Simulation methods for Brown-Resnick processes
These models define particular ways to simulate Brown-Resnick processes.
RPbrmixed(phi, tcf, xi, mu, s, meshsize, vertnumber, optim_mixed,
optim_mixed_tol,lambda, areamat, variobound)
RPbrorig(phi, tcf, xi, mu, s)
RPbrshifted(phi, tcf, xi, mu, s)
RPloggaussnormed(variogram, prob, optimize_p, nth, burn.in, rejection)phi,variogram |
object of class |
tcf |
the extremal correlation function; either |
xi, mu, s |
the shape parameter, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details. |
lambda |
positive constant factor in the intensity of the Poisson
point process used in the M3 representation, cf. Thm. 6 and Remark 7
in Oesting et. al (2012); can be estimated by setting
|
areamat |
vector of values in [0,1]. The value of the kth
component represents the portion of processes whose maximum is located at a
distance d with k-1 <= d < k from the origin
taken into account for the simulation of the shape function in the M3
representation. |
meshsize, vertnumber, optim_mixed,
optim_mixed_tol, variobound |
further arguments
for simulation via the mixed moving maxima (M3) representation; see
|
prob |
to do |
optimize_p |
to do |
nth |
to do |
burn.in |
to do |
rejection |
to do |
The functions RPbrorig, RPbrshifted and RPbrmixed
simulate a Brown-Resnick process, which is defined by
Z(x) = max_{i=1, 2, ...} X_i * exp(W_i(x) - gamma),
where the X_i are the points of a Poisson point process on the
positive real half-axis with intensity 1/x^2 dx,
W_i ~ Y are iid centered Gaussian processes with
stationary increments and variogram gamma given by
model. The functions correspond to the following ways of
simulation:
RPbrorigsimulation using the original definition (method 0 in Oesting et al., 2012)
RPbrshiftedsimulation using a random shift (similar to method 1 and 2)
RPbrmixedsimulation using M3 representation (method 4)
The functions return an object of class
RMmodel.
Advanced options for RPbroriginal and RPbrshifted
are maxpoints and max_gauss, see RFoptions.
Oesting, M., Kabluchko, Z. and Schlather M. (2012) Simulation of Brown-Resnick Processes, Extremes, 15, 89-107.
# RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again ## currently does not work
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