Covariance models valid for max-stable random fields


This page summarizes the models that can be use for tail correlation functions


The following models are available

Completely monotone function allowing for arbitray scale

RMbcw Model bridging stationary and intrinsically stationary processes for alpha <= 1 and beta < 0
RMdagum Dagum model with β < γ and γ ≤ 1
RMexp exponential model
RMgencauchy generalized Cauchy family with α ≤ 1 (and arbitrary β> 0)
RMmatern Whittle-Matern model with ν ≤ 1/2
RMstable symmetric stable family or powered exponential model with α ≤ 1
RMwhittle Whittle-Matern model, alternative parametrization with ν ≤ 1/2

Other isotropic models with arbitray scale

RMnugget nugget effect model

Compactly supported covariance functions

RMaskey Askey's model
RMcircular circular model
RMconstant identically constant
RMcubic cubic model
RMgengneiting Wendland-Gneiting model; differentiable models with compact support
RMgneiting differentiable model with compact support
RMspheric spherical model

Anisotropic models

none up to now.

Basic Operators

RMmult, * product of covariance models
RMplus, + sum of covariance models or variograms

Further Operators

RMbernoulli correlation of binary fields
RMbrownresnick tcf of a Brown-Resnick process
RMschlather tcf of a Schlather process

See RMmodels for cartesian models.


Martin Schlather,


  • Strokorb, K., Ballani, F., and Schlather, M. (2015) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, 18, 241-271

See Also

coordinate systems, RM, RMmodels, RMtrafo


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

## an example of a simple model
model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget

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