RPbrownresnick: Brown-Resnick process
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Note Author(s) References See Also Examples

RPbrownresnick defines a Brown-Resnick process.

1	RPbrownresnick(phi, tcf, xi, mu, s)

`phi`	specifies the covariance model or variogram, see RMmodel and RMmodelsAdvanced.
`tcf`	the extremal correlation function; either `phi` or `tcf` must be given.
`xi, mu, s`	the extreme value index, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details.

\GEV

The functions RPbrorig, RPbrshifted and RPbrmixed perform the simulation of a Brown-Resnick process, which is defined by

Z(x) = max_{i=1, 2, ...} X_i * exp(W_i(x) - gamma^2),

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 phi.

For simulation, internally, one of the methods RPbrorig, RPbrshifted and RPbrmixed is chosen automatically.

Advanced options are maxpoints and max_gauss, see RFoptions.

Further advanced options related to the simulation methods RPbrorig, RPbrshifted and RPbrmixed can be found in the paragraph ‘Specific method options for Brown-Resnick Fields’ in RFoptions.

\marco

; \martin

Brown, B.M. and Resnick, S.I. (1977). Extreme values of independent stochastic processes. J. Appl. Probab. 14, 732-739.
Buishand, T., de Haan , L. and Zhou, C. (2008). On spatial extremes: With application to a rainfall problem. Ann. Appl. Stat. 2, 624-642.
Kabluchko, Z., Schlather, M. and de Haan, L (2009) Stationary max-stable random fields associated to negative definite functions Ann. Probab. 37, 2042-2065.
Oesting, M., Kabluchko, Z. and Schlather M. (2012) Simulation of Brown-Resnick Processes, Extremes, 15, 89-107.

RPbrorig, RPbrshifted, RPbrmixed, RMmodel, RPgauss, maxstable, maxstableAdvanced.

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again


## for some more sophisticated models see 'maxstableAdvanced'