RandomFields: RMqam – R documentation

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RMqam

Quasi-arithmetic mean

Description

RMqam is a univariate stationary covariance model depending on a submodel phi such that psi( . ) := phi(sqrt( . )) is completely monotone, and depending on further stationary covariance models C_i. The covariance is given by

C(h) = phi(sqrt(sum_i theta_i (phi^{-1}(C_i(h)))^2))

Usage

RMqam(phi, C1, C2, C3, C4, C5, C6, C7, C8, C9, theta, var, scale, Aniso, proj)

Arguments

`phi`	a valid covariance `RMmodel` that is a normal scale mixture. See, for instance, `RFgetModelNames(monotone="normal mixture")`.
`C1, C2, C3, C4, C5, C6, C7, C8, C9`	optional further univariate stationary `RMmodel`s
`theta`	a vector with positive entries
`var,scale,Aniso,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

Details

Note that psi( . ) := phi(sqrt( . )) is completely monotone if and only if phi is a valid covariance function for all dimensions, e.g. RMstable, RMgauss, RMexponential.

Warning: RandomFields cannot check whether the combination of phi and C_i is valid.

Value

RMqam returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

Porcu, E., Mateu, J. & Christakos, G. (2007) Quasi-arithmetic means of covariance functions with potential applications to space-time data. Submitted to Journal of Multivariate Analysis.

Examples

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

model <- RMqam(phi=RMgauss(), RMexp(), RMgauss(),
               theta=c(0.3, 0.7), scale=0.5)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

RandomFields

Simulation and Analysis of Random Fields

v3.3.10

GPL (>= 3)

Authors

Martin Schlather [aut, cre], Alexander Malinowski [aut], Marco Oesting [aut], Daphne Boecker [aut], Kirstin Strokorb [aut], Sebastian Engelke [aut], Johannes Martini [aut], Felix Ballani [aut], Olga Moreva [aut], Jonas Auel[ctr], Peter Menck [ctr], Sebastian Gross [ctr], Ulrike Ober [ctb], Paulo Ribeiro [ctb], Brian D. Ripley [ctb], Richard Singleton [ctb], Ben Pfaff [ctb], R Core Team [ctb]

Initial release