RandomFields: RMmqam – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

RMmqam

multivariate quasi-arithmetic mean

Description

RMmqam is a multivariate 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_{ij}(h) = φ(√(θ_i (φ^{-1}(C_i(h)))^2 + θ_j (φ^{-1}(C_j(h)))^2 ))

where φ is a completely monotone function, C_i are suitable covariance functions and θ_i≥0 such that ∑_i θ_i=1.

Usage

RMmqam(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 stationary `RMmodel`s
`theta`	is a vector of values in [0,1], summing up to 1.

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

RMmqam 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. (2009) Quasi-arithmetic means of covariance functions with potential applications to space-time data. Journal of Multivariate Analysis, 100, 1830–1844.

Examples

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

RFoptions(modus_operandi="sloppy")
model <- RMmqam(phi=RMgauss(),RMgauss(),RMexp(),theta=c(0.4, 0.6), scale=0.5)
x <- seq(0, 10, 0.02)
plot(model)
z <- RFsimulate(model=model, x=x)
plot(z)

RFoptions(modus_operandi="normal")

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