| 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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