simulation technique.
For the extremal skew-t model, only 'exact'
or 'direct'
are allowed.
In control
: default 1000 if NULL
.
In control
: default reasonable values, e.g., 3.5 for the Schlather model.
A list containing:
A n \times d
matrix with n
observations at d
locations.
A n \times d
matrix of hitting scenarios. Elements with the same integer
indicate maxima coming from the same 'storm' or process.
Simone Padoan simone.padoan@unibocconi.it https://faculty.unibocconi.it/simonepadoan/; Boris Beranger borisberanger@gmail.com https://www.borisberanger.com;
Beranger, B., Stephenson, A. G. and Sisson, S. A. (2021). High-dimensional inference using the extremal skew-t process. Extremes, 24, 653–685.
fExtDepSpat
# Generate some locations
set.seed(1)
lat <- lon <- seq(from = -5, to = 5, length = 20)
sites <- as.matrix(expand.grid(lat, lon))
# Example using the extremal-t
set.seed(2)
z <- rExtDepSpat(1, sites, model = "ET", cov.mod = "powexp", DoF = 1,
nugget = 0, range = 3, smooth = 1.5,
control = list(method = "exact"))
fields::image.plot(lat, lon, matrix(z$vals, ncol = 20))
# Example using the extremal skew-t
set.seed(3)
z2 <- rExtDepSpat(1, sites, model = "EST", cov.mod = "powexp", DoF = 5,
nugget = 0, range = 3, smooth = 1.5, alpha = c(0,5,5),
acov1 = sites[,1], acov2 = sites[,2],
control = list(method = "exact"))
fields::image.plot(lat, lon, matrix(z2$vals, ncol = 20))
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