RandomFields (version 3.1.16)

BrownResnick: Brown-Resnick process

Description

RPbrownresnick defines a Brown-Resnick process.

Usage

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

Arguments

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.

Details

The extreme value index xi is always a number, i.e. $\xi$ is constant in space. In contrast, $\mu$ and $s$ might be constant numerical value or given a RMmodel, in particular by a RMtrend model. The default values of $mu$ and $s$ are $1$ and $z\xi$, respectively.

The functions RPbrorig, RPbrshifted and RPbrmixed perform the simulation of a Brown-Resnick process, which is defined by $$Z(x) = \max_{i=1}^\infty X_i \exp(W_i(x) - \gamma^2), $$ 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 model. For simulation, internally, one of the methods RPbrorig, RPbrshifted and RPbrmixed is chosen automatically.

References

• 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.

See Also

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

Examples

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 'maxstamableAdvanced'